UNIVERSITÀ DEGLI STUDI DI TRIESTE
Sede Amministrativa del Dottorato di Ricerca
Posto di dottorato attivato grazie al contributo dell’ INFM (Istituto Nazionale Fisica della Materia)
Laboratorio TASC di Trieste
TESI DI DOTTORATO
XVIII CICLO DEL
DOTTORATO DI RICERCA IN FISICA
RELEVANT MAGNETIC PROPERTIES OF LOW DIMENSIONAL SYSTEMS:
AN XMCD INVESTIGATION OF THE MAGNETISM AT THE INTERFACE
FE/GAAS(001) BY MEANS OF A NEW MAGNETIC MARKER METHOD
AND A SOFT X-RAYS SCATTERING METHOD FOR THE PROBING OF
MAGNETIC CONFIGURATION IN SUBMICROMETRIC PATTERNS.
DOTTORANDO
MAURO FABRIZIOLI
COORDINATORE DEL COLLEGIO DEI DOCENTI
CHIAR.MO PROF. GAETANO SENATORE, Università’ di Trieste
RELATORE
CHIAR.MO PROF. GIORGIO ROSSI, Universita’ di Modena e Reggio Emilia
TUTORE
CHIAR.MO PROF. ALBERTO MORGANTE, Universita’ di Trieste
Index
Introduction
i
1
1
2
3
4
Spintronics
1.1 Spin-dependent transport
1.2 Electrical spin injection
1.2.1 Ohmic injection: the conductivity mismatch problem
1.2.2 Tunnel injection: the Schottky barrier
1.3 Magnetoelectronics
1.3.1 Arrays of magnetic structures
1
3
4
5
9
11
Measuring interfacial magnetization
15
Synchrotron light and the APE beamline
41
The Fe/GaAs(001)-(4 × 6) interface system
49
2.1 Interface magnetization profiling
2.1.1 Co influence on and from the Fe magnetic environment
2.1.2 Analogy with Mössbauer experiments
2.2 Preparation of atomically clean interfaces
2.2.1 The role of the GaAs(001) surface preparation
2.3 Low Energy Electron Diffraction
2.4 Photoemission Spectroscopy
2.5 Magnetic characterization
2.5.1 MOKE
2.5.2 Magnetic Circular Dichroism in X-ray absorption
3.1 Third generation synchrotron radiation
3.2 The APE beamline
3.2.1 General layout
3.2.2 High-Energy beamline
3.2.3 Kerr/preparation chamber
4.1 Fe/GaAs(001): sample preparation and structural analysis
4.1.1 GaAs surface
4.1.2 Film deposition
4.1.3 Growth morphology
4.2 Experimental results
4.2.1 MOKE
4.2.2 XPS
4.2.3 XMCD
4.3 Discussion
15
16
17
17
18
20
23
26
26
29
41
43
43
45
47
49
49
50
53
54
54
58
62
67
5
6
7
Magnetic patterned samples prepared by
nano-lithography techniques
75
Computational and experimental techniques
for the study of magnetic patterns
87
XRMS results: structural analysis, magnetic response
and comparison with computation
99
5.1 Fabrication of arrays of nanostructures
5.2.1 E-beam lithography with scanning electron microscopes
5.2.2 X-ray Lithography
5.2 Sample preparation
6.1 Micromagnetic simulations
6.2 X-ray resonant scattering: principles and experimental concerns
6.2.1 XRMS
6.2.2 Experimental scattering geometries
6.2.3 Instrumentation and polarization selection with
synchrotron radiation
7.1 Energy and angular dependence of the diffuse scattering
7.2 Magnetic field dependence of the scattered intensity
7.2.1 Comparing first and zero order geometry
7.2.2 Demagnetizing field effects
7.2.3 Probing correlations between dots at half order parameter
7.2.4 Hysteresis at nth order peak
7.3 Conclusions
Conclusions and perspectives
Perspectives
75
78
80
81
87
89
89
92
95
99
105
105
108
115
120
123
127
131
Introduction
Spintronics is the science and the technology program to design devices using the electron
spin as the fundamental information carrier throughout a semiconductor (SC) structure. In the
last decade, the electron spin, a pure quantum behaviour of electrons that can assume only the
two values + /2 and – /2, is at the basis of devices already adopted by the information
industry:
spin
valves,
giant
magnetoresistance
(GMR)
structures
and
tunnelling
magnetoresistance (TMR) structures. In all these cases the spin dependent scattering of
electrons is exploited as a quantity that can be modified by selectively reversing the
magnetization of parts of the electronic circuit.
Several physics and engineering issues must be addressed on the way to develop a
spintronic technology: among these, the understanding of the magnetic state in a
ferromagnetic-semiconductor interface and the individual vs. collective magnetic behaviour
of dense matrices of ferromagnetic nanoparticles. In this thesis I adopted a multi-technique
approach to address these issues by designing experiments that use the polarised synchrotron
radiation from ELETTRA as probe of magnetism, and surface science and nanoscience
techniques for the preparation and fabrication of proper samples.
The interface issue implied to adopt a surface science approach to the preparation, in
UHV, of atomically clean and ordered interfaces. The lateral definition of the samples was
pursued by means of moveable masks that permitted to fabricate double wedge structures
with monolayer resolution on GaAs. The dense arrays of magnetic particles were fabricated
by means of e-beam and X-ray lithography ex situ. Finally I started the original development
of an in-situ method for growing dense arrays of magnetic dots on atomically clean substrates,
by deposition in UHV through a mask. This will allow in the future to perform experiments
combining the two approaches followed in this thesis in situ, on the same samples.
In 1990 the spintronics scenario was set by the proposal of a scheme for a spin field effect
transistor by Datta and Das, requiring spin injection and transport into semiconductors.
Among natural candidate materials there are ferromagnetic (FM) films (spin reservoir) in
intimate contact with semiconductors. Spin injection is the main open problem when
i
following this approach. For example, a conducting nonferromagnetic interfacial region might
be a source of undesired spins that could degrade the polarization of spin current.
In the first part of this thesis we discuss experiments on the Fe/GaAs(001) interface. This
is a prototypical interface system due to the possibility of low-defect epitaxial growth of Fe
on single crystal GaAs(001).
An important issue on this system is the existence a
magnetically “dead” layer at the interface that was hinted to by several previous studies. An
experimental program was carried out on the APE beamline of TASC-INFM on the
ELETTRA storage ring, under the supervision of Prof. Giorgio Rossi. This work was done in
collaboration with Dr. Luca Giovanelli, the whole APE group and the University of
Regensburg.
We introduced a magnetisation profiling method based on the use of Co
magnetic impurities as local magnetic markers in the Fe film and on X-ray absorption
Magnetic Dichroism as a probe of the interface magnetic moments (spin and orbital,
separately). We could definitely rule out the presence of a magnetically dead interface layer,
and monitored the increase of the orbital moment at the interface and the role of the As
segregation in reducing the magnetic moments at the surface.
Another fundamental issue is the behaviour of arrays of magnetic particles at the
microscopic and nanoscopic scales. We therefore approached the study of a collection of
submicrometric dots in a regular matrix: such systems are prototypical to magnetic storage
devices. The desired ultra high density requires high resolution lithographic process for
fabrication like X-ray lithography that was carried out at the LILIT beamline of TASC-INFM
at ELETTRA in collaboration with the group of Prof. Enzo Di Fabrizio, collaborating in
particular with Dr. Patrizio Candeloro.
The samples were then studied by resonant and polarized X-ray scattering in collaboration
with Dr. Maurizio Sacchi (CNRS, Paris) and Dr. Carlo Spezzani (CNR, ELETTRA) who built
a reflectometer on the CIPO-CNR beamline at ELETTRA. This diffractive technique couples
the advantages of structural analysis to the ones of electron spectroscopy, and is sensitive to
the magnetic order of the scattering medium, in a complementary way compared to X-ray
absorption. We have interpreted these measurements also by comparison with our
micromagnetic calculations on the same systems.
The thesis is divided in 7 chapters and is organised as follows.
Chapter one defines the technological framework of spintronics. The electrical spin
injection is predicted to be more efficient in tunneling transport than in diffusive one: FM/SC
interfaces which exhibit natural Schottky barriers are perfect candidates and in fact promising
results have been recently obtained for epitaxial Fe on GaAs. Another effect of spin polarized
ii
currents observed in magnetic multilayers is the magnetoresistive effect: its technological
applications are reviewed from spin-valves as read head in hard disks to next-to-come non
volatile magnetic random access memories.
In chapter two we discuss the difficulties of conventional techniques in measuring the
magnetic properties of an interface, finally proposing a new method consisting in magnetic
heterogeneous impurities acting as magnetic markers: these impurities sit at different
distances from the interface and are selectively probed by XMCD. All the UHV techniques
involved in the preparation and characterization of this epitaxial system are reviewed (MBE,
LEED, MOKE, XPS) with particular attention to the crucial XMCD.
Chapter three describes the instrumentations used on APE beamline facility at ELETTRA
where the complete set of measurements has been performed taking advantage of the
interconnected system of UHV chambers.
Chapter four presents all the data and in particular discuss the results of the magnetic and
chemical characterization: a part being element selective, XMCD offers the unique
opportunity to separately measure the local spin and orbital magnetic moments, and
considerations on the trend of such quantities follow as well as comparison with theoretical
models.
Chapter five describes the conventional lithography steps of patterned sample preparation:
we used X-ray lithography at LILIT beamline of ELETTRA to replicate a mask to finally
obtain arrays of permalloy rectangular dots, 1000 nm × 250 nm.
Chapter six introduces the principles of micromagnetic simulations and the features of
polarized soft X-rays scattering both as a structural and spectroscopic tool: the effect of the
magnetization using a defined state for the light polarization is evidenced.
Chapter seven reports the structural and the magnetic characterization of the samples by
means of XRMS. Shape anisotropy and thickness effects of the rectangles are analysed by
monitoring the hysteresis loops: good agreement was found with micromagnetic simulations
performed with OOMMF code. Magnetic correlations between pairs of rectangles have also
been checked. Then the possibility to predict the field dependent scattered intensities at
geometries corresponding to the different Bragg peaks starting from micromagnetic
simulations is discussed.
A final chapter summarising the conclusions and indicating the perspective works
concludes the thesis.
iii
Chapter 1
Spintronics
Spintronics is a multidisciplinary field whose central theme is the active manipulation of
spin degrees of freedom in solid-state systems.[1, 2] Its goal is to understand the interaction
between the particle spin and its environment in order to make, by means of the acquired
knowledge, useful devices where not only the electron charge but also the electron spin
carries
information.
This
new
generation
of
devices
should
combine
standard
microelectronics with spin-dependent effects that arise from the interaction between spin of
the carrier and the magnetic properties of the material. Fundamental studies of spintronics
include investigation of spin transport in electronic materials, as well as spin dynamics and
spin relaxation.
In this introductory chapter we review the main ideas and experimental results that
support such developments, with particular care on the aspects (arrays of magnetic structures
and spin injection efficiency in ferromagnetic-semiconductor interface) that constitute the
final subjects of the experimental studies discussed in the following chapters.
1.1 Spin-dependent transport
Spin-polarized transport will occur naturally in any material for which there is an
imbalance of the spin populations at the Fermi level, which is typically the case for the
ferromagnetic phase of iron, cobalt, nichel, gadolinium and several of their alloys. The
exchange split sub-bands are shifted in energy with respect to each other determining a net
spin polarization of the states near the Fermi level and in parts of the conduction band (Fig.
1.1). The unequal filling of the spin polarised bands defines the net magnetic moment for the
materials. The densities of scattering states for electrons within a few kT of the Fermi level
are therefore different for spin-up and spin-down electrons. To this correspond different spindependent mean free path and mobility.
1
A ferromagnetic metal can be used as a source of spin-polarized carriers to be injected
into a semiconductor, a superconductor, or a normal metal or for tunnelling through an
insulating barrier. The nature of the specific spin-polarized carriers and the electronic energy
states associated with each material must be identified in each case.
The most dramatic effects are generally seen for the highly polarized electron currents;
therefore, there are continuing efforts to find 100% spin-polarized conducting materials (socalled half ferromagnets). These are materials where the majority band is fully occupied and
its top lies below, or well below the Fermi level. The metallic character of the solid is
therefore entirely due to the minority band crossing Fermi energy (EF) leading to the
definition of half-metals. In strong ferromagnets (like Co) the majority d band lies entirely
below EF, but polarised sp bands, as well as the minority d band cross EF.
The spin-polarization P is defined in terms of the number of carriers n that have spin up
(n ) or spin down (n ), as P = (n – n )/(n + n ).
Figure 1.1. A schematic representation of the density of electronic states available to
electrons in a normal metal and in a ferromagnetic metal whose majority spin states are
completely filled. E, the electron energy; EF, the Fermi level; N(E), density of states.
Conventional ferromagnets i.e. Fe, Co, Ni, and their alloys, have a polarization P of 40 to
50%. They can be employed to develop spintronic-aimed devices.
Because of the spin polarization of an electron current, the effects seen in solid state
devices can be most readily visualized if one assumes that the current is 100% polarized (Fig.
1.1). In that case, the only states that are available to the carriers are those for which the spins
of the carriers are parallel to the spin direction of those states at the Fermi level. If the
magnetization of the materials is reversed, the spin direction of those states also reverses.
2
Thus, depending on the direction of magnetization of a material relative to the spin
polarization of the current, a material can function as either a conductor or an insulator for
electrons of a specific spin polarization.
1.2 Electrical spin injection
We report in Fig. 1.2 the generic spintronic scheme of a famous prototypical device, the
Datta-Das spin field effect transistor (SFET, see Ref. [3]). The scheme shows the structure of
the usual FET, with a drain, a source, a narrow channel, and a gate for controlling the current.
The gate either allows the current flow (ON) or does not (OFF). The spin transistor is similar
in that the result is also a control of the charge current through the narrow channel. The
difference, however, is in the physical realization of the current control. In the Datta-Das
SFET the source and the drain are ferromagnets acting as the injector and detector of the
electron spin. The source injects electrons with spins parallel to the transport direction. The
electrons are transported ballistically through the semiconductor channel and when they arrive
at the drain their spin is detected. In a simplified picture the electron can enter the drain (ON)
if its spin points in the same direction as the spin of the drain. Otherwise it is scattered away
(OFF). The role of the gate is to generate an effective magnetic field (in the direction of Ω in
Fig. 1.2), arising from the spin-orbit coupling in the substrate material, from the confinement
geometry of the transport channel, and the electrostatic potential of the gate. This effective
magnetic field causes the electron to precess. By modifying the voltage, one can cause the
precession to lead to either parallel or antiparallel (or anything between) electron spin at the
drain, effectively controlling the current.
One of the crucial issues emerging already from this example is the ability of efficiently
injecting (and detecting) strongly spin-polarized currents into a semiconductor. For practical
applications, it is of course highly desirable that the generation, injection, and detection of
such spin currents be accomplished without requiring the use of extremely strong magnetic
fields and that these processes be effective at or above room temperature: that is why the use
of ferromagnetic metallic electrodes appears to be essential for most practical all-electrical
spin-based devices until and unless useful ferromagnetic semiconductors (FS) are developed.
3
Figure 1.2. Scheme of the Datta-Das spin field-effect transistor (SFET). The source (spin
injector) and the drain (spin detector) are ferromagnetic metals or semiconductors, with
parallel magnetic moments. The injected spin-polarized electrons with wave-vector k move
ballistically along a quasi-one-dimensional channel formed by, for example, an
InGaAs/InAlAs heterojunction in a plane normal to n. Electron spins precess about the
precession vector , which arises from spin-orbit coupling and which is defined by the
structure and the materials properties of the channel. The magnitude of is tunable by the
gate voltage at the top of the channel. The current is large if the electron spin at the drain
points in the initial direction (top row) – for example, if the precession period is much
larger than the time of flight – and small if the direction is reversed (bottom).
1.2.1 Ohmic injection: the conductivity mismatch problem
In a ferromagnetic metal (FM), the electrical conductivity of the majority spin (spin-up)
electrons differs substantially from minority spin (spin-down), resulting in a spin-polarized
electric current. The most straightforward approach to spin injection is the formation of an
ohmic contact (low and voltage independent resistance of the contact) between a FM and a
semiconductor, anticipating a spin-polarized current in the semiconductor. Actually, after
disappointing results found in preliminary experiments, recent work by Schmidt et al.[4] has
pointed out a fundamental problem regarding ohmic spin injection across ideal FMnonferromagnet (NFM) interfaces. The effectiveness of the spin injection depends on the ratio
of the (spin-dependent) conductivities of the FM and NFM electrodes,
When
F
N,
F and
N,
respectively.
as in the case of a typical metal, then efficient and substantial spin injection
can occur, but when the NFM electrode is a semiconductor,
F
>>
N
and the spin-injection
efficiency will be very low (the so-called conductivity mismatch problem).
This limit can be overcome by making use of magnetic semiconductor as a spin aligner:[5,
6] spin-injection efficiencies up to 90 % have been reached[5] but with the above-mentioned
disadvantage to be restricted to low temperatures (< 100 °K). The measurement of the carrier
polarization was made by optical detection in spin LED (light emitting diode) structures: as
non-magnetic semiconductor, a GaAs/AlGaAs LED monitors the degree of circular
4
polarization of the electroluminescence (EL) to finally extrapolate, via associated quantum
selection rules, the spin polarization of injected carriers.
1.2.2 Tunnel injection: the Schottky barrier
Successful spin injection in vacuum tunnelling process (STM with a ferromagnetic tip)[7]
and the development of MTJ with high magnetoresistance (see following section 1.3) have
demonstrated that tunnel barriers can result in the conservation of the spin polarization during
tunneling, suggesting that tunneling may be a much more effective means for achieving spininjection than diffusive transport. Systematic theoretical understanding of tunnel injection was
provided as well, starting from the work of Rashba.[8] Thus, either a metal-insulatorsemiconductor tunnel diode or a metal-semiconductor Schottky barrier diode that uses a FM
electrode can be expected to be an effective means for injecting spins into a semiconductor
system.
•
Schottky Barrier
We consider now an ideal metal-semiconductor junction to illustrate the origin of
Schottky barrier. Depending on the difference between the work function q
M
of the metal
and the electron affinity qχSC of the semiconductor, different situations may arise. We
consider here a high-work-function metal and n-type semiconductor, as shown in Fig. 1.3.
Figure 1.3. Band diagram of high-work-function metal and n-type semiconductor, before
(left) and after (right) the contact.
In thermal equilibrium the Fermi levels in the two materials must be aligned and this
causes electrons to flow from semiconductor to metal when the two materials are brought into
5
contact: a dipole layer is built at the interface but while in the metal the participating charge is
screened within a few Ångstroms, in semiconductor the free carrier concentration is orders of
magnitude lower and thus shielding is much less effective. Thus the space charge extends
hundreds of Ångstroms into the crystal forming a depleted surface region (from interface to
xd) where the ionized donor impurities create an electric field which balances the diffusion of
the electrons towards the metal. Bringing the separated band diagram together with the same
vacuum level, the result (see Fig. 1.3) is a band bending where the bult-in potential q
the potential across this depleted region and is related to the potential barrier q
B,
i
equals
called the
Schottky barrier. In this oversimplified approach, proposed by Schottky, this barrier is equal
to the difference q
M
- qχSC.
The rectifying action of our metal-semiconductor junction is depicted in Fig. 1.4. When
positive (forward) bias is applied to the metal, its Fermi energy is lowered and this results in a
smaller drop potential across the semiconductor: this finally leads to a positive current
through the junction at a voltage comparable to the built-in potential. As a negative (reverse)
voltage is applied, the potential across the semiconductor increases, yielding a larger
depletion region and a larger electric field at the interface: the barrier, which restricts the
electrons to the metal, is unchanged so that barrier, independent of the applied voltage, limits
the flow of electrons. In this condition the electrons may still flow through the barrier via
quantum-mechanical tunneling: this requires enough doping in the semiconductor (1019 cm-3)
in order to reduce the width of the depletion region down to 3 nm or less.
Figure 1.4. Energy band diagram of a metal-semiconductor junction under a forward (left)
and reverse (right) bias Va.
6
Actually the chemical reactions at the interface between semiconductor and metal alter the
barrier height and so do interface states at the surface of semiconductor. So the experimental
data deviate from the Schottky model predictions even if some general trend can still be
observed as for the case of n-Si where the barrier height increases for metals with higher work
function.[9] GaAs on the other hand is known to have a large density of surface states so that
the barrier height becomes virtually independent of the metal. Generally speaking, it seems
that the surface preparation and the deposition conditions of the metal may play a relevant
role in determining parameters crucial for the tunneling transport regime. These problems
have been studied for three decades since metal semiconductor contacts and
semiconductor/semiconductor heterojunctions are at the basis of microelectronics.
•
Schottky contact in Fe/GaAs
A number of groups are active in the development on the epitaxial growth of
ferromagnetic thin films on semiconductors with emphasis on forming abrupt, high-quality
Schottky barriers. In fact a Schottky barrier provides a natural tunnel barrier between a metal
contact and a semiconductor, obviates the need for a discrete layer, and is already a routine
ingredient in semiconductor device technology.
Between the most studied systems, Fe ultrathin films on GaAs[10, 11] and ZnSe[12, 13]
zincblende semiconductors present optimal epitaxial conditions, due to the small mismatch
(1.4 % and 1.0 % respectively) between bcc Fe lattice parameter (aFe = 2.866 Å) and half the
GaAs and ZnSe one (aGaAs = 5.654 Å and aZnSe = 5.67 Å): in fact, Fe may grow epitaxially on
GaAs(001) with the epitaxial relationship Fe(001)<100> GaAs(001)<100> and the same
holds for ZnSe(001), as shown in Fig. 1.5. Fe on GaAs represents a highly intriguing FM/SC
system as it is formed by the well known 3d transition metal and the most popular III-V
semiconductor in use today.
Particularly promising from the spin-injection point of view are the recent results on
Fe/GaAs Schottky diode. Zhu et al. [10] reported a room temperature spin injection efficiency
of ~ 2 % for the Fe/GaAs interface, with the injected spin polarization being detected by the
degree of circular polarization of the electroluminescence (EL) emitted by InxGa1-xAs/GaAs
spin LED structures: so the authors suggested that Fe forms Schottky-type contact on GaAs.
Even more recently, Hanbicky et al.[11] obtained electron-spin polarizations of 32 % in a
GaAs quantum well structure (always forming a spin LED) via electrical injection through a
reverse-biased Fe/AlGaAs(001) Schottky contact: in fact, the analysis of the transport
7
demonstrated that tunneling is the dominant transport mechanism.
Figure 1.5. Schematic of the crystal growth of Fe bcc structure on ZnSe and GaAs
zincblende structures with (001) surfaces. (Left) 3D disposition of the atoms: the vertical
profile includes a unit cell period of bcc Fe on a unit cell period of ZnSe (Zn-terminated):
the semiconductor sp3-hybrid bonds are represented by red segments. This puts in evidence
that there are two different positions for Fe atoms at the interface. One is situated at a site
where a SC atom would have been situated if the zinc-blende structure was to continue
across the interface, and so experiments the dangling sp3-hybrid bonds environment, the
other is situated at a position that corresponds to a void in the zinc-blende structure (and is
labelled ES, empty sphere, in the right figure). (Right) Similarly, layer-by-layer atomic
disposition at the Ga-terminated GaAs surface (z = -1/4 and z = 0) covered with Fe (z = 1/4
and z = 1/2): the unequivalent Fe atomic sites are distinguished. The convention for III-V/
II-VI (001) surfaces is to label [1-10] as the direction of the element V/VI dimers. The
anisotropic interface bonding is considered the main responsible of the long studied and
intriguing in-plane uniaxial magnetic anisotropy (UMA), between [1-10] and [110]
directions, observed in these systems, see for instance Ref. [14] concerning theory, and Ref.
[15] for experimental results.
•
Fe/GaAs(001): the issue of magnetically dead layer at interface
The presence of a magnetically dead layer at the generic FM/SC interface, due to chemical
bonding and intermixing between FM and SC, apart being an interesting question from a
fundamental point of view, is considered a potentially deteriorating factor: in fact, the
conducting non-ferromagnetic interfacial region might be a source of unpolarised spins
reducing the polarization of spin current. Another related issue is the possibility that this
region may be a source of spin-flip scattering: this should be a more remote concern as the
expected spin diffusion length in a metal is in the order of microns.[16]
This is a long debated point for the Fe/GaAs(100) interface. From the beginning, the
results on the magnetic properties of thin and ultrathin Fe films grown on this surface gave
8
strong indication that magnetisation should be absent or reduced at the interface.[17] This
was supported also by the detection of As segregation and Ga diffusion and finally confirmed
by the discovery of a diluted intermixed phase at the interface.[18] Then, if from one side the
attention turned towards other FM/SC interfaces, as the less intermixing-affected
Fe/ZnSe(001), from the other it was also noticed that magnetic dead layer in Fe/GaAs(001)
might be absent depending on the growth conditions.[19] What’s more the last promising
results in spin-injection (mentioned above), renewed the interest in studying the detailed
properties of this interface. The recent developments of diluted magnetic semiconductors
based on GaAs doped with Mn or Co further encourage to deepen the understanding of these
interfaces.
The first part of this thesis (chapters 2, 3 and 4) focuses on the magnetic properties study
of this system. 6 Fe MLs are deposited in UHV conditions with MBE (molecular beam
epitaxy) techniques on a GaAs(001)-(4 × 6) clean reconstruction. The uncapped film is
studied in situ with XMCD, a synchrotron light spectroscopy that has a direct, atom-specific
magnetometric power. Co impurities dispersed in Fe film serve as a local probe to obtain a
layer-dependent magnetization profile from the interface to the surface of the iron layer. Other
experiments have been recently performed with XMCD to tackle this long debated issue on
the magnetically dead interface, both in Fe/GaAs(001) and Fe/ZnSe(001) systems.[20, 21]
1.3 Magnetoelectronics
Even though the definition of spintronics is recent, having been introduced by S. A. Wolf
in 1996, contemporary research in spintronics relies closely on a long tradition of results
obtained in diverse areas of physics, mainly magnetism, semiconductor physics and optics.
Some of the well-established schemes and results form the so called magnetoelectronics
branch, including magnetoresistive effects: giant magnetoresistence (GMR) and tunneling
magnetoresistence (TMR) structures are already exploited as magnetic read heads in computer
hard drives, non-volatile magnetic random access memory (MRAM), and circuit
insulators.[22]
The basic action of the magnetoresistive effect is illustrated in Fig. 1.6, where it is
assumed that the electrons are travelling from a ferromagnetic metal, through a normal metal,
and into a second ferromagnetic metal. When the magnetizations (or, equivalently, the
magnetic moments) of the two ferromagnetic metals are in an aligned state, the resistance is
9
low, whereas the resistance is high in the anti-aligned state: to evidence the effect, again a
100% polarized ferromagnet is used.
Figure 1.6. Schematic representations of spin-polarized transport from a ferromagnetic
metal, through a normal metal, and into a second ferromagnetic metal for aligned and antialigned magnetic moments; Ø: disallowed channel.
The effect was discovered in 1988 in multilayers structures displaying a GMR[23] and
found application in the so-called ‘spin valve’ system, constructed so that the magnetic
moment of one of the ferromagnetic layers is very difficult to reverse in an applied magnetic
field, whereas the moment of the other layer is very easy to reverse. This easily reversed (or
“soft”) layer then acts as the valve control and is sensitive to manipulation by an external
field. The device can be used to measure or monitor those fields and can have numerous
applications, mostly since the discovery of a large room temperature GMR.[24] The most
famous application, due to its major economic impact on the market since the late 90’s, is the
‘read head’ for magnetic hard disk drives. Another fundamental application is the realization
of non-volatile memory, i.e., magnetic RAM, using GMR elements fabricated in arrays.
An alternative approach for obtaining MRAM, exploits another manifestation of spinpolarized transport, i.e. spin-polarized tunneling. This effect was reported already in
1975,[25] but only the discovery of large room-temperature TMR through an alumina barrier
in 1995[26] has renewed interest in its study and application. As in any tunnelling device, two
10
conducting layers are separated by a very thin insulating layer, so that the electron can
quantum mechanically ‘tunnel’ through the barrier under voltage application: if the two
conductors are ferromagnetic (see Fig. 1.7), the same issues that were associated with the
GMR effect also arise, namely, the spin description of the states that are available for
tunneling.
Figure 1.7. A magnetic tunnel junction formed by a thin insulating barrier separating two
ferromagnetic metal films. Current passing through the junction encounters higher
resistance when the magnetic moments are anti-aligned and lower resistance when they are
aligned.
The devices equivalent to spin-valves (pinned layer and free layer) for TMR effect are the
magnetic tunnel junctions (MTJ) whose magnetoresistive effects are typically 20 to 40 %,
bigger than the spin valve ones (< 20 %). On the other hand, the high resistance of MTJ, even
if interesting for portable devices that have limited power, may prove to be unattractive in
terms of response time or noise, and the problem increases as device sizes are reduced (the
current is perpendicular to the plane of films and, as the area of the device shrinks, the
resistance increases).
1.3.1 Arrays of magnetic structures
An example of MTJs application in memory array architecture is shown in Fig. 1.8: a xy
intersecting grid array is used with a tunnel junction that is located at every point of
intersection. This approach provides essentially a four-point probe arrangement (two that
provide current and two that permit an independent voltage measurement) that is attached to
every device. Furthermore, the leads can provide a dual service, because pulse currents, which
are directed to run above and below rather than through the device, can provide the necessary
magnetic fields to manipulate the magnetization directions in the ferromagnetic layers, i.e. the
11
stored magnetic information: MRAM uses magnetic hysteresis to store data and
magnetoresistance to read data. It offers advantages both compared with semiconductor RAM
(non-volatility) and compared with silicon electrically erasable programmable read-only
memory (EEPROM) having 1000 times faster write times, no wearout with write cycling and
lower energy for writing. The commercial availability of MRAM is still next to come.
The addressing scheme of the GMR-based MRAM holds a similar configuration as well.
For both of them, lithographic process is a fundamental step to obtain regular and ordered
magnetic multilayer structures, with high density and uniform and controlled fabrication: the
state-of-art lithographic techniques may reach ultra-high density of more than 100
Gbits/inch2, resulting in single particle size of few tens of nanometers.
Figure 1.8. A schematic representation of RAM that is constructed of magnetic tunnel
junctions connected together in a point contact array. The conducting wires provide current
to the junctions and permit voltage measurements to be made. They also enable the
manipulation of the magnetization of the elements by carrying currents both above and
below the magnetic junctions to create magnetic fields.
More generally, a single magnetic nanosized structure is the constitutive element of every
spintronic solid-state device. Novel physical properties emerge as the structure size becomes
comparable to or smaller than certain characteristic length scales (spin diffusion lengths,
magnetic domain wall width, …) and to tackle the challenge of characterizing such small
nanostructures, more laterally resolved investigation techniques arise.[27] In practice, it is
highly desirable to fabricate arrays of such nanostructures over macroscopic areas: this allows
to resort to standard averaging techniques to study the magnetic properties of large arrays of
‘identical’ particles, and what’s more, these ordered arrays fully simulate technological
devices as MRAMs. So one can probe both the individual and collective behaviour
(eventually affected by inter-dots coupling) of the elements in a well-defined and reproducible
fashion. Significant amount of work has been done by the scientific community over recent
years to address different aspects of ordered magnetic nanostructures, from fabrication to
12
characterization, both theoretically and experimentally.[28] The full control on the magnetic
state of the structure relies on the study of the magnetisation switching, both from the static
and dynamic point of view.
In the second part of this thesis (chapters 5, 6 and 7) we present the fabrication of
prototype magnetic patterned samples in the submicrometric regime, in order to study the
magnetisation reversal, comparing theoretical micromagnetic simulations and experimental
X-ray magnetic resonant scattering measurements (XRMS) in order to illustrate the
potentiality of this quite novel synchrotron light technique.
[1] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L.
Roukes, A. Y. Chtchelkanova, D. M. Treger, Science 294, 1488 (2001).
[2] Igor Žuti , J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004).
[3] S. Datta, B. Das, Appl. Phys. Lett. 56, 665 (1990).
[4] G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, and B. J. van Wees, Phys. Rev. B
62, R4790 (2000).
[5] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L.W.
Molenkamp, Nature 402, 787, (1999).
[6] Y. Ohno, D. K. Young, B. Beschoten, F. Matsukura, H. Ohno, and D. D. Awschalom,
Nature (London) 402, 790 (1999).
[7] S. F. Alvarado, Ph. Renaud, Phys. Rev. Lett. 68, 1387 (1992).
[8] E. I. Rashba, Phys. Rev. B 62, R16267 (2000).
[9] H. Luth, Surfaces and interfaces of solid materials, Springer Verlag, Berlin 1995.
[10] H. J. Zhu, M. Ramsteiner, H. Kostial, M. Wassermeier, H.-P. Schönherr, and K. H.
Ploog, Phys. Rev. Lett. 87, 016601 (2001).
[11] T. Hanbicky, O. M. J. van’t Erve, R. Magno, G. Kiosleoglou, C. H. Li, B. T. Jonker, G.
Itskos, R. Mallroy, M. Yasar, and A. Petrou, Appl. Phys. Lett. 82, 4092 (2003).
[12] M. Eddrief, M. Marangolo, S. Corlevi, G.-M. Guichar, V. H. Etgens, R. Mattana, D. H.
Mosca, and F. Sirotti, Appl. Phys. Lett. 81, 4553 (2002).
[13] R. Bertacco, M. Riva, M. Cantoni, F. Ciccacci, M. Portalupi, A. Brambilla, L. Duò, P.
Vavassori, F. Gustavsson, J.-M. George, M. Marangolo, M. Eddrief, and V. H. Etgens, Phys.
Rev. B 69, R16267 (2004).
[14] E. Sjöstedt, L. Nordström, F. Gustavsson, and O. Eriksson, Phys. Rev. Lett. 89, 267203
(2002).
[15] O. Thomas, Q. Shen, P. Schieffer, N. Tournerie, and B. Lépine, Phys. Rev. Lett. 90,
17205 (2003).
[16] M. Johnson, J. Supercond. 14, 273 (2001).
[17] J.J. Krebs, B.T. Jonker and G.A. Prinz, J. Appl. Phys 71, 2596 (1987).
[18] A. Filipe, A. Schuhl, and P. Galtier, Appl. Phys Lett. 70, 129 (1997).
[19] M. Zölfl, M. Brockmann, M. Köhler, S. Kreuzer, T. Schweinböck, S.Miethaner, F.
Bensch, G. Bayreuther, J. Magn. Magn. Mater. 175, 16 (1997).
[20] J.S. Claydon, Y. B. Xu, M. Tselepi, J.A.C. Bland, G. van der Laan, Phys. Rev. Lett. 93,
037206 (2004).
[21] M. Marangolo, F. Gustavsson, M. Eddrief, Ph. Sainctavit, V. H. Etgens, V. Cros, F.
Petroff, J. M. George, P. Bencok, and N. B. Brookes, Phys. Rev. Lett. 88, 217202 (2002).
[22] G. Prinz, Science 282, 1660 (1998).
[23] M. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).
13
[24] S. Parkin, D. Mauri, Phys. Rev. B 44, 7131 (1991).
[25] M. Jullière, Phys. Lett. A 54, 225 (1975).
[26] J. Moodera, L. Kinder, T. Wong, R. Meservey, Phys. Rev. Lett. 74, 3273 (1995).
[27] M. R. Freeman and B. C. Choi, Science 294, 1484 (2001).
[28] J. I. Martín, J. Nogués, Kai Liu, J. L. Vicent, Ivan K. Schuller, J. Magn. Magn. Mat. 256,
449-501 (2001).
14
Chapter 2
Measuring interfacial magnetization
Interface science has developed from surface science since identical requirements of
atomic control both in structure and in composition is needed in order to study the intrinsic
properties of the interface systems. Whenever low energy properties, like magnetism and
electron transport through the interface, are concerned the exact conditions of interface
preparation are extremely crucial. With this understanding it has been planned a surfacescience style suite of experiments for the study of the Fe/GaAs(100) interface. Hereafter I
introduce the main ingredients of the experimental program, i.e., the techniques used to
prepare in atomically controlled way the interfaces and to probe in atom-specific way the
local magnetization.
2.1 Interface magnetization profiling
An open question on the Fe/GaAs(001) system is the magnetic state of the interface layer.
Early investigations suggested the presence of a magnetically dead layer at the interface
between the two materials.[1] The interest arose about this problem since, as mentioned in the
introduction, the presence of a metallic, non magnetic or magnetically disordered layer would
act as a non polarised scattering layer for the carriers, therefore deteriorating the efficiency of
spin-polarized current injection in possible spintronics applications. Due to the reactivity of
transition metals with semiconductors, this is a general issue in the ferromagneticsemiconductor junctions. Magnetic profiling an interface and overlayer is not trivial: even
high sensitivity magnetometries, capable of probing monolayers, do in fact average over the
whole magnetic material, and the surface sensitive approaches are only partially useful for
buried interfaces. Destructive techniques often employed in depth profiling (like SIMS for
studying compositional profiles) are not suitable when the low-energy properties of materials,
like magnetism, are of interest.
We have attempted an original approach to tackle this point which consists in seeding a
15
half monolayer of Co impurities at different distances from the interface and up to the surface
of a 6 ML Fe film: Co atoms act as magnetic impurity markers, that we assume sensitive to
their magnetic environment at the interface and within the iron overlayer. They can be
individually monitored by exploiting the element selectivity of the XMCD technique, which
allows to detect both the spin and the magnetic moment in the submonolayer regime, and the
lateral resolution of the technique (moderate in the present implementation), that was matched
to the topological configuration of the samples.
The samples were grown in UHV conditions by MBE technique, over atomically clean
GaAs substrates. The sample architecture includes a Fe wedge over the GaAs surface, up to 6
ML maximum thickness, the Co ‘impurities’ distributed on the iron wedge surface, and a Fe
counter-wedge, which finally form together an evenly thick 6 ML Fe film with Co atoms
embedded at different distances from the GaAs substrate.
2.1.1 Co influence on and from the Fe magnetic environment
We adopted Co as the best candidate to serve as a magnetic marker, due to its proximity to
Fe in the periodic table of elements, and consequently easy spectral access on the relevant L2,3
transitions - L3 and L2 edges are respectively at 707 and 720 eV for Fe and 778 and 793 eV for
Co - and ease to apply the sum-rules of the XMCD analysis. From the structural point of
view, Fe1-xCox/GaAs(001) is known to grow with the same lattice parameter as Fe/GaAs(001)
at least with x as high as 0.66:[2] furthermore also pure Co on GaAs(001) is known to initially
grow in a single-crystalline bcc phase.[3]
The small amount of Co atoms was chosen in order to keep unchanged the magnetic
environment of the interface; at the same time the submonolayer sensitivity of XMCD
guarantees a good signal even when this is coming from the most buried Co atoms, also due
to the adequate probing depth of electron yield absorption measurement (at least 20 Å).[4]
The reciprocal magnetic influence between Co and Fe in Fe-Co alloys has been observed
over a wide composition range (see Ref. [5] and references there in): the magnetic moments
of both Fe and, at a minor extent, Co, change as a function of the relative concentration.
Nevertheless this change is not abrupt and is observed to become smoother for reduced
symmetry as in the case of surface confined alloys.[5] It is reasonable to imagine that going to
the limit of dispersed impurities of submonolayer equivalent thickness, Fe ferromagnetic
environment will be substantially preserved and act as a fundamental source of exchange
interaction for the Co atoms, and so these will locally reflect possible magnetic variation like
magnetisation reduction.
16
2.1.2 Analogy with Mössbauer experiments
The idea of burying a probe for the local analysis near surfaces, interfaces and in thin
films was introduced first, and exploited in several studies, on the basis of conversion electron
Mössbauer spectroscopy (CEMS).
include
57
Co and
57
By selectively depositing Mössbauer isotopes (which
Fe) within a film made of the respective non-Mössbauer isotope, which
does not contribute to the Mössbauer spectrum, one can locally analyse the hyperfine
interaction parameters without affecting the chemical and electronic environment.[6] Korecki
and Gradmann[7] performed a pioneering experiment by seeding one monolayer of 57Fe in a
56
Fe utrathin film so controlling the change in surface magnetism from the first to the second
layer, through the estimation of the magnetic hyperfine field. This kind of experiments is still
of great actuality and interest (see for example Ref. [8]) in the field of surface and interface
magnetism, though time-demanding and limited to the use of magnetic Mössbauer isotopes
(Co and Fe).
Comparing CEMS with our technique, a big advantage of CEMS is that the magnetic
marker can be, at least in the case of Fe and Co, an isotope of the studied material, which also
means that there is no stringent requirement on the amount of used marker, whereas in our
case one should remain in the ‘impurity’ regime; another advantage comes from a bigger
depth sensitivity due to the high energy of the electrons emitted in the decay of the γ-excited
nuclei (7.3 keV for K conversion electrons from
57
Fe). As a disadvantage, one cannot
disentangle the orbital and spin component, but only extract a total magnetic moment.
In principle our approach could be generalised to a wider range of systems, but it remains
that the role of the impurity could be more complex then just a “local magnetization probe”
with an active role of the impurity itself in determining the local magnetization.
The very high dilution could help. In the present experiment the Co is not very highly
diluted in the probed layer, but a factor 10 in higher dilution would make it better to
approximate the weak perturbation introduced in the system by the impurity itself, while still
allowing for high quality data.
The recent improvements in stability of the APE-HE beamline go in the direction of
allowing for experiments on less concentrated impurities.
2.2 Preparation of atomically clean interfaces
The interatomic forces at the surface are considerably different with respect to the bulk:
one may expect altered atomic positions and a surface structure that does not agree with that
of bulk, i.e surface reconstructions. The distortion due to the existence of a surface is usually
17
different for semiconductors, which have significant directional bonding, and for metals,
which have delocalised electrons and a chemical bond which is not strongly directed. For
most clean metals the surface structure is identical with the substrate structure (except for
possible vertical displacements of the surface planes), whereas with clean semiconductor
surfaces considerable deviations may occur, due to the recombination of the dangling bonds
into a superstructure: what’s more this recombination may often lead to different ordered
reconstructions, depending on the detailed conditions of the surface preparation. So, in
studying ultrathin metallic films deposited on a semiconductor, the specific used
reconstruction is indicated as a crucial parameter which may play a relevant role for the
interface properties.
This is also the case for the clean GaAs substrate and the Fe film that we deposit on it. As
the former may exhibit a big number of different ordered reconstructions, in the following I
try to summarise the results so far obtained for the different cases in order to better locate and
justify the choice made in our experiments.
2.2.1 The role of the GaAs(001) surface preparation
Since the discovery of the epitaxial growth of Fe on GaAs(001)[9] the magnetic, structural
and morphologic properties of Fe/GaAs(001) interface have been widely studied in the last 25
years, both theoretically and experimentally, and the emerging differences demonstrate the
importance of the substrate preparation and growth conditions.
A first important ingredient is the termination of the substrate: surface reconstructions are
divided between As-terminated and Ga-terminated depending on the atomic species
occupying the last reconstructed layer. It is seen by calculations[10] that the much stronger
interaction, due to a larger pd hybridisation, between As and Fe rather than between Ga and
Fe can highly reduce the magnetic moment of Fe atoms bonded to As depending on the
specific environment; on the contrary Ga itself does not influence the magnetic moment, but
Ga in the Fe film should reduce As segregation. So these authors[10] suggest that the famous
reports[1, 11, 12, 13] on the presence of reduced magnetic moment or even zero magnetic
moment close to the interface were related to the use of As-rich surfaces, simply obtained by
annealing at 580-600 °C to induce the oxide desorbtion: in one of this work[12] a first proof
of the existence of a chemically intermixed phase at the interface was also given. Firstly, we
must point out that the classification of these surfaces as As-rich[10] or As-terminated[14], is
not so convincing: Gester et al.[13] explicitly refer also to a Ga-rich surface and the coauthors of Ref. [1] identify in a later work[15] the same substrate preparation (oxide
18
desorption at 585 °C) with the Ga-rich (4 × 6) reconstruction. So, the role of the Astermination as a discriminating factor for the presence of a reduced or dead magnetic layer
still remains fuzzy: what’s more a study [16] on a well-ordered As-rich (2 × 4) surface, grown
in situ by MBE, deduced a fully ferromagnetic interface from the fact the Kerr signal per ML
was similar at different coverage, consistently with a simple model in which the
magnetization incorporates virtually all Fe layers. Secondly, other common factors in the
early works which show the presence of reduced magnetization were the absence of
sputtering in surface preparation, which results in C-contaminated surfaces[13, 17], and,
probably even more crucial, the high temperature of the substrate (> 150 °C) during Fe
deposition. In fact, magnetic measurements by Filipe et al.[12, 18] show that the reduced
magnetism is a function of the growth temperature and that, as mentioned above, it is
consistent with the formation of the ternary Fe3Ga2-xAsx phase at the Fe/GaAs interface; in
later investigations[19] the post-annealing of a Fe/GaAs film at 450 °C is seen to result in the
formation of a reacted region comprised of Fe3Ga1.8As0.2 and Fe2As and the proved possibility
of subsequently growing epitaxial Fe films at room temperature directly on this reacted region
which has epitaxial character[20, 21] is consistent with the initial formation of a reacted
epitaxial phase at the interface when Fe is grown directly on GaAs at growth temperatures of
more than 170 °C: both the lower magnetic moment of Fe in the ternary phase and the
antiferromagnetic character of Fe2As alloy would explain the decrease of the magnetization at
the interface. As Fe–Ga–As reactions can be minimized by growing at temperatures below 95
°C[22] and on the other hand the best crystalline quality materials are generally obtained from
deposition at high growth temperatures[23] we choose room temperature deposition as a
reasonable and simple compromise.
The definitely characterizing ingredient of the well prepared and ordered surfaces is the
specific surface reconstruction due to the dimerization of the dangling bonds of the surface
atoms. Actually, it does not seem to play any crucial role for the magnetic properties of Fe, as
it is evidenced by some experiments respectively on As-rich[24] and Ga-rich[25, 26]
reconstructions. This is in agreement with a theoretical expectation[27] showing that Ga and
As surface dimers become unstable under Fe adsorption and Fe-Ga or Fe-As bonds form
instead. A big influence of the specific reconstruction was rather detected [24, 26] on the
morphology of the film, mainly at the first stage of growth when the size and the shape of the
Fe islands as well as their sites of nucleation and their distribution were found to be strongly
dependent upon the specific surface dimerization.
With all these considerations in mind, we decided to use in our experiments the Ga-rich (4
× 6) reconstruction which is quite simple to be prepared starting from a commercial GaAs
wafer;[17, 26] the driving idea was to limit the As segregation so to prevent any related
19
residual issue about the effect of the As-rich surfaces on the magnetization reduction.
Furthermore, it is more difficult to prepare well-ordered surfaces for the As-rich
reconstructions.[28] Last but not least, the wide body of information available in the scientific
literature[17, 29, 30, 31, 32, 33] on the magnetic properties of the thin Fe film grown at room
temperature on GaAs(001)-(4 × 6), make it a paradigmatic reference.
2.3 Low Energy Electron Diffraction
In surface physics[34] Low Energy Electron Diffraction (LEED) is used as the standard
technique to check the medium range /long range crystallographic quality of a surface,
prepared either as a clean surface, or in connection with ordered adsorbate overlayers. A
monochromatic beam of electrons with a primary energy variable between 30 and 300 eV is
incident on the surface: the elastically backscattered electrons give rise to diffraction spots
that are imaged on a phosphorous screen. This energy range is particularly suited to surface
studies since it corresponds to the lowest values of the quasi-universal curve for the mean free
path of electrons in solid (see Fig. 2.1); furthermore, according to the De Broglie relation λel =
(150.4/E)1/2 for the wavelength λel (in Å) of an electron of energy E (in eV), typical LEED
wavelengths are in the Angstrom range of the interatomic distances in a solid.
Figure 2.1. The mean free path as a function of the kinetic energy of the electrons:[34] the
scattered measured point represent different crossed materials.
To understand the essential features of such an experiment, the so-called kinematic
diffraction theory is sufficient: the resulting Bragg equation, in analogy with the treatment of
X-ray interferences in crystals, determines the directions of the interference maxima (Bragg
beams) and their positions on the fluorescent screen. This approach forms the basis of the
20
geometrical theory of diffraction, which easily provides the geometry of the unit cell - the
diffraction pattern corresponds essentially to the surface reciprocal lattice - but does not
explicitly carry information on the location of the atoms within this unit: this further
information requires a detailed measurement of the diffracted intensities and a more thorough
description of the scattering process using the so-called dynamic theory of diffraction, which
takes into account relevant effects as the multiple-scattering events due to the ‘strong’
interaction of low energy electrons with matter.
In our experiments we simply made use of LEED to monitor the crystallographic structure
of our prepared surfaces in order to assure a complete control on the sample preparation also
by comparison with the results obtained in previous studies of the same interface: so we limit
our discussion to some basic concepts of the LEED technique within the frame of the
kinematic theory.
The condition for the occurrence of an elastic Bragg spot is that the scattering vector K
must have the component parallel to the surface equal to a vector G// of the 2D surface
reciprocal lattice, that is
K// = k’//-k// = G//
(2.1)
where k and k’ are the wave vectors of the incident and backscattered electron.
In order to extend the well-known Ewald construction to our 2D problem we must relax
the restriction of the third Laue equation, the one concerning the component perpendicular to
the surface, whereas the two components parallel to the surface must satisfy the other Laue
equations (2.1): this is done by attributing to every 2D reciprocal lattice point (h, k) a rod
normal to the surface, as shown in Fig. 2.2. In the 3D problem we have discrete lattice points
in the third dimension rather than rods, and these are the sources of the third Laue condition
for constructing the scattered beams.
In the 2D case, the possible elastically scattered beams (k’) can be obtained by the
following construction illustrated in Fig. 2.2. According to the experimental geometry the
wave vector k of the primary beam is positioned with its end at the (0, 0) reciprocal lattice
point and a sphere is constructed around its starting point: the condition K// = G// is so fulfilled
for every point at which the sphere crosses a “reciprocal lattice rod”. In contrast to the 3D
scattering problem of X-rays in bulk solid-state physics, the occurrence of a Bragg reflection
is not a singular even: the loss of the third Laue condition in our 2D problem ensures a LEED
pattern for all scattering geometries. So, by collecting the elastically scattered electrons under
these conditions, we obtain a pattern corresponding to the projection of the surface reciprocal
21
lattice.
Figure 2.2. Ewald construction for elastic scattering on a 2D surface lattice. The
corresponding 2D reciprocal lattice points (h, k) are plotted on a cut along kx.
Connecting the surface periodicity with the substrate (bulk) structure is advantageous
because the LEED pattern can be readily identified and linked with the known bulk structure:
so the classification of surface structures follows a nomenclature where the relation between
the surface lattice (basis vectors b1 and b2) and the substrate lattice (basis vectors a1 and a2) is
expressed by the ratios of the basis vectors (and the angle of rotation between the two lattices,
if any), i.e., m × n with m = | b1|/| a1| and n = | b2|/| a2|.
The essential elements of a LEED system are an electron gun for producing a sufficiently
parallel and monoenergetic electron beam with energies typically varying between 30 and 300
eV and a detection system for the elastically scattered electrons.
A typical LEED system is exhibited in Fig. 2.3. A heated cathode emits electrons which,
travelling through a lens systems, are focused and accelerated to the desired energy before
leaving the last aperture which is usually at the same potential of the sample; the same is true
for the last hemispherical transparent grid, thus a field-free space is established between the
sample and the display system through which the electrons travel to the surface and back after
scattering. The fluorescent screen (collector) has to be biased positively (∼5kV) in order to
achieve a final acceleration of the slow electrons to make their impact visible on the screen
which is usually transparent from its backside. A second grid (suppressor) is at a negative
potential whose magnitude is slightly smaller than the primary electron energy in order to
repel the inelastically scattered electrons which would produce an isoptropic background: this
repelling grid is usually replaced by a double grid which reduces the field inhomogeneities.
Standard LEED optics are often used also as a retarding field energy analyser (RFA), by
22
superimposing an AC voltage at the suppressor voltage and using a phase-sensitive current
detection on the collector by means of a lock-in amplifier: this allows, simply switching the
configuration of the same instrument, Auger electron spectroscopy (AES) which is a powerful
technique in surface science, as popular as LEED, due to its ability to check the chemical
composition of a surface by measuring the element-dependent energy of the emitted Auger
electrons, so detecting down to fractions of percentage of possible contaminants. We will not
go into further details about this standard technique as we just used it to check the absence of
contaminants, like O and C, on the surface of the GaAs substrate.
Figure 2.3. Schematic of four-grid LEED optics for electron diffraction experiments.
2.4 Photoemission Spectroscopy
One of the most important and widely used experimental techniques to gain information
about occupied electronic states is photoemission spectroscopy. The experiment is based on
the photoelectric effect whose explanation by Einstein in 1905 is well-known as a milestone
of the quantum theory. The photoelectron spectroscopy requires a monochromatic photon
source, an electron spectrometer and good high vacuum conditions to let the photoelectron
run unperturbed to the spectrometer. From the quasi-universal curve for the mean free path of
electrons in solid follows the high sensitivity of photoemission technique to the surface (~ 10
Å in 100-1000 eV range, see Fig. 2.1). These conditions created the scientific case of “surface
23
science” since it became clear that the vacuum was not just needed for electron collection, but
it was a key condition in order to retrieve signal from the wanted surface. Indeed the
photoemission spectroscopy at UV and soft-X-ray photon energies is intrinsically surface
sensitive. It is therefore mandatory to prepare and preserve atomically clean surfaces, as well
as to understand that the electronic states at surfaces may differ intrinsically from those in the
bulk.
The solid surface is irradiated by mono-energetic photons of energy h which may be
absorbed by an electron of energy E1 (see Fig. 2.4): the electron is then emitted into the
vacuum with a kinetic energy Ekin = h - EB - (Evac - EFermi), where the difference between
brackets corresponds to the sample work-function eϕ. So, by analysing the kinetic energy of
the emitted electrons one can gain information on the energy distribution of electron states in
solid surface, i.e. on their binding energy EB; anyway, it is worthwhile to underline that the
assumption that this measured binding energy is equal to the orbital energy of the emitted
electron in the N electron initial state is just an approximation known as Koopman’s theorem
which does not take into account that the remaining N – 1 electrons experience an altered
situation in the presence of a hole and may relax to minimize their total energy. The formation
of the complete photoemission spectrum is illustrated on the right side of Fig. 2.4, where only
the primary photoelectrons are taken into account: a real measured spectrum also deals with
the secondary electrons resulting in relevant tails on the lower kinetic energy side of each
primary peak.
When photons in the ultraviolet spectral range are used the technique is called UPS (UV
Photoemission Spectroscopy) whereas with X-ray radiation it is called XPS. With synchrotron
radiation one can cover the whole spectral range from the near-UV to the far X-ray regime.
The typically used laboratory sources provide photons with fixed energy: these sources are
the X-ray tubes for the soft X-ray regime (Mg and Al targets provide respectively 1253.6 eV
and 1486.6 eV photons) and the noble gas discharge lamp for low energy (He resonance lamp
provide 21.2 eV, 40.8 and weaker satellite line photons).
Low energy electrons (UPS) are better suited to study the outermost less tightly bound
electrons of the valence band region, due to higher energy resolution of the photon: as a
consequence the detected kinetic energy is small and resolved and adding the information on
the direction of the emission by means of an electron energy analyser with small angular
aperture (these are the experimental ingredients of Low Energy branch of APE beamline as
discussed in the next chapter), it is possible to investigate the dispersion of the electronic
bands in k-space. High energy photons may interact also with higher binding energy innershell electrons which are associated with specific atoms, so performing a chemical analysis of
the surface and eventually detecting element specific core-level shifts depending on the
24
chemical state of the atom: that’s why XPS is historically known also with the acronym of
ESCA which stands for Electron Spectroscopy for Chemical Analysis.
Figure 2.4. On the left, a schematic view of the energy conservation in the photoemission
process. On the right, a more complete picture illustrating the formation of the kinetic
energy spectrum starting from the energetic states of a metal.
The intensity of a photoelectron peak is determined first of all by the transition probability
(photoelectric cross section) from the initial state to the final state under the influence of the
incident electromagnetic wave. The interaction of the Hamiltonian Hi which couples the
electron and photon fields is given, in the weak relativistic limit, by[35]
H i = e / (mc )
i
pi Ai
(2.2)
where pi is the momentum of the ith core electron in the system, Ai is the electromagnetic field
vector potential, and e, m, and c are, respectively, the electron charge, the electron rest mass,
and the speed of light; the vector potential can be decomposed in a superposition of transverse
plane waves A0eqeikr, where k is the photon wave-vector k=ω/c, and eq is the transverse
polarization vector. Quite generally, in the photo-absorption process, the photon wavelength
is large compared to the spatial extent of the initial state one-electron wave function, so the
25
exponential function of the vector potential can be expanded in (1 + ikr + …) and only the
first term can be considered as the condition kr << 1 is found to be fully satisfied at least in
the soft X-rays region. Thus in the expression of the Fermi’s Golden Rule only the
momentum operator p appears in the matrix element. Because the momentum operator
commutates with the position operator r, the transition probability can be finally written in
terms of the dipole matrix element resulting in the so-called dipole approximation:
W fi =
2π
f r i δ (E f − Ei − ω ) .
2
(2.3)
The number of electrons that can escape from solid without collision decreases with depth
d, so that an exponential attenuation of the peak intensity is expected when the concerned
atoms, from which the photoelectrons are emitted, are buried under increasing coverage of
another material: the attenuation factor is d/µ where µ is the mean free path depending upon
both the photoelectron energy and the composition of the crossed material.
In our studies we made use of the XPS technique with soft X-ray at the APE-HE beamline
in order to check the changes of the core-level photoemission intensity as a function of
thickness of Fe ultrathin overlayers.
By monitoring the
core-level energy shift of the
substrate, we were able to obtain information on the interface interdiffusion .
2.5 Magnetic characterization
An interface layer contains typically 1÷10 × 1014 atoms per cm2. This implies that one
needs to employ a magnetometry with adequate sensitivity for detecting a magnetic signal
from such small amount of matter. Furthermore if the magnetism is present in part of the
sample (the substrate or the overlayer or both) and one wants to address the very interface
layer then an atom specific probe is needed.
We have expoloited magneto-optic effects that are characterised by large enough matrix
elements to allow addressing the average magnetization of ultrathin films, down to
monolayers and submonmolayer quantities: the magneto-optic KERR effect (MOKE or
SMOKE in its UHV version) and the X-ray absorption magnetic circular dichroism.
2.5.1 MOKE
Michael Faraday discovered the first magneto-optic effect in 1845 by observing the
26
rotation of the polarization plane of the light transmitted through a flint glass under an applied
magnetic field. The corresponding effect in the reflection was discovered 32 years later by
John Kerr and since that it is known as the magneto-optic Kerr effect (MOKE). Though a
phenomenological description of these effects was quickly achieved within Maxwell’s
electromagnetic theory taking into account different indices of refraction for the left and right
circularly polarized light (circular birefringence) in which linearly polarized incident wave
can be decomposed,[36] a correct microscopic theory of magneto-optic effect in a quantum
mechanical framework was proposed only in 1955.[37]
In a standard MOKE experiment, the magnetic state of the sample is studied by
illuminating it with linearly polarized light and measuring the polarization or intensity change
of reflected light, this change being, in first approximation, proportional to the magnetization
of the sample. Unfortunately it is almost impossible to extract the absolute value of the
magnetization and the Kerr effect is used mainly to record its relative variations under the
application of an external magnetic field: from this ability to generate hysteresis loops also for
ultrathin magnetic films stems the broad acceptance of this technique in the field of surface
magnetism, with the acronym of SMOKE which stands for surface magneto-optic Kerr
effect.[38]
As a consequence of the light adsorption in the investigated medium, the probing depth of
the technique is finite. In the case of thin magnetic films with a thickness much smaller than
the penetration depth of the light (for example thinner than 200 Å for the visible light), the
intensity of the Kerr effect depends upon the total magnetic moment of the film: this means
that the Kerr intensity depends linearly on the thickness if the magnetization is thickness
independent and constant along the film profile.[39]
Depending on the relative orientation of the magnetization compared to the light incidence
plane and the surface plane, one distinguishes the polar, longitudinal and transverse (or
equatorial) Kerr effect.[36] These three possible geometries for MOKE are illustrated in Fig.
2.5.
In the polar effect the magnetization M is oriented perpendicular (out-of-plane) to the
surface plane [Fig. 2.5(a)]. The polar Kerr signal is proportional to the Kerr amplitude R ≈
cosΘ and shows its maximum at Θ = 0. Θ is the angle between the surface normal and the
direction of the incident light. In the longitudinal Kerr geometry the magnetization lies in the
intersection between the sample plane and the plane of incidence, which is created by the
incoming light and the normal to the sample plane [Fig. 2.5(b)]. In this case the Kerr
amplitude vanishes for Θ = 0 and is proportional to sinΘ. With the transverse Kerr effect the
magnetization lies in the film plane but perpendicular to the plane of incidence [Fig. 2.5(c)].
As no light component propagates in direction of the magnetization vector, the reflected light
27
does not change the rotation in the polarization direction. Only changes in the variation of the
amplitude, which is also proportional to sinΘ, are detected.
Figure 2.5. The three MOKE geometries: polar (a), longitudinal (b) and transverse (c)
magneto-optic Kerr effect. E denotes the incident polarization vector, N the regular
component of the reflected light and R denotes the perpendicular part of the Kerr amplitude
after reflection.
The MOKE setup (see Fig. 2.6) mainly consists of three components: a light source to
illuminate the sample, an electromagnet to apply a magnetic field to the sample and a
photodiode detector to measure the reflected intensity of light.
Figure 2.6. Scheme of MOKE apparatus.
28
2.5.2 Magnetic Circular Dichroism in X-ray absorption
The magneto-optic effects on core levels are much larger due to the 100-fold increase of
the spin-orbit interaction in the 2p core states with respect to the valence bands in 3d
transition metals. Magneto-optic effects in X-ray absorption spectroscopy (XAS) were
recognized to be directly proportional to the magnetic order of the sample. Furthermore, for
L2,3 edges in transition metals and M4,5 edges in rare earths it was proposed that a quantitative
analysis of the XAS dichroism, based on the optical theorem (sum rules) could translate the
XAS technique into a very powerful atom-specific magnetometry, within a relatively well
understood approximation on the electronic structure of the material.
Starting from the principles of XAS, I introduce the basic concepts of X-ray Magnetic
Circular Dichroism (XMCD) in absorption and finally end with the sum rules description.
•
XAS
In X-ray absorption (XAS) the x-ray energy is scanned and the absorbed x-ray intensity is
measured, which strictly requires the use of a broad band X-ray radiation source, i.e.
practically only synchrotron radiation. In XAS the photoionization cross section exhibits
sharp jumps, called edges, when the photon energy is equal to a core level binding energy: in
a simplified single-particle approach the Golden rule becomes equal to a matrix element
coupling the core wave function to the valence state, multiplied by the density of states above
Fermi energy which represent the first empty states of the system[40]
W fi (ω ) ~ φv (ω ) r φ c
2
⋅ ρ (ω ) .
(2.4)
It is clear that there is a close similarity between absorption spectroscopy and
photoelectron spectroscopy, as far as the primary physical process is concerned (see Fig. 2.7):
a photon is absorbed by the atom with the consequent excitation of a core electron into an
empty state above Fermi energy. However it must be kept in mind that in photoelectron
spectroscopy the electron is promoted in a continuum state with an energy well above the
Fermi energy and it behaves as a free electron, whereas the electron in the final state of a
near-edge x-ray absorption process is located in the empty states close to the Fermi energy,
which means that the electron is involved in the screening of the inner-shell vacancy.
29
Figure 2.7. The comparison between photoelectron and absorption processes.
In absorption the effect of this stronger interaction between the excited electron and the
solid, is the fine structure exhibited by the cross section near an absorption edge which is
related to the scattering of the photoelectron by the electron cloud of the neighbouring atoms:
these interference effects lead to wiggles in the energy dependence of the cross section. Near
Edge X-Ray Absorption Fine Structure, NEXAFS, and Extended X-Ray Absorption Fine
Structure, EXAFS, are techniques aimed to extract structural information from the analysis of
these modulations.
XAS spectra can be recorded in different ways: the most common methods are
transmission and electron yield measurements, as indicated in the Fig. 2.8(a). The
transmission technique requires very thin foils, down to below 100 nm in certain
conditions:[41] because of the problems associated with making samples of interest in the
form of free-standing films, the electron yield technique is generally used for conventional
samples.
In the electron yield technique the absorbed X-ray intensity is not measured directly, but
through the collection of the electrons emitted in the de-excitation process: in fact the core
holes created in the photoabsorption process may be filled by Auger decay which is dominant
over X-ray fluorescence in the soft X-ray region [see Fig. 2.8(b)]. One possibility is to
measure only the intensity of the emitted primary Auger electrons by means of an electron
spectrometer, the so-called Auger electron yield (AEY) measurement, which is highly surface
sensitive, similar to XPS. As they leave the sample, the primary Auger electrons create
scattered secondary electrons [see Fig. 2.8(c)] and collecting the intensity of all these exiting
electrons, where the secondary ones dominate, is called total electron yield technique (TEY),
and is usually performed measuring the small sample current as shown in the Fig. 2.8(a).
30
Another possibility for electron yield is the use of a channeltron with a polarized entrance
acting as a retarding field analyser, the so called partial electron yield.
Figure 2.8. (a) Two methods of recording X-ray absorption spectra: transmission and
electron yield. (b) Two possible decay processes as a consequence of the core hole refilling: photon emission (fluorescence) and Auger electron. (c) The second is dominant in
the soft X-rays region and induce a scattering cascade of secondary electrons: the ones
which gain the surface with energy higher than the work function form the total electron
yield intensity.
The TEY cascade involves several scattering events and originates from an average depth,
the electron sampling depth L which is typically a few nanometers, while it is often less than
1 nm for AEY measurements: due to the larger absorption depth of the incident soft X-rays,
the absorption coefficient µ is obtained as the direct ratio of the detected intensities Ie and
incident intensity Io in electron yield measurements, whereas the logarithm of the ratio is used
in transmission measurements, as indicated in Fig. 2.8(a).
Finally it is also possible the use of total Fluorescence Yield (TFY) to measure the
absorption coefficient: compared to TEY, the signal-to-noise ratio is much worse for soft Xrays region as Auger decay is dominant and the probing depth is much higher due to the much
lower interaction of exiting photons with matter compared to the strong Coulomb electronelectron interaction.
The dipole approximation, discussed in section 2.4, has the consequence that the transition
in X-ray absorption must obey the following selection rules[40, 42] concerning the angular
momentum quantum numbers JM of the initial and final states
∆J = 0,±1 ∆M = q
(2.5)
31
where q stands for the elicity of light in
units: q = ±1 corresponds to left (right) handed
circularly polarized light and q = 0 corresponds to linearly polarized light; in the singleparticle picture these selection rules should be read as l = ±1 and s = 0, where the spin is
conserved since it does not appear in the interaction Hamiltonian Hi (see eq. 2.2). As
discussed below, this state selection becomes particularly stringent when one can control the
photon polarization and can establish the direction (as in magnetically oriented atoms) or the
orientation (oriented anisotropic crystals or molecules) of the quantization axis in the system.
So by exciting a core of a given symmetry, one will select only excited states with symmetry
consistent with these selection rules and that have an appreciable overlap with the core-state
radial wave function, i.e., states localized around the photo-excited atom (see equation 2.4).
As mentioned before, XAS is element specific because the X-ray absorption edges of
different elements have different energies. As an illustrative example the graph of Fig. 2.9
reports the absorption spectra of a NiFe/Co/Cu multilayer,[43] showing the distinctive edges
for each 3d transition metal. In this case the excited core levels are the ones of the 2p shell,
i.e. the utilized dipole transitions are p
d and p
s ( l = ±1): the electrons are excited from
the spin-orbit split 2p3/2 and 2p1/2 levels to empty d and s valence states. The splitting arises
from the spin-orbit interaction H sp −or = λ p l ⋅ s which is particularly strong for the 2p shell and
results in two well-separated peaks which correspond to the L3 and L2 absorption edges (their
relative height ratio is about two and is due to the different degeneracy of the 2p3/2 and 2p1/2
split core levels): the only exception is Cu which actually has an electronic configuration d10
and therefore a filled d shell with the only remaining contributions in intensity coming from
p
s transitions. This illustrates the dominance of the p
d over the p s transition intensity:
because of the localized nature of the d valence states depicted in the right panel of Fig. 2.9,
such transitions are very intense and are often referred to as ‘white lines’ whereas the density
of states of the s band is smaller and is represented in the figure by a continuum above the
Fermi energy.[44]
The reason for choosing such an example comes from the magnetic information that can
be extracted by the polarization dependence of these white line intensities. In fact, the
magnetic properties of the 3d transition metals (Fe, Co and Ni) are mostly due to their d
electrons[45] since the interest in exciting p core electrons, exploiting p d dipole transitions
to explore their 3d unfilled valence-shell; similar considerations hold for the 3d
4f
transitions in magnetic rare earths. It must be underlined that for the 3d elements Fe, Co and
Ni it is advantageous to excite the 2p shell because L3,2 absorption edges exhibit much larger
edge jumps or signal-to-background ratios than the shallower 3p or M3,2 edges and, also, the
M3 and M2 edges overlap energetically, which is not favourable for the application of the sum
rules, whereas the larger splitting of the 2p shell ranges from 13 to 17 eV going from Fe to Ni.
In the following subsection the dependence of the absorption coefficient µ on the state
(handness) of circular polarization of the light is discussed.
32
Figure 2.9. Absorption spectra of a NiFe/Co/Cu multilayer[43] recorded for different
energy intervals to put in evidence the element-specific edges: the background before edge
is subtracted. Fe, Co, Ni and Cu are 3d transition metals consecutive in the periodic table,
as can be seen by the higher binding energy of the 2p core levels. Fe, Co and Ni are the
well-known magnetic transition metals. On the right side, the schematic representation of
the 3d valence shell empty states, strongly localized above the Fermi energy: their
occupation in absorption process generates the two white lines L3 and L2 depending on the
initial core state (2p3/2 and 2p1/2). The p s transition intensity is usually represented by a
double step function as the s band can be approximated by a flat continuum above Fermi.
•
XMCD
In optics, the term "dichroism" refers to changes in the absorption of polarized light on
passing through a material in two different directions: the material appears with two different
colors for the two light directions, that is it is di(two)-chroic(coloured). In spectroscopy the
term is used more generally to indicate the dependence of the photon absorption of a material
on the light polarization. The origin of the dichroism effect can be anisotropies in the charge
or in the spin of the material and in the latter case we speak of magnetic dichroism. Magnetic
dichroism techniques in X-ray region are X-ray Magnetic Circular Dichroism (XMCD) and
X-ray Magnetic Linear Dicrhoism (XMLD) depending whether the effect rises from the use
of circular polarization of opposite handness or from linear polarization of perpendicular
orientation. Circularly polarized light can be very useful for studying systems that do not have
inversion symmetry on a specified quantization axis as ferromagnetically aligned systems,
whereas linear polarization is more suitable when an orientation is privileged with no
preferential direction as antiferromagnetically ordered systems: this is well illustrated in Fig.
2.10[46] where in a XMCD experiment the photoabsorption is measured with the photon spin
vector parallel and antiparallel to the magnetic moments of the sample, i.e. flipping the elicity
33
of the photon spin or the versus of the magnetization leads to the same dichroic effect.
A complete and step-by-step description of the basic concepts of XMCD for 3d transition
metals is found in Reference [43] and we would rather try to underline the main issues and the
conclusions. The more intuitive idea of the origin of XMCD can be obtained by looking
separately at the spin up and spin down parts of the wave functions, using the so called two
step model as shown in Fig. 2.11(a), which only considers the spin-orbit coupling of the p
core levels and the d band splitting into unequally populated spin-up and spin-down states due
to the exchange interaction (the so called Stoner model).
Figure 2.10. Illustration of the geometry of, respectively, XMCD and XMLD experiments
with the recordable dichroic intensities.
Figure 2.11. Schematic energy bands and electronic transitions involved in (a) x-ray
magnetic circular dichroism and (b) in the magneto-optic Kerr and Faraday effects. In (a)
transitions occur from a core shell (here L shell) to empty conduction-band states above
Fermi level and the light is circularly polarized: for magnetic materials, spin-up and spindown bands are unequally populated. In (b) transitions occur between filled and unfilled
electronic band states through linearly polarized light: the right and left circularly polarized
components may be absorbed differently and the emitted (reflected or transmitted) radiation
will then reflect this imbalance.
In the first step, the interaction of the circularly polarized X-rays with the p shell leads to
34
the excitation of spin-polarized electrons. This can be calculated[47] by using the spherical
harmonics Yl,ml representation for the |j,mj> core state and treating the final state as an
incoherent sum of the different Yl,ml (l = 2) states: applying the dipole selection rule ml =
−1(+1) for right(left) circularly polarized (RCP and LCP) light and s = 0 (constant spin) and
making use of the relevant expressions for the dipole matrix elements for transitions from a
state characterized by angular momentum l to the state l + 1 (i.e. l = +1 as is the case for
p
d), the result is that at the L2 edge, LCP (RCP) excites 25% (75%) spin up and 75% (25%)
spin down electrons and at the L3 edge LCP (RCP) excites 62.5% (37.5%) spin up and 37.5%
(62.5%) spin down electrons. In a non-magnetic material, the absorption of LCP and RCP
light is the same, but as soon as there is an unbalance in the number of available empty spin
up and spin down states, the absorption of the two polarization will be different, with a
difference which is opposite at the L2 and L3 edge (see Fig. 2.10): so we can visualize the
second step, in which the spin-polarized electrons originating from the p shell are analysed by
a “spin-resolving detector” consisting of the exchange-split d final states and the relative size
of the observed dichroism effect is simply proportional to the difference in spin-down and
spin-up holes, i.e. to the magnetic spin moment.
An interesting comment on this calculation carried out within a simple one-electron
atomic model[43] is that a detailed comparison reveals that the sum of the L2 and L3
dichroism effect is directly proportional to the corresponding orbital momentum ml of the
specific considered d subshell Y2,ml and also the total dichroic effects cancel as the average
over the five d states yelds <lz> = 0. This relationship, the proportionality between the orbital
momentum of the d shell and the total dichroic effect at L2 and L3 edge, is a special case of a
more general sum rule. In fact in Ref. [43] it is shown to hold even when the one electron
model is made more realistic by including the spin-orbit coupling also in the d band, which
results in a splitting in d5/2 and d3/2 energy levels: as the latter has the lowest energy, a partly
filled band will therefore contain more empty d5/2 states, which will favour L3 edge absorption
with respect to the L2 edge (p1/2
d5/2 are dipole forbidden as j = ±1,0). To conclude, it has
been shown by Thole at al. [48] that the proportionality between the orbital momentum <Lz>
and the total dichroism integrated on both edges is general and not just a property of the
model mentioned here. This is in fact one of the two powerful sum rules, derived in the
beginning of the 1990’s, which directly relate the experimental dichroic intensities to the
ground state expectation of the orbital, <Lz>, and spin, 2<Sz>,[49] magnetic moments, where
the z subscript means that the components of the total moments projected on the propagation
direction of the X-rays are considered.
Before giving the exact formula of the sum rules and some comments in the following
subsection we want to stress once more the importance of using tunable X-rays to get a piece
35
of information which is element and symmetry specific. Whereas most conventional
techniques used for the study of magnetic materials measure the total magnetic response
which for complex materials contain the contributions from the various magnetic elements –
and the conventional Faraday and Kerr techniques are no exception since the band structure of
the material is a complicated function of the elemental composition [see Fig. 16(b)] – the
magnetic properties of a complex material can be studied by XMCD element by element,
better yet, different edges of the same element provide information on the magnetic
contributions of different kinds of valence electrons through the dipole selection rules.
•
Sum rules
The capability of XMCD to probe the magnetic properties of composite materials goes
beyond the chemically sensitive magnetometry: making use of the magneto-optic sum
rules,[48, 49] it is possible to measure separately the orbital and spin momenta expectation
values on a per-atom base in
units. Here we skip the general form[47] of the orbital and spin
sum rule and give directly the formula for the L3,2 edges:
(10 − n3d )
< Lz >= 2(∆L3 + ∆L2 ) ×
(µ + + µ − + µ 0 )
,
L3 + L2
(2.6)
< S z >=
(10 − n3d )
3
(∆L3 − 2∆L2 ) ×
2
(µ + µ + µ )
+
−
0
−
7
< Tz > ,
2
L3 + L2
(2.7)
where ∆L3 and ∆L2 are the dichroic intensities at the L3 and L2 edges, n3d is the number of 3d
electrons in the valence shell, and µ+, µ− and µ0 are the absorption coefficients for LCP light,
RCP light and light which is linearly polarized with the polarization vector parallel to the
quantization axis. In the absence of linear dichroism (which is usually very small in metallic
transition metals) µ0 will be the average of µ+ and µ− and
( µ + + µ − + µ 0 ) can be obtained
L3 + L2
from the sum of the experimental dichroic spectra subtracting a proper background
accounting for transitions other than 2p
3d, as discussed in Fig. 2.9 for p
s transitions. For
n3d usually a value obtained from band-structure calculations is used. <Tz> is the expectation
value of the magnetic dipole operator, due to the anisotropy in the spin moment: with respect
36
of the spin moment, this term has usually a minor influence mostly in bulk systems with a
cubic symmetry,[44] and we will not take it into account for our estimations. It must be
pointed out that, by neglecting the <Tz> term, the orbital to spin relative sum rule, i.e., Eq.
(2.6) divided by Eq. (2.7), does not require some sensible pieces of information as the
electron population number and the background subtraction simulating the p
s transitions.
This is true also for the experimental corrections on the dichroic signal µ+(ω) − µ−(ω), which
take into account the angle θ between photon incidence and magnetization direction
(geometrical correction) and the circular polarization degree ε of the light (polarization
correction): in fact, the dichroic signal must be multiplied by [1/cos(θ)]/ε while keeping the
isotropic intensity µ+(ω) + µ−(ω) the same.
In order to finally get the relative magnetic moments in µB (Bohr’s magneton) units, one
should use the following relationship for the spin, orbital and total magnetic moments:
M S = −2S ,
M L = −L ,
M tot = −(2S + L) .
(2.8)
In practice, the orbital moment is typically reduced in transition metals by crystal field
effects such that the spin contribution to the total moment dominates. Nevertheless, the orbital
moment is of considerable importance because its direction is “locked in” by anisotropies in
the lattice, which through the spin-orbit interaction leads to the anisotropy of the total
moment. Hence, even though the orbital moment is small in transition metals, its quantitative
determination is of fundamental importance for the understanding of magnetocrystalline
anisotropy.
The sum rules have been definitely confirmed for Co and Fe in transmission experiments
by Chen et al.[44] and in this paper one can find also a detailed explanation of experimental
procedures.
[1] J.J. Krebs, B.T. Jonker and G.A. Prinz, J. Appl. Phys 71, 2596 (1987).
[2] M. Dumm, B. Uhl, M. Zölfl, W. Kipferl, and G. Bayreuther, Journ. Appl. Phys. 91, 8763
(2002).
[3] Ultrathin Magnetic Structures, edited by B. Heinrich and J. A. C. Bland (Springer-Verlag
Berlin, Heidelberg, 1994), Vol. II.
[4] R. Nakajima, J. Stohr and Y. U. Idzerda, Phys. Rev. B 59, 6421 (1999).
[5] M. Liberati, G. Panaccione, F. Sirotti, P. Prieto, and G. Rossi, Phys. Rev. B 59, 4201
(1999).
[6] T. Yang, A. Krishnan, N. Benczer-Zoller and G. Bayreuther, Phys. Rev. Lett. 48, 1292
(1982).
[7] J. Korecki and U. Gradmann, Phys. Rev. Lett. 55, 2491 (1985).
37
[8] F. Gustavsson, E. Nordström, V. H. Etgens, M. Eddrief, E. Sjöstedt, R. Wäppling, and J.M. George, Phys. Rev. B 66, 24405 (2002).
[9] J. R. Waldrop and R. W. Grant, Appl. Phys. Lett. 34, 630 (1979).
[10] S. Mirbt, S. Sanyal, C. Isheden, and B. Johansson, Phys. Rev. B 67, 155421 (2003).
[11] D. P. Pappas, G. A. Prinz, and M. B. Ketchen, Appl. Phys. Lett. 65, 3401 (1994).
[12] A. Filipe, A. Schuhl, and P. Galtier, Appl. Phys Lett. 70, 129 (1997).
[13] M. Gester, C. Daboo, R. J. Hicken, S. J. Gray, A. Ercole, and J. A. C Bland, J. Appl.
Phys. 80, 347 (1996).
[14] S. Park, M. R. Fitzsimmons, X. Y. Dong, B. D. Schultz, and C. J. Palmstrøm, Phys. Rev.
B 70, 104406 (2004).
[15] B.T. Jonker, G.A. Prinz, and Y. U. Idzerda, J. Vac. Sci. Technol. B 9, 2437 (1991).
[16] E. M. Kneedler and B.T. Jonker, J. Appl. Phys. 81 (8), 4463 (1997).
[17] M. Zölfl, M. Brockmann, M. Köhler, S. Kreuzer, T. Schweinböck, S. Miethaner, F.
Bensch and G. Bayreuther, J. Magn. Magn. Mat. 175, 16 (1997).
[18] A. Filipe, and A. Schuhl, J. Appl. Phys 81, 4359 (1997).
[19] Lépine, S. Ababou, A. Guivarc’h, G. Jévéquel, S. Députier, R. Guérin, A. Filipe, A.
Schuhl, F. Abel, C. Cohen, A. Rocher, and J. Crestou, J. Appl. Phys. 83, 3077 (1998).
[20] C. Lallaizon, B. Lépine, S. Ababou, A. Schussler, A. Que´merais, A. Guivarc’h, G.
Jézéquel, S. Députier, and R. Guérin, Appl. Surf. Sci. 123/124, 319 (1998).
[21] C. Lallaizon, B. Lépine, S. Ababou, A. Guivarc’h, S. Députier, F. Abel, and C. Cohen, J.
Appl. Phys. 86, 5515 (1999).
[22] B. D. Schultz, H. H. Farrell, M. M. R. Evans, K. Lüdge and C. J. Palmstrøm, J. Vac. Sci.
Technol. B 20(4), 1600 (2002).
[23] A. Prinz and J. J. Krebs, Appl. Phys. Lett. 39, 397 (1981).
[24] E. M. Kneedler, B. T. Jonker, P. M. Thibado, R. J. Wagner, B. V. Shanabrook, and L. J.
Whitman, Phys. Rev. B 56, 8163 (1997).
[25] F. Bensch, G. Garreau, R. Moosbühler, G. Bayerheuther and E. Beaurepaire, J. Appl.
Phys. 89 (2001) 7133.
[26] R. Moosbülher, F. Bemsch, M. Dumm, and G. Bayreuther, J. Appl. Phys. 91, 8757
(2002).
[27] S. C. Erwin, S.-H. Lee, and M. Scheffler, Phys. Rev. B 65, 205422 (2002).
[28] P. M. Thibado, E. Kneedler, B. T. Jonker, B. R. Bennett, B. V. Shanabrook, and L. J.
Whitman, Phys. Rev. B 53, R10481 (1996).
[29] Y. B. Xu, E. T. M. Kernohan, D. J. Freeland, A. Ercole, M. Tselepi, and J. A. C. Bland,
Phys. Rev. B 58, 890 (1998).
[30] Y. B. Xu, M. Tselepi, C. M. Guertler, C. A. F. Vaz, G. Wastlbauer, J. A. C. Bland, E.
Dudzik and G. van der Laan, J. Appl. Phys. 89, 7156 (2001).
[31] M. Madami, S. Tacchi, G. Parlotti, G. Gabbiotti, and R. L. Stamps, Phys. Rev. B 69,
144408 (2004).
[32] J.S. Claydon, Y. B. Xu, M. Tselepi, J.A.C. Bland, G. van der Laan, Phys. Rev. Lett. 93,
037206 (2004).
[33] M. Brockmann, M. Zölfl, S. Miethaner, G. Bayreuther, J. Magn.Magn. Mat. 198-199,
384 (1999).
[34] The description of the following techniques can be found in several books; here we quote
two of them which have been particularly useful mainly for the introduction to LEED and
XPS: H. Lüth, Surface and Interfaces of Solid Materials (Sprinter-Verlag, Berlin, 1995) - G.
Ertl and J. Kuppers, Low Energy Electrons and Surface Chemistry (Verlagsgesellschaft,
Weinheim, 1985).
[35] F. Sette, New Directions in Research with Third-Generation Soft X-Ray Synchrotron
Radiation Sources, NATO ASI Series, Series E: Applied Science, Vol. 254, 251-257 (Eds. A.
S. Schlachter and F. J. Wuilleumier, 1994).
[36] M. J. Freiser, IEEE Transactions on Magnetism 4, 152 (1968).
[37] P. N. Argyres, Phys. Rev. 97, 334 (1955).
[38] S. D. Bader, J. Magn. Magn. Mater. 200, 664 (1999).
38
[39] S. D. Bader, J. Magn. Magn. Mater. 100, 440 (1991).
[40] F. de Groot, X-ray and inner-shell process, AIP Conference Proceedings 389, 497-519
(Eds. R. L. Johnson, H. Schmidt-Böcking and B. F. Sonntag, 1996).
[41] E. Goering, J. Will, J. Geissler, M. Justen, F. Weigand, G. Schuetz, J. Alloys Comp. 328,
14 (2001).
[42] J.-M. Mariot and C. Brouder, Magnetism and Sinchrotron Radiation, Springer, Lecture
Notes in Physics, Vol. 565 24-59 (Eds. E. Beaurepaire, F. Scheurer, G. Krill and J.-P.
Kappler, 2001).
[43] J. Stöhr and Y. Wu, New Directions in Research with Third-Generation Soft X-Ray
Synchrotron Radiation Sources, NATO ASI Series, Series E: Applied Science, Vol. 254, 221250 (Eds. A. S. Schlachter and F. J. Wuilleumier, 1994).
[44] C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E.
Pellegrin, and F. Sette, Phys. Rev. Lett. 75, 152 (1995).
[45] A. Aharoni, Introduction to the Theory of Ferromagnetism, The International Series of
Monographs on Physics, Vol.93, Oxford Science Pubblications (Eds. J. Birman, S. F.
Edwards, R. H. Friend, C. H. Llewellyn Smith, M. Rees, D. Sherrington, G. Veneziano,
1996).
[46] http://www-ssrl.slac.stanford.edu/stohr/
[47] M. Sacchi and J. Vogel, Magnetism and Sinchrotron Radiation, Springer, Lecture Notes
in Physics, Vol. 565 24-59 (Eds. E. Beaurepaire, F. Scheurer, G. Krill and J.-P. Kappler,
2001).
[48] B. T. Thole et al., Phys. Rev. Lett. 68, 1943 (1992).
[49] P. Carra et al., Phys. Rev. Lett. 70, 694 (1993).
39
40
Chapter 3
Synchrotron light and the APE beamline
In the chapter 2 we considered all the surface science experimental techniques used in the
preparation and characterization of the Fe/GaAs(001) interface. These capabilities are all
available, at the UHV APE beamline laboratory of synchrotron light facility of ELETTRA,
where the study of the system has been carried out. So we decide to introduce in this chapter
some technical details on the instrumentations available at the beamline, spending few initial
words on the use of synchrotron radiation sources.
3.1 Third generation synchrotron radiation
The light generated by bending the path of relativistic electrons by means of a magnetic
field is called synchrotron radiation. It was an undesired energy-loss mechanism in early
accelerators used primarily for particle physics studies in the 50’s and 60’s, and its fully
dedicated exploitation started only with second generation synchrotrons since late 70’s, due to
the novel and interesting possibility to achieve radiation with high intensity and collimation
over a wide range of frequency, from visible light to hard X-rays region: relativistic electrons
confined in a UHV-pumped storage ring and repeatedly accelerated by means of bending
magnets (see Fig. 3.1) produce radiation with continuous spectrum whose brightness is
several orders of magnitude bigger than in conventional laboratory sources. As shown in Fig.
3.1, the bending magnets are separated by straight sections where the electrons run
unperturbed.
The undulators and the wigglers are insertion devices widely used in third-generation
synchrotrons and hosted along straight sections of the storage ring. They consist of a linear
array of north-south magnetic dipoles of alternating polarity as sketched in Fig. 3.1(a). The
normal vertical orientation of the dipoles forces relativistic electrons into a local zig-zag path
41
in the horizontal plane, so that a beamline located at the end of such path can collect light
which is emitted several times by the same electrons and not only once as it is the case for the
bending magnet radiation, with a consistent increase of the emitted brightness as illustrated in
Fig. 3.1(b). In the undulator regime an important effect comes into play, generating
synchrotron radiation with enhanced characteristics: because of the rather gentle perturbation
of the electron trajectory around the straight path, the radiation emitted from successive
undulator periods adds coherently and this interference behaviour gives rise to a sharply
peaked radiation spectrum consisting of a fundamental and several harmonics.
a)
b)
Figure 3.1. Layout of a storage ring. The inner booster ring provides accelerated electrons.
In the left-bottom panel a zoom of a period of the storage ring indicating the position of the
main constituent devices, between which the bending magnets. (a) Scheme of an undulator
device which forces the electron to wiggle and to emit synchrotron light. (b) Spectral
brightness for several synchrotron radiation sources and conventional x-ray sources. The
data for conventional x-ray tubes (two-order-of-magnitude ranges) should be taken as rough
estimates only, since brightness depends strongly on such parameters as operating voltage,
take-off angle and anode tubes configuration (stationary, rotating, microfocusing).
42
The photon energy corresponding to the maximum intensity of the undulator harmonic
can be tuned from high to low values simply by decreasing the undulator gap between the
faced magnetic poles, thereby increasing the magnetic field inside them.
Another valuable feature available in synchrotron radiation facilities is the light
polarization control. The planar insertion devices just described produce radiation which is
linearly polarized in the horizontal plane of the electron orbit, which can be a very useful
additional feature for some experiments. What’s more the polarization can also be tuned:
concerning the undulators, by properly shifting, parallely to the light propagation direction,
the position of one set of the undulator permanent magnets respect to the other set (crossedfield undulators), it is also possible to generate vertical polarized beams and elliptically
polarized beams, in particular, circularly polarized beams. The idea is to dephase the facing
opposite dipoles by a fraction of the undulator period, so inducing a longitudinal component
in the magnetic field which causes the electrons wiggling also out of plane.
3.2 The APE beamline
3.2.1 General layout
All the measurements on Fe/GaAs(001) interface have been performed on the APE
(Advanced Photoemission Experiment) beamline[1] of TASC-INFM on the ELETTRA
storage ring operating routinely at 2.0 GeV and 2.4 GeV.
The light sources of APE are two variable-polarisation undulators installed in a zig-zag
configuration on the section number 9 of the storage ring, generating two independent photon
beams aimed at a 2 mrad angle one with respect to the other in the horizontal plane. The first
insertion device is a quasi-periodic undulator emitting a fundamental line in the far-VUV
energy range (<8-100 eV) while the second insertion is a periodic undulator emitting in the
soft X-ray range where, by using up to the third harmonic of the fundamental line one can
cover the 100-2000 eV range. The two beams are partly overlapped at the sources and are
completely separated at 24 m from the undulators (48 mm horizontal distance between the
axes of the two beams). At this distance each one of the two photon beams reaches a first
silicon spherical mirror that deviates it into a dedicated branch, the so-called Low Energy-LE
and High Energy-HE lines as it is shown in Fig. 3.2. Both these mirrors are hosted in the
same chamber (Fig. 3.2, A), the so-called crossing beams mirror chamber, and are maintained
43
free from thermal load slope errors by cryogenic cooling by means of circulating pressurised
and refrigerated He gas (10 atm, 50K). With such a design APE is able to perform
independent experiments simultaneously on the LE and HE end stations, i.e. the two
undulator sources can independently be optimized for energy and polarization and deliver
radiation to the correspondent beamline simultaneously.
Each Plane Grating Monochromator (Fig. 3.2, B and C) is equipped with 3 water-cooled
variable line spacing/variable groove depth (VLS/VGD) holographic gratings that cover the
respective energy range. The conjugated spherical mirrors for each grating are housed in a
downstream chamber. Each spherical mirror focuses the monochromatic light on the
respective exit slit (Fig. 3.2, D and E).
Figure 3.2. Layout of APE beamlines.
HE and LE sagittal toroidal mirrors (Fig. 3.2, F and G) refocus the respective beams onto
a 20-150 micrometer spot on the sample surface in the HE and LE end stations respectively
(Fig. 3.2, J and K). The fully independent end stations are part of a unique system of
interconnected UHV chambers, which includes shared preparation and characterization
modules and load-locks. The possibility to transfer the samples between these experimental
chambers provides the accessibility to their different facilities without breaking the vacuum,
which is a crucial requirement for studies of surface science.
Our experiments mainly involved the use of HE beamline and the preparation chamber
(Fig. 3.2, M), so we will skip a detailed description of the LE branch which is more suited for
high-resolution angular-dependant valence band photoemission, being equipped with a
Scienta SES-2002 analyzer and with an automated two rotational degree manipulator for
complete Fermi surface mapping.
Finally, a small chamber (Fig. 3.2 L) is directly coupled with the preparation chamber and
is equipped with a room temperature scanning tunnelling microscope (STM) stage and with a
fast load-lock chamber for the sample insertion and removal.
44
3.2.2 High-Energy beamline
This beamline is designed to operate in the 140-1500 eV energy range by means of three
different variable spacing grating of 900, 1400 and 1800 lines/mm, each dedicated at a
different energy range. The power resolution of the photon after the exit slit using the 900
lines/mm grating was determined to be 7000 at 400 eV and poorer than 4000 at 800 eV: this is
the grating we used for our measurements. The photon flux is 1011 photons/s at 400 eV.
The grating can be tilted with high angular resolution (energetically corresponding to
about 10 meV) and via software, so to easily perform dense and precise energy scans for
absorption experiments. The monochromator position corresponding to the zero of energy can
be periodically calibrated by performing a so-called zero-order scan, which is an angular scan
of the momochromator around the position of specular reflection to check and reset the
occasional off-set: at specular reflection all the energies are let through the grating modulated
only by its transmission function. A photodiode detector or in alternative a semi-transparent
molybdenum mesh is used to measure the intensity of the beam entering the HE end station
which is an important parameter to carefully normalise the recorded spectra.
In Fig. 3.3 we show the calculated intensities for several harmonics at a given
configuration of the HE undulator corresponding to circular light polarization: the black curve
represents the corresponding degree of circular polarization which oscillates and decreases as
the harmonics do at increasing order; it must be reminded that the real degree of polarization
at the end station can result further degraded because of the effect of the optical elements
encountered by the light along the path. In XMCD measurements the dichroic effect can be
measured by using circular polarization of opposite handness along energy intervals of 30-40
eV. The idea is to set the gap of the undulator in order to have the desired energy range on the
top of some harmonic and the phase of the magnetic field acting on the stored electrons:
inside this energy range, a smooth change in flux intensity and in polarization is desirable due
to problems in data normalization and analysis if the contrary is true. A compromise between
this issue, a good intensity and a good polarization degree, suggests the use of second or third
harmonic (see Fig. 3.3), the first having a too strict shape for both intensity and polarization.
45
5
4
st
1 harmonic
3
0.9
nd
2
2
harmonic
0.8
rd
3 harmonic
10
0.7
14
0.6
6
5
4
0.5
3
Degree of circular polarization
Photons/sec
2
400
800
1200
Photon energy (eV)
0.4
1600
0.3
Figure 3.3. An undulator spectrum at HE APE beamline calculated for circularly polarized
X-rays and the corresponding degree of circular polarization. On the peak of the most used
second and third harmonics the degree of circular polarization is 85 and 75 % respectively.
The sample holder can be transferred inside the end station of HE branch and mounted
onto a horizontal manipulator which can be moved by stepper motors with X, Y and Z
scanning capability and a linear resolution of 0.5 µm. The spot size on the sample, after the
refocusing of the toroidal mirror, was about 100 µm (vertical) × 200 µm (horizontal) in our
experiments and can be optimised up to 25 µm × 150 µm.
The end-station chamber (basic pressure 3×10-10 mbar) is equipped with an hemispherical
electron energy analyzer (Omicron EA 125) with 125 mm of mean radius and a detector
consisting of an array of 7 channeltron electron multipliers, aimed to core-levels
photoelectron emission spectroscopy. The best achievable instrumental resolution is about 10
meV. In our measurements we searched for a time-statistics-resolution compromise, setting
the overall energy resolution (photons + analyzer) to
200 meV, adequate for core level
studies where the intrinsic lifetime width of the lines is comparable or larger than this value.
For absorption experiments we can measure in total electron yield mode by monitoring the
sample current extracted from the chamber and read by a Kethley picoamperometer, or in
partial electron yield mode by means of an in situ channel electron multiplier operated
alternatively in current or pulse counting mode.
The system also features a vectorial Mott detector system for the measure of the spin46
polarization of the electron yield.
This apparatus was under commissioning during the
present work. Future developments concern the installation of a scanning Fresnel zone plate
to perform photoelectron and magnetic microscopy (spot size
100 nm), also with time
resolved capability (see the time structure of synchrotron radiation, related to the aggregation
of accelerated electrons in periodical bunches).
3.2.3 Kerr/preparation chamber
The samples have been prepared and characterized under UHV conditions in the so-called
preparation chamber (Fig. 3.2 M). The base pressure of the chamber is about 5×10-11 mbar.
The sample holder is mounted at the end of a vertical manipulator (which can be cooled with
liquid N2, letting the sample reach temperature as low as about 100 °K) allowing the
movement in all three directions (z vertical range is about 250 mm, x and y horizontal range
about 35mm), as well as a complete polar rotation around the vertical axis of manipulator. In
this way the sample can properly reach all the different experimental facilities inside the
chamber:
a) 100-1000 eV argon-ion sputtering gun, to remove the topmost layers of the sample
surface by means of accelerated ions;
b) high temperature heating stages (up to 2000 °C);
c) water-cooled electron beam evaporators[2] for molecular beam epitaxial (MBE)
growth of metal thin films;
d) water-cooled quartz micro-balance to calibrate[3] the growth rate of the
evaporators before depositing on the sample;
e) LEED-Auger instrumentations, for both structural and chemical characterization of
the sample surfaces: LEED apparatus is a rear-view 4-grid SPECTALEED optics
by Omicron, with a EG&G lock-in amplifier for Auger spectroscopy; the size of
the electron beam on the sample is less than 300 µm;
f) set of Helmholz-like coils to perform magneto-optical Kerr effect measurements
with the field applied along different directions (transverse, longitudinal and polar
MOKE geometries).
In our experiments we only performed transverse MOKE measurements by positioning
the sample in the middle of two Helmholz-like coils, with the resulting applied magnetic field
lying vertically in the plane of the sample and reaching a maximum field of about 600 Oe: the
light source and the detector are mounted externally (i.e. out of UHV) on two properly
47
designed view-port flanges, forming with the sample an horizontal plane which coincides
with both the incident and specular reflection plane of the light, the photodiode detector is
positioned to receive the reflected beam.
A laser diode serves as a light source (ILEE LDA-2000 model: λ = 675 nm, P < 40 mW)
and a system of focussing lenses (a scheme of a typical MOKE apparatus is illustrated in Fig.
2.6) provides a light spot on the sample with a size less than 300 µm in both directions and
with very low astigmatism. Because of the high stability of the laser diode a lock-in technique
was not strictly necessary. Two Glan-Thompson prism polarizers are used to linearly polarize
the incoming and the reflected light with the desired direction. Incoming p polarization is
used for transverse geometry as in this case the only magnetization-dependent quantity is the
reflection coefficient connecting the incident and reflected p polarized light.[4]
A photodiode provides a photocurrent proportional to the intensity of the reflected light:
the current is amplified and converted into a voltage. Computer controlled hysteresis loops are
taken by setting the coil current and reading the MOKE signal via an ADC converter. To
improve the signal to noise ratio, several hysteresis curves are taken and averaged.
[1] http://www.elettra.trieste.it/experiments/beamlines/ape/
[2] EV40-FC water-cooled evaporation sources of Ferrovac gmbh - http://www.ferrovac.ch
[3] Chih-shun Lu, J. Vac. Sci. Technol. 12, 578 (1975).
[4] J. M. Florczak and E. Dan Dahlberg, Phys. Rev. B 44, 9338 (1991).
48
Chapter 4
The Fe/GaAs(100)-(4 × 6) interface system
In this chapter we present the experimental results on the interface Fe/GaAs(100)-(4 × 6),
from the early steps concerning the surface preparation and controlled deposition of iron, to
the final profiling magnetometry by means of XMCD. The results are discussed also in
comparison with recent experimental and theoretical data present in literature and with
preliminary calculations on an ideal system simulating our samples.
4.1 Fe/GaAs(001): sample preparation and structural analysis
4.1.1 GaAs surface
Si-rich n doped GaAs(001) commercial wafers were cut to obtain small area (∼4×9 mm2)
samples to be fixed on the molybdenum transferable sample holders used at APE. The
substrates were cleaned by cycles of sputtering and annealing in the UHV conditions of the
preparation chamber. As a first step after the insertion in vacuum, the samples were heated at
about 850 K in order to degas most of the surface impurities coming from the air-exposed
sample and sample holder, so to avoid the presence of contaminants during the subsequent
final annealing step: this procedure was carried on until the pressure firmly stabilized to an
adequate value of 2×10-9 mbar. At such temperatures the native surface oxide desorbs but
other contaminants, like C, remain on the surface.[1, 2]
The sputtering is made by bombarding the sample with 0.8 KeV Ar+ ions in an Ar
atmosphere of 1×10-6 mbar - the current measured on the grounded sample is less than 10 µA
- and half an hour was found to be enough to clean the surface to the level of undetectable
impurities. Because of the selective action of the ion-sputtering, the resulting surface was As49
depleted and in order to reconstruct it the sample needed to be annealed at about 850 K for 20
minutes. The annealing was performed by facing the back of the sample holder, positively
biased at 200 V through the isolated manipulator, to a resistively heated W filament in order
to accelerate the thermo-emitted electrons against the sample holder: by varying the current
supplied to the filament one can finely tune the electron current hitting the sample holder (ebombardment) therefore controlling the transmitted power and finally the temperature. This
was checked by means of a pyrometer pointing at the sample surface through a view-in port
flange. Also the value of a tungsten-rhenium thermocouple, sitting on the manipulator at a
certain distance from the heated sample holder, was used as a relative reference during the
repeated cycles. In fact it is often necessary to repeat the preparation procedure slightly
varying the annealing temperature from one cycle to the other in order to have the desired
well-defined Ga-rich (4 × 6) reconstruction. The variation of few tens of degrees in the final
annealing temperature may favour the reconstruction of the (4 × 2) or the (2 × 6) phases.[3]
In Fig. 4.1(a) it is shown the obtained LEED pattern of the (4 × 6) reconstruction: it
unambiguously confirms the [110] and [110] crystallographic axes, corresponding to the ‘× 6’
and ‘× 4’ directions, which are respectively the easy and hard magnetic axes for Fe films of
ultrathin thickness showing a relevant UMA (Uniaxial Magnetic Anisotropy).[4, 5]
4.1.2 Film deposition
As stressed out before, our aim is to extract the magnetization profile along a Fe epitaxial
film to check the magnetization behaviour mainly at the interface where it could be reduced or
suppressed. The central idea is to exploit the element selectivity feature of XMCD technique:
so we bury half a ML of Co inside a 6 ML film of Fe at different distances from the
underlying substrate in order to introduce a non-invasive magnetic marker that allows the
careful monitoring of the magnetic properties of the Fe film as a function of the distance from
the FM/SC interface.
This is realised by depositing a Fe wedge, the Co impurities and a Fe counter-wedge as
shown in Fig. 4.2.
Deposition of Fe and Co atoms on the clean (4 × 6) reconstructed GaAs(001) substrates is
performed at room temperature inside the preparation chamber by means of two water-cooled
electron bombardment evaporators: each evaporator contains inside its heated crucible a target
of highly pure material (> 99.99%), Fe and Co respectively. The deposition rate of each
50
source and its stability in time are monitored by the removable quartz balance at the same
position where the substrate is moved for the deposition: a stable rate of 0.2 ML/min is used.
A rotating shutter on the top of the evaporating source may obstruct the flux of the evaporated
material so determining the deposition interval and finally the deposited equivalent thickness.
Another shutter could be placed in front of the sample to deposit film with variable thickness:
in fact the manipulator can be moved by a PC-controlled stepper motor, so a wedge can be
obtained by progressively and uniformly hiding the sample surface behind this shutter. During
the deposition the vacuum conditions slightly deteriorated up to 5×10-10 mbar, due to the high
thermal load on the evaporators. We define 1 ML of Fe as 1.21×1015 atoms/cm2,
corresponding to the density of the bcc Fe(001) surface, which would produce a film 1.4 Å
thick if deposited uniformly on Fe(001).
Figure 4.1. LEED patterns for different Fe coverage as indicated in the corner of each
picture: a) clean GaAs(001)-(4 × 6) reconstruction; b) the same pattern is fainter but still
visible at the first stage of Fe deposition; c) no pattern is distinguished in this range of
deposition; d) pattern of the cubic bcc Fe.
The detailed procedure to prepare the composite film sketched in Fig. 4.2 is the following:
(a) a thin wedge-shaped layer of Fe is deposited on a freshly prepared GaAs(001)-(4 × 6)
substrate. The thickness ranges from 0 to 6 ML over a sample length of 6 mm along the [110]
easy magnetization direction. A small area of 1 mm is left uncovered near the edge of the
51
sample. (b) On this wedge a single monolayer of Fe0.5Co0.5 is co-evaporated from the two
adjacent sources in order to deposit a constant amount of Co atoms, with an equivalent
thickness of half a monolayer, at variable distances from the GaAs(001) substrate. (c) A
second wedge with opposite orientation is deposited. Also in this case, the first mm at the
thick side of the first wedge is left uncovered so that on this side the Co half-monolayer is
sitting on a 6 ML thick Fe film without any further Fe capping. The so-obtained evenly thick
6-ML film is expected to be ferromagnetic as the ferromagnetic phase was seen to onset at
room temperature for films thicker than 3.5 ML.[5, 6]
Figure 4.2. The cartoon of the sample and experimental geometry: the double-wedge
structure consists of (a) an Fe wedge ranging from 0 to 6 ML deposited on the GaAs(001)(4 × 6) and covering 6 out of 7 mm of the total substrate length; (b) a single layer of
Fe0.5Co0.5 covering the whole sample length; (c) a 6-ML-thick Fe wedge oppositely
oriented. The sample was remanently magnetized in plane along the [110] direction. The
sample has been scanned along the [110] direction by the beam of the different techniques
(electron beam for LEED, laser for MOKE, X-rays beam for XPS and XMCD) so probing
different thickness - sample (a) and (b) - or the Co atoms lying at variable distances from
the interface - sample (c). This thickness/distance is referred as X in the figure.
After each stage of the film preparation, the sample was studied by LEED, MOKE and
XPS; XMCD is performed only on the fully characterised sample. The constant steepness of 1
ML/mm for the single wedge is low enough to allow a fine control of the thickness (or, in
alternative, of the distance of the Co atoms from the interface) probed by the beams whose
sizes never exceed 0.3 mm.
52
4.1.3 Growth morphology
The study of the morphology of the Fe growth on GaAs substrates has shown that at low
coverage Fe atoms aggregate into islands: as already mentioned, the specific surface
reconstruction may strongly influence the nucleation site, size and distribution of these islands
[7, 3].
On some experiments on As-terminated substrates heated at 175 °C during the deposition,
[7, 8, 9] these islands showed essentially a two-dimensional (2D) character and immediately
coalesced at low coverage (~1ML), so that Fe can be considered growing predominantly in a
layer-by-layer mode. On the other hand, Chambers et al. [10] firstly found that Fe deposition
at 175 °C on Ga-rich GaAs(001)-c(8 × 2) reconstruction initially exhibits a three-dimensional
growth (3D, Volmer-Weber mode) with islands of up to 3 ML height which start to coalesce
into a continuous film only at about 3-4 ML of nominal coverage. This behaviour was then
confirmed also for (4 × 6) Ga-terminated surfaces, [1, 11], even in the case of a deposition
temperature of the substrate higher than room temperature (150 °C).[12, 13] This dependence
of the growth mode on the substrate termination has been ascribed to the stronger interaction
of Fe with As which should favour the interaction between substrate and layer atoms for a Asterminated surface, whereas the opposite is true for a Ga-terminated surface where Fe clusters
become strongly favoured adsorption sites to minimize the contact with Ga.[8]
A straightforward confirmation of the 3D growth was shown in a recent STM study were
Fe islands on (4 × 2) and (2 × 6) Ga-terminated surfaces have been directly imaged [3].
Analogous measurements with consistent results have also been performed in the STM
chamber of APE facility, imaging at different low coverage (0.2, 0.4, 1.0, 2.2, 3.3 Å) the Fe
grown at room temperature on the here-discussed (4 × 6) reconstruction, prepared with
identical procedure:[14, 15] the average size of the islands is of few nanometers, depending
on the deposited thickness.
One of the fingerprint of the islands formation and coalescence is the progress of the
LEED pattern [4, 5] as a function of the deposited thickness: at the very initial coverage (<
0.5 ML) the pattern related to the surface superstructure fades but is still visible as the just
nucleated islands leave uncovered a consistent part of the surface, then the pattern disappears
as a bigger area is covered by the islands hindering a coherent diffraction from the substrate,
and finally the (1 × 1) LEED pattern of the bcc Fe(001) appears again at a thickness around
2.5 - 3 ML corresponding at the islands coalescence and gets sharper at higher coverage. This
thickness dependence is measured also on our single wedge samples as it is reported in Fig.
53
4.1, in good agreement with the quoted papers. On the completed double-wedge sample the
LEED pattern is present all along the sample, due to its uniform thickness.
Along with LEED also MOKE measurements were performed as a function of thickness
and the results, discussed in the following section, enlighten the strong correlation between
the onset of the ferromagnetic phase and the film morphology.[4, 5, 6]
The corrugation of the film is an undesired feature for our experiment and must be kept in
mind in the following when discussing the analysis of the data. In the ideal design of our
sample (see Fig. 4.2) the Co atoms are well localized as Fe is sketched to form a perfectly
smooth wedge. But this is true only considering its average (i.e. nominal) thickness. The iron
deposit is in fact strongly irregular at the first grown monolayer (3D islands formation), and
the Co is deposited on this corrugation resulting in a local dispersion of its distance from the
substrate. So when probing Co atoms sitting at a certain nominal thickness X of the first Fe
wedge, we are actually probing all these atoms dispersed essentially in a ± 1 ML interval
around its average position X.
4.2 Experimental results
4.2.1 MOKE
In situ transverse MOKE loops were performed at room temperature on freshly prepared
samples. The [110] direction was set perpendicular to the scattering plane in order to probe
the magnetization along the easy axis of the UMA. The Figures 4.3(a), 4.3(b) and 4.3(c)
present the hysteresis loops as measured respectively on the three subsequent steps (a), (b)
and (c) of the double-wedge preparation described in previous section: as it is sketched in the
small drawings inserted in the figures, the different loops are recorded by shining the focused
laser light at different positions of the sample and their labels indicate the corresponding
thickness in ML of the first deposited Fe wedge [which is equal to the distance of the Co
marker layer with respect to the GaAs substrate in the Figures 4.3(b) and 4.3(c)]. In order to
better distinguish the trend in the magnetic behaviour we only report some of the measured
loops.
The first striking evidence is the onset of the ferromagnetic phase at about 2.6 ML for
both wedge samples (always remember that to obtain the total probed thickness in figures
4.3(b) the marker monolayer of FeCo must be added to the reported distance). Starting from
54
this thickness the hysteresis loops open and assume a nice square shape with full remanence,
typical of an easy magnetic axis, and with a coercivity of some tens of Oe in agreement with
previously reported studies.[1, 5, 6, 7, 16]
Kerr intensity (arb.units)
0.10
b)
a)
0.05
Fe 0-6ML
GaAs
FeCo1ML
0.00
0.00
0.00
-0.05
-0.10
6.0 ML
4.0 ML
2.8 ML
2.4 ML
2.2 ML
-100
c)
0
Oe
100
Fe 6-0ML
6.0 ML
4.8 ML
3.6 ML
2.4 ML
1.2 ML
0.0 ML
6.0 ML
4.0 ML
2.0 ML
1.6 ML
1.4 ML
-50
0
Oe
50
-50
0
Oe
50
100
Figure 4.3. Hysteresis loops measured respectively on the three subsequent steps of the
double-wedge preparation as sketched in the relative inset: (a) single wedge of Fe, (b)
single wedge uniformly covered by 1 ML of Fe0.5Co0.5, (c) double-wedge.
In figures 4.4(a) and 4.4(b) we summarized the thickness/position dependence of the Kerr
intensity and of the coercivity: the three curves marked with wedges, coloured wedges and
coloured squares correspond respectively to the three subsequent samples (a), (b) and (c) – the
colour alludes to the Co presence and the shape of the marker is chosen to be selfexplanatory. Under 2ML no Kerr rotation was detectable with the fields at our disposal (up to
600 Oe). In the range between 2 and 2.5 ML a Kerr signal was visible but the film was not
remnant and the magnetization seems to saturate only at high field: as an example of such
behaviour one can check the curves at 2.2 ML and 2.4 ML of figure 4.3(a) where the
hysteresis are reported on a much more expanded range for the x-axis of the applied field. For
these curves we reported in fig. 4.4(a) the values of Kerr intensity at saturation using empty
markers in order to distinguish them from the values of the ferromagnetic phase where the
Kerr intensity is the same at saturation and at remanence.
The non-remnant hysteresis loops of the 2-2.5ML thickness range open and become
remnant by cooling the system [14], which indicates that the Curie temperature of the Fe film
is lower than the room temperature. In fact, Bensch et al.[6] showed accurately how the Curie
temperature increases with thickness for this system, in agreement with what happens for
other ultrathin magnetic films. They found the Curie temperature to cross room temperature at
55
~3.6 ML and deduced a critical Fe coverage of ~2.5 ML for the onset of ferromagnetism,
which means a non-zero Curie temperature, in correspondence with the coalescence of Fe
islands. As soon as the islands are separated, the presence of a superparamagnetic phase is
Coercive field (Oe)
Kerr intensity (arb.units)
expected due to their nanometric size and has been much debated in several studies.[5, 6, 15]
1.0
a)
0.5
0.0
60
0
2
4
6
b)
40
20
0
0
2
4
6
Height of first wedge (ML)
Figure 4.4. The Kerr analysis results. (a) Kerr intensity plotted as a function of thickness of
the first Fe wedge (triangles for the Fe wedge, coloured triangles for the Fe wedge covered
with 1 ML of Fe0.5Co0.5, and coloured squares for the double wedge); (b) The coercive field
as a function of the thickness of the first Fe wedge [the symbol code is the same as (a)].
Compared to the above discussed paper, we found a smaller value of 2.6ML for the onset
of the ferromagnetic phase at room temperature; it is always difficult to exclude an
inconsistent calibration of our evaporation rate and those quoted in the literature, but even
admitting a rescaling of the thickness from 6 to 8 ML it would not affect the philosophy of
our experiment which was to check the profile of the magnetization with particular attention
to the interface layer. What’s more it should be stressed that another study reports a different
value of 4.8 ML.[5]
As introduced in the MOKE section (chapter 2), the Kerr intensity depends on the
thickness for uncapped ultrathin films; in this sense the good uniformity of the values of the
56
double-wedge sample plotted in Fig. 4.4(a) is an indirect confirmation of the even thickness
of the completed sample. The other two curves of Fig. 4.4(a) reveal a continuous progress of
the Kerr signal with thickness. These curves overlap very nicely by shifting the one of sample
(b) 1ML forward, as one expects due to its total thickness: the overlapping is perfect
excluding the last point at the edge of the sample (possibly affected by a partial impinging of
the laser beam on the sample) and a linear trend is evident once the ferromagnetic phase has
firmly developed and loops are fully open (after 3 and 2 ML respectively). By supposing the
magnetization as being thickness independent one could try to fit linearly these points in order
to extrapolate the thickness of the magnetic part of the film: this approach was used by Y. B.
Xu et al.[5] to exclude the presence of a magnetically dead layer but they also underlined that
big care must be taken to reliably monitor the thickness dependence of the MOKE intensity.
Adding to this observation the relevant fact that this procedure would lead to a different
conclusion for our data, one should conclude that MOKE, which averages the information of
all the probed thickness, is not the best suited technique to extract a layer-sensitive
information.
Concerning Fig. 4.4(b), the coercive field of the only-Fe single wedge seems to saturate at
the maximum value of about 26 Oe. On the other hand the behaviour of the coercive field for
the double wedge sample deserves a more accurate, even if not ultimate, discussion. The
presence of a number of lattice defects in this hetoroepitaxial system would suggest that the
magnetization reversal occurs through the domain walls nucleation and motion or rotation.
Such a phenomenon is normally hindered by the presence of pinning centers. The observed
increase of the coercive field at the center of the sample is interpreted as due to a higher
concentration of pinning centers which are reasonably related to the presence of Co
impurities: in fact, an increase of the coercive field is already present with an analogous
position dependence in the curve of the sample (b), where the single wedge is covered with
Co impurities. In the double wedge sample the effect seems to be amplified where these Co
atoms may be thought as forming a double interface with Fe, whereas is suppressed when the
Co atoms sit at the interface or at the surface.
Summarizing the MOKE results, the thickness dependent measurements on the wedgeshaped samples give the indication that remnant hysteresis appear about at the same thickness
of the appearing LEED pattern of cubic Fe, strongly relating the coalescence of the Fe islands
to the onset of ferromagnetism. For the double wedge sample the magnetization is fully
remnant and remains quite constant over the whole sample area, which is crucial for the
validity of the XMCD analysis.
57
4.2.2 XPS
Photoemission experiments were performed at the APE-HE end station at room
temperature, in normal incidence geometry, and 45° off-normal emission using in-plane
linearly polarized X-rays of h = 450 eV. Overall energy resolution (photons + analyzer) was
set to
200 meV.
The chemical composition of the sample and its evolution as a function of steps (a), (b),
and (c) to produce the double wedge were studied by means of this surface-sensitive
technique: by focusing the X-ray beam onto different regions of the sample and measuring the
intensity attenuation of the core levels, we monitored the composition of the sample surface
for different Fe thickness as well as the distance from the sample surface of the sensing Co
layer.
In Fig. 4.5(a) we show the XPS spectra of the Fe wedge deposited on freshly prepared
GaAs(001)-(4 × 6) with the nominal film thickness ranging from 0 to 6 ML. The topmost
spectrum refers to a region of clean, uncovered GaAs(001)-(4 × 6); from top to bottom,
spectra corresponding to regions with increasing thickness of Fe are shown. The acquisition
time for the complete data set was 1 h. In the spectrum of clean GaAs(001)-(4 × 6), the
valence band and both the Ga and As 3d core levels are clearly visible, respectively, at 430 eV
and 408 eV of kinetic energy, together with the relative plasmon losses at about 15 eV higher
binding energy (BE). As the Fe thickness increases, the growing intensity of Fe 3p core levels
located at 396 eV and Fe 3d valence band are accompanied by the reduction of the Ga and As
related peaks. The Fe 3p peak has a constant BE all through the series of spectra. On the other
hand, the core levels of the substrate atoms show a progressive shift to lower BE for
increasing Fe thickness.
Figure 4.5(b) shows the same sample after the deposition of 1 ML of Fe0.5Co0.5. The line
shapes are practically unaffected, except for a slight reduction of Ga and As peaks as
compared to the Fe one; Co 3p core levels appear at 392 eV, i.e., 4 eV higher BE with respect
to Fe 3p.
Figure 4.5(c) presents the spectra for the complete double-wedge sample where we
observe that the Fe, As, and Ga features are rather constant in intensity while there is an
increase of the Co 3p peak only at one side of the sample.
58
a)
C L intensity (arb. units)
Increasing
Fe thickness
3
1
Fe 3p
2
9
8
7
6
5
1
4
0
3
0
2
4
6
Height 1st wedge (ML)
C L intensity (arb. units)
b)
3
1
9
8
7
Fe 3p
2
Increasing Co distance
from interface
c)
5
1
Co 3p
0
3
400
420
440
Kinetic Enegy (eV)
4
3
4
0
2
4
6
Height 1st wedge (ML)
As 3d
Fe 3p
2
Ga 3d
1
0
380
Ga 3d
As 3d
6
0
2
4
6
Height 1st wedge (ML)
C L intensity (arb.units)
Intensity (arb. units)
0
2
4
6
Height 1st wedge (ML)
Increasing
Fe thickness
Ga 3d
As 3d
Co 3p
0
2
4
6
Height 1st wedge (ML)
Figure 4.5. Left panels: the XPS spectra taken at different position on the sample of (a) the
Fe wedge, the upper spectrum corresponds to the bare GaAs(001)-(4 × 6) substrate; (b) the
Fe wedge covered with 1 ML Fe0.5Co0.5; (c) the double-wedge sample, the upper spectra
correspond to the to the region of the sample in which the Co atoms are in direct contact
with the substrate. Right panels: the upper and middle panels represent the core level
intensity corresponding to increasing film thickness. The substrate core-level intensities are
normalized to the values of the bare substrate. The right lower panel represents the doublewedge core levels along the sample length.
The intensities of the As 3d, Ga 3d, Fe 3p, and Co 3p core levels are presented as side
panels in Fig. 4.5 for the corresponding samples. In the right panel of Fig. 4.5(a) the Ga and
As 3d peak intensities normalized to the ones of the clean sample are plotted on a logarithmic
scale. The attenuation of the substrate signal follows an almost exponential behaviour up to a
nominal coverage of about 3 ML, as one would expect by applying a simple model of layerby-layer growth without interdiffusion. For coverage between 3 and 4 ML, the Ga-related
intensity decreases less rapidly than the As one and, finally, this tendency is inverted for
higher coverage. The intensity of the Fe 3p peak increases almost linearly up to about 3 ML
59
coverage, then also in this case a sudden change is found in the growing trend. It is interesting
to note that this thickness corresponds to the coalescence of Fe islands. Once the single layer
of Fe0.5Co0.5 is deposited over the Fe wedge, the Co 3p core levels appear as a feature at the
high BE side of the Fe 3p levels. The Co 3p intensity is constant through the whole wedge,
suggesting that the diffusion of Co atoms into the Fe film is negligible. The Fe 3p core levels
increase in intensity similarly to what was found for the simple Fe wedge and the same holds
for the Ga and As features, although the As-to-Ga ratio increases on the thick side of the
sample.
The analysis of the double-wedge sample is presented in Fig. 4.5(c). The intensity of the
Fe 3p, Ga 3d, and As 3d levels is constant within the error expected from the XPS thickness
analysis. An evaluation of the film thickness variation through the core level intensities shows
that there is an increase of the Fe film height
15 % between the two edges of the sample.
For what concerns Co 3p, a sizable signal is found only within 2.5 ML from the surface, as
expected when considering the attenuation of the Fe counterwedge.
The XPS analysis of the samples reveals important features on the chemical profile of the
Fe/GaAs interface. Firstly, the overall sample thickness is constant along the whole sample
area and the Co atoms are spatially well confined within the two oppositely oriented Fe
wedges, see Fig. 4.5(c); that the Co sensing layer does not diffuse or intermix into Fe is also
suggested from the fact that the Co 3p intensity remains constant through the whole wedge, as
shown in Fig. 4.5(b): this consideration is crucial for the use of Co as a profile marker.
Secondly, looking at the evolution of the Fe 3p signal, we notice that starting from 3 ML the
observed trend changes considerably, see Fig. 4.5(a). This can be taken as the fingerprint of
the coalescence of the Fe islands: by melting in a continuous film, the contribution of Fe
atoms whose intensity was screened by the topmost atoms of the islands is increased. The
exponential saturation observed for the highest coverage can be ascribed to the finite probing
depth of the photoelectrons: the effect could be amplified by the presence of substrate atoms
segregating in the near-surface region, as it is discussed below.
Some important details of the Ga and As out-diffusion are revealed from the XPS spectra.
The thickness-dependent core-level shift for Ga and As signals the change of the chemical
environment for the atoms of these species, suggesting that an amount of both Ga and As
atoms diffuse from the substrate along the Fe overlayer, occupying interstitial sites in the
metal matrix. In Fig. 4.6 we zoom on the spectra of As and Ga 3d core levels extracted from
curves of Fig.4.5(a): each spectrum has been background-subtracted, normalized to its peak
intensity and vertically offset for graphical clarity. The shift is small for the As 3d levels (
60
0.15 eV) and more pronounced for the Ga 3d core level, reaching a maximum of
0.8 eV:
this behaviour is in good agreement with previous XPS studies[9, 10] which also found a
more pronounced shift of Ga.
Ga 3d
Intensity (arb. units)
As 3d
Increasing
Fe thickness
Increasing
Fe thickness
405 406 407 408 409 410 428 429 430 431 432 433
Kinetic Energy (eV)
Figure 4.6. XPS spectra of As and Ga 3d core levels as a function of Fe coverage on
GaAs(001)-(4 × 6). Each spectrum has been normalized to its peak intensity and vertically
offset for clarity.
Recent first-principle density functional calculations from Mirbt et al. [17] support the
segregation of both Ga and As through the Fe film: As segregation is expected even at 0 °K,
whereas the one of Ga occurs in a diffusive way, thus preferring to disperse within the film
rather than to localize at the interface. Moreover, Ga segregation towards the surface is
inhibited if As is already present in the topmost layers. This picture is consistent with
experimental studies on both Ga-terminated[10] and As-terminated[9] substrates where the
abundance of As in the surface was confirmed by angular-dependent XPS. In summary, the
Fe deposition induces at low coverage the disruption of the substrate liberating Ga and As in
approximately equal amounts up to about 1 ML: a fraction of As segregates on top of Fe film,
whereas Ga diffuses only inside the film getting more and more diluted with increasing
coverage.
To address the issue of segregation, we can also use our XPS data. For the clean substrate
- upper spectrum of Fig. 4.5(a) - the ratio between As and Ga 3d peaks depends on the
relative abundance of the substrate atoms in the surface region and on the relative
61
photoionization cross sections. Both these parameters are difficult to assign due to the large
errors introduced by the unknown values of surface sensitivity and cross sections in real
systems. In order to evaluate the segregation dynamics as a function of the Fe film thickness,
we have normalized to unity both As and Ga 3d intensities for the clean GaAs(001)-(4 × 6)
surface. Although this may appear as an arbitrary assumption, it is justified when the relative
amount of segregation is concerned. Turning the attention to the As-to-Ga ratio for increasing
Fe thickness, our XPS data show that the diffusion rate of the Ga and As is uneven across the
film. In fact, once the Fe islands have coalesced in a bcc structure at around 3 ML, the Ga
diffusion rate is more pronounced up to a nominal thickness of 4 ML. For higher coverage the
As segregation prevails, thus inhibiting further Ga migration to the surface and leading to the
formation of the well-known As-rich Fe surface with Ga distributed within the film. It must
be stressed that for the highest coverage, the XPS sampling depth in the Fe matrix is limited
to a few ML as shown by the Co 3p attenuation depth, see Fig. 4.5(c).
4.2.3 XMCD
The double-wedge samples are measured with the light impinging at 45° with respect to
the normal direction and with respect to the in-plane magnetization (see Fig. 4.2), whose full
remanence is checked by previously discussed MOKE. The Fe/Co L2,3 absorption edges are
measured in partial electron yield mode by collecting the secondary electrons with a
channeltron placed above the sample. XMCD spectra are obtained by flipping the circularly
polarized radiation, scanning the sample along the easy axis direction with steps of about 0.7
mm. Given the double-wedge geometry, this step entails probe regions with Co atoms at
different distances from the FM/SC interface, at steps of 0.7 ML within the Fe film. Since no
appreciable diffusion of the Co atoms is detected by XPS, the error bar of the probing depth
can be confidently assigned within the portion of the Co probe enlightened by the X-ray
beam, i.e., ~ 300 µm or 0.3 ML. Actually this is correct only as far as the Co atoms position is
considered as an average of the probed Co atoms, as commented in the section 4.1.3
discussing the growth morphology.
In Fig. 4.7 we show three representative XMCD spectra, corresponding to 4.6, 1.8, and
0.4 ML from the GaAs substrate. The spectra have been normalized to the incident photon
flux as measured on a calibrated photodiode. Although all three spectra display nonzero
dichroism, their intensity at the L3 and L2 edges differs significantly as a function of the
62
distance from the interface. Since the samples are magnetized, the asymmetry at L3 — i.e., the
dichroic signal [µ+(L3) − µ−( L3)] normalized to the total (and so isotropic) absorption cross
section, i.e., 1/2[µ+(L3) + µ−( L3)] — can be considered as proportional to the local
magnetization.[18]
X = 4.6 ML
Intensity (arb. units)
X = 3.2 ML
X = 0.4 ML
X = 4.6 ML
X = 3.2 ML
X = 0.4 ML
770
775
780
785
790
795
800
Photon energy (eV)
Figure 4.7. XMCD results. Upper panels: Co L2,3 X-ray absorption spectra for opposite
light elicity for Co atoms lying respectively at X=4.6, 1.8, and 0.4 ML from the interface.
The spectra are normalized to the incident photon flux. Lowest panel: the three
representative dichroic spectra normalized to the XMCD intensity at L2.
Obviously, only the absorption cross section coming from the Co edges must be
considered which means that a proper background, comprising the presence of about 6ML of
Fe on GaAs, must be subtracted. As the Co edges stand on the EXAFS oscillations of the Fe
L3,2 edges which have lower excitation energies and much bigger intensities due to the sample
63
composition, in order to evaluate such a background we measure as a reference a Co-free
epitaxial Fe film grown on GaAs(001). In Fig. 4.8(a) we report this absorption cross section
(labelled ‘Fe XAS’) for the range of Co L3,2 edges, which matches very well the pre-edge big
bump recorded in the XAS measurements on our sample (labelled ‘Sum’) and shows the
oscillatory behaviour of the Fe-related background whose evaluation becomes of great
importance in order to correctly estimate the Co-related intensities used in sum rules
application.
17
+
16
Intensity (arb. units)
−
b1) Sum(µ +µ )
b2) Fe XAS
b3) Iso = b1 - b2
a)
15
760
b)
1
770
780
790
800
a1) Dichr
a2) Int(Dichr)
b3) Iso
b4) 4s
b5) Int(Iso - 4s)
20
0
0
760
780
Photon energy (eV)
800
Figure 4.8. The illustration of the complete analysis procedure for the sum rules
application: the absorption spectra are relative to the X = 6ML position. (a) The sum of the
as recorded opposite-elicity spectra µ+ + µ− must be subtracted by the only-Fe absorption
spectrum, in order to obtain the total absorption spectrum for the Co L2,3 edges only (here
called ‘Iso’, i.e., isotropic). (b) In order to obtain the integral functions used in sum rules
[Eqs. (2.6-7)], one must take the dichroic signal µ+ − µ−, i.e. ‘Dichr’, and the isotropic
spectrum, ‘Iso’, subtracted by the a proper background simulating the flat 4s band,‘4s’, and
do the integrative operation in the proper energy interval.
Finally, after this proper background subtraction, Fig. 4.9(a) summarizes the values of the
asymmetry measured at the Co L3 edge versus the Co position along the double wedge. We
observe the presence of a net dichroic signal through the whole interface, including the case
of Co atoms in direct contact with the GaAs substrate. The asymmetry is higher in the center
of the layer and it is reduced both near the interface and near the surface. We remind here
64
that, in order to estimate the real dichroism, the correction for the geometry and the circular
polarization degree must be taken into account, that is the dichroic signal must be respectively
diveded by cos(45°) and by 0.75; this last value comes from the calculations shown in Fig. 3.3
considering that the third harmonic is chosen due to its smoother peak of both intensity and
polarization.
In order to apply magneto-optical sum rules, Eqs. (2.6-7), we set the value of n3d = 8.38
electrons in the Co 3d band as reported in a previous study for a thick FeCo film.[19] The
detailed spectra analysis procedure is described in the caption of Fig. 4.8. In Figs. 4.9(b) – (d)
the values of morb, mspin, and their ratio as a function of the distance X from the interface are
presented. In the figures, we report for comparison the values corresponding to an hcp thick
film[20] (dashed line) and those measured for a thick bcc FeCo film, that is, morb = 0.173 µB,
mspin = 1.48 µB (continuous line, our data). The Co spin magnetic moment through the entire
film is sensibly lower than that of a thick hcp film and it is reduced also with respect to the
bcc FeCo film. Nevertheless it is quite close to the value of 1.44 µB found in a recent XMCD
study performed on a 36-Å-thick bcc Co film on Ge(100).[21] The behaviour of the spin
magnetic moment within the 6-ML film shows a reduction in proximity of the interface and at
the surface of the sample. The orbital magnetic moment is instead, on the average, aligned
with reference values, but its layer dependence shows a noticeable augmentation in the
vicinity of the interface. This is readily seen in Fig. 4.7(d) where the XMCD spectra relative
to 4.6, 1.8, and 0.4 ML probing thickness are shown normalized to the L2 intensity. Since the
L3 intensity increases for the spectra relative to Co atoms sitting closer to the FM/SC
interface, from Eq. (2.6) it follows that the orbital moment within the Fe film increases when
approaching the interface.
The error bars of 10% associated with the measurements take into account the
experimental uncertainties (< 10%) as well as small corrections (few %) related to different
approximations (see details in Ref. [20]) like the omission of the <Tz> term, the omission of
the small contributions of the 4s/4p components to the magnetic moments and the arbitrary
position of the thresholds for the two-step function simulating 4s band. In our measurements
saturation effects do not need to be considered because of the small thickness of the probed
film[18, 22]. On the other hand, the uncertainty on other parameters as n3d electrons and the
degree of circular polarization introduces a systematic error, which is of less relevance for the
following discussion concerning more the relative change of the moments along the profile
rather than their absolute values.
65
XMCD at L3
0.70
0.65
0.60
a)
0.55
0.50
0
1
2
3
4
5
6
mspin(µµB)
1.6
1.4
b)
1.2
1.0
0.8
0
1
2
3
4
5
morb (µµΒ)
0.28
6
c)
0.24
0.20
0.16
0.12
0
1
2
3
4
5
d)
0.30
morb / mspin
6
0.25
0.20
0.15
0.10
0
1
2
3
4
5
6
X (ML)
Figure 4.9. Layer selective XMCD analysis. (a) The asymmetry intensity at Co L3 edge.
(b)–(c) Respectively the spin and orbital magnetic moments of Co atoms as calculated by
means of the sum rules. (d) The orbital-to-spin magnetic moment ratio. X indicates the
distance of Co atoms from the interface: X=0 represents Co atoms in direct contact with the
GaAs and X=6 represents Co atoms lying at the surface of the Fe film. The dashed and
continuous horizontal lines indicate reference values for Co hcp (Ref. [20]) and FeCo bcc
(our data) thick films. The data are corrected for the incomplete light polarization (75%)
and for 45° incidence angle with respect to the magnetization direction.
66
In Fig.4.10 the analysis of the XMCD measurement for the Fe edges is reported at a given
position. Using a value of 3.39 for the parameter n3d,[20] the sum rules give uniform values in
the range of 2.0±0.05 µB for the spin moment at different positions, in perfect agreement with
the value of 1.98 µB for the Fe bulk, while the values of the orbital moment stand in the range
0.17±0.05 µB, which marks an increase compared to the value of 0.085 µB of the Fe bulk.
150
8
+
6
Intensity (arb. units)
−
Sum(µ +µ )
4s
Int(Sum - 4s)
100
50
4
2
700
0
720
0
+
µ
4
−
µ
Dichr
Int(Dichr)
2
0
-5
-10
700
720
740
Photon energy (eV)
Figure 4.10. Complete analysis procedure for the sum rules application in the case of Fe L3,2
edges with Fig. 4.8 (refere to it for the detailed procedure). Here no oscillatory background
must be carefully measured and subtracted. We also report the original measured spectra µ+
and µ−, to be summed (‘Sum’) and subtracted (‘Dichr’).
4.3 Discussion
XMCD is performed on the Co sensing layer corresponding to Co atoms evenly enveloped
in a macroscopically magnetized Fe film, thus coordinated with Fe neighbours. Our
67
straightforward hypothesis is that Co is exchange coupled to iron and therefore that its local
moment must reflect the average magnetic environment of the Fe film at the “depth”
corresponding to the location of the Co probes. In this way we can define a “profile” of the
local magnetization from the interface up to the surface. We observe a net dichroic signal
through the whole interface, including for Co atoms in direct contact with the substrate [Fig.
4.9(a)]: this evidence directly rules out the long-debated presence of a magnetically dead
interface layer which is a crucial issue for efficient spin-injection. This is a first relevant
result.
We stress that such result could not be retrieved from a layer-by-layer growth
experiment since it is only for a certain thickness that Fe is ferromagnetic at a given
temperature (lower then the bulk Curie temperature). Without magnetic markers the
ferromagnetism of the interface layer could hardly be addressed, being confused with the
magnetic signal of the overlayer.
Furthermore, from our set of data it is possible to follow separately the spin and orbital
magnetic moments along the Fe film thickness in more detail and one observes that the spin
polarization is maximum at the center of the film and it decreases for smaller probing
distances as well as for the layers closer to the Fe film surface. The reduction of the spin
magnetic moment measured for the Co atoms in the vicinity of the interface can be explained
as being due to the presence of As and Ga atoms segregating from the substrate. In fact, as
pointed out by recent theoretical calculations,[17] at the earlier stages of adsorption of Fe on
GaAs(001), the Fe atoms tend to break the top Ga-As bonds to create Fe-As bonds through
3p-3d hybridization, with Ga taking interstitial sites. Since the magnetic phase diagram of the
thin film depends critically on the small details of the Fe electronic configuration, a change in
the coordination and distance between Fe and segregating atoms can modify the Fe 3d states
delocalization and hinder the exchange interaction. Such a modification in the exchange force
among the Fe atoms will result in a reduced magnetization at the interface with the SC as
measured via the Co magnetic marker.
Similarly, the presence of foreign atoms at the top of the Fe film, as indicated by our XPS
measurements as well as in several previous reports, can explain the reduction of the
measured spin-polarization at the surface of the sample. Actually, in Ref. [17] a big
quenching of the Fe magnetic moments is predicted at the surface for a configuration where
1ML of As is segregated on the top: such a configuration is in fact seen to be the most
favourable for the system (always by calculations presented in same reference) and this also
seems to be confirmed by experimental estimations.[9, 10] In any case this almost complete
quenching expected at the surface renormalizes to magnetization reduction in our
68
experimental results and this discrepancy may be due to the fact that the local chemistry is
more complex than predicted theoretically due to the presence of the intermixing of different
phases. Actually, a simple reduction is supported by other ‘ideal’ calculations as discussed in
the following.
The unambiguous demonstration that the Fe/GaAs(001)-(4 × 6) interface is ferromagnetic
is in agreement with a recent work of Claydon et al.[23] where XMCD measurements
exhibited bulk-like spin moment also on submonolayer Fe coverage (0.25, 0.5 and 1ML)
deposited on GaAs(001)-(4 × 6) and capped with a thick Co layer in order to provide the
otherwise-paramagnetic Fe islands with a source of exchange interaction and to disperse the
segregating and magnetization-affecting As. They also measured other thicknesses in the
ferromagnetic range (> 4ML) still finding bulk-like spin moment. We would like to point out
how, for both ranges, their experimental point of view differs from our conditions: concerning
the submonolayer coverage, it’s the system itself which is not a Fe ultrathin film, but rather
the Fe atoms can be considered impurities dispersed at the interface of Co and GaAs, while
for coverage higher than few monolayers all the thickness is measured and the layer
dependent information is lost. These considerations show the importance of our measurement
design which offers the capability of depth resolved investigation (not only at the
interface[24] or at the surface[25]) and so the possibility of directly studying the ‘complete’
system, where the film is thick enough to be ferromagnetic at room temperature, which is an
unavoidable requirement for the development of spintronics devices. What’s more we want to
point out that Claydon et al.[23] used 3 T external magnetic field in order to fully align the
magnetisation out of plane parallel to the incoming photon direction whereas our
measurements are performed at zero applied external field with the sample remanently
magnetised, which is the real operative condition for a potential electronic device.
As shown in Fig. 4.9(c) the orbital moment measured for the Co atoms embedded in the
bcc Fe film increases as approaching the interface. An increase of the orbital moment
compared to the bulk value was also detected by Claydon et al. and by Xu et al. [26] for Fe
grown on GaAs(001)-(4 × 6). It is expected that this enhancement is due to the reduction of
symmetry in comparison with the bulk structure and in fact the orbital sum rule has been
extensively used since its discovery to show an increase of the orbital moment at
interfaces[27], surfaces[28] and for impurities[29], and, more recently, for organised
structures of dimensionality lower than 2D [30, 31]: the reduced atomic coordination or the
reduced symmetry, due to the presence of a heterogeneous interface or to the surface
termination, lead to 3d-electron localization and finally to an increased atomic-like orbital
69
moment.
Claydon et al. found an increased average orbital moment for Fe thickness smaller than 12
ML (about 250-300% respect to the Fe bulk value), which remained rather constant down to
submonolayers. Our data show a somehow different trend: the Co orbital moment across the 6
ML of Fe increases sensibly only when approaching the interface with GaAs(001)-(4 × 6).
This disagreement is only apparent and comes from the fact that we are comparing the orbital
moment of the Co atoms localized at different positions in the Fe matrix, with the averaged
one of the Fe film. In fact, looking at our data for the Fe magnetic moments of the doublewedge 6 ML thick Fe sample, we also find a bulk-like spin moment and an increased orbital
moment which is about 200% compared to the value of Fe bulk.
The observed reduction of the Co orbital moment at the surface is unexpected in the
discussed framework of the reduction of symmetry which should induce similar effects both
at interfaces and surfaces. To reduce the uncertainty on the magnetic moment values
measured by the sum rules, one often refers, see Fig. 4.9(d), to the ratio between the orbit and
the spin moments, which is independent of final state electronic configuration and isotropic
spectrum. The resulting ratio shows an increased value with respect to Co hcp and FeCo bcc
reference samples and we note that in this case no significant decrease is detected at the
surface while the feature of a higher orbital moment holds at the interface. So, one could also
argue that the reduction of both spin and orbital moments at the surface might be an artifact
given by a change of the electronic configuration, i.e., the value of n3d electrons, due to the
surface. Another explanation, consistent with an unchanged value of the spin-orbit ratio,
could be that a given percentage of the surface layer atoms result to be magnetically dead,
having both spin and orbital moments equal to zero, due to their stronger interaction with
segregated As.
Finally we would like to compare our experimental results with first principles
calculations[30] which have been tailored to simulate our system: an ideal situation has been
considered with the half ML of Co atoms subsequently located in every ML of a 6 ML Fe
film ideally grown (no intermixing, perfect interface) on Ga-terminated GaAs(100). Spin and
orbital magnetic moments are calculated layer by layer for both Fe and Co atoms. The
comparison with experimental data must be taken carefully due to the simplification of the
70
simulated system.
In Fig. 4.11 the spin moments calculated by Ebert et al. are shown: the first striking
evidence is that no significant reduction of magnetism is found at the interface or anywhere
else.[31] Concerning the mutual influence of two magnetic species, Fe moments change
slightly as a function of Co position, dancing around their bulk-like values: it seems that Co
atoms make the moments of the neighbouring Fe atoms, the 1 ML-lower and 1-ML upper
ones, increase. On the other hand Co spin moment ‘feels’ more the interface than Fe moment
does, showing a relatively higher reduction, which is in agreement with our results. At the
free clean surface, Fe spin moment is enhanced much more than Co one.
Figure 4.11. Calculated layer-by-layer spin magnetic moments in 6ML Fe film, with Co
markers, on a Ga-terminated GaAs(001) substrate: half ML of Co atoms are positioned
from the first to the last Fe layer forming NFe/Fe0.5Co0.5/(5-N)Fe with N varying from 0 to
5. The values for Co and Fe atoms are indicated respectively by red squares and blue
circles. For each layer two points are plotted as two non-equivalent sites are considered in
the bcc matrix: the one corresponding to ideal occupation of a zincblende structure site of
the SC and the symmetric one, corresponding to interstitial occupation inside zincblende
structure.
In any case, even if small, the Co moment enhancement at the surface leads to
inconsistency with our data, which is overcome when 1ML of As is added as a surface
capping layer: as shown in Fig. 4.12 the calculated spin moment results suppressed and the
71
qualitative agreement is established again. The calculated abrupt variations from the
outermost or the innermost Co layers and the quite constant values of the internal fully
symmetric layers renormalize to a gradual trend in our data [Fig. 4.9(b)] showing a maximum
at the center of the film: this disagreement can be understood by considering that in our
sample a relevant fraction of the Co atoms sitting nominally on the second (fifth) layer from
the interface lie actually on the first (sixth) layer, so undergoing a reduction of magnetism.
Concerning the behaviour of the orbital magnetic moment illustrated in Fig. 4.13, similar
comments can be made. In this case the relative Co changes seem to reflect better the Fe ones:
in particular Fe orbital moments undergo a relevant enhancement at the interface and even
more at the surface (as expected by symmetry reduction considerations) and so do Co
moments. This trend is confirmed by our data only at the interface whereas at the surface a
change of opposite sign is found and in this case the additional presence of the segregated As
layer does not provide an easy explanation, as the calculated value of the orbital moment for
the topmost Co layer results reduced but still higher than at the inner positions.
Figure 4.12. The spin magnetic moments calculated for Co atoms embedded at different
position in the 6 ML film. Note the reduction of the values for the last layer when 1 ML of
segregated As is added. SC and ES label refer respectively to semiconductor-equivalent and
not (ES = ‘Empty Sphere’) sites (see Fig. 4.11).
72
Figure 4.13. Analogous to Fig. 4.11 for orbital spin moments of Fe and Co.
[1] M. Zölfl, M. Brockmann, M. Köhler, S. Kreuzer, T. Schweinböck, S.Miethaner, F.
Bensch, G. Bayreuther, J. Magn. Magn. Mater. 175, 16 (1997).
[2] M. Gester, C. Daboo, R. J. Hicken, S. J. Gray, A. Ercole, and J. A. C Bland, J. Appl. Phys.
80, 347 (1996).
[3] R. Moosbülher, F. Bemsch, M. Dumm, and G. Bayreuther, J. Appl. Phys. 91, 8757 (2002).
[4] M. Madami, S. Tacchi, G. Parlotti, G. Gabbiotti, and R. L. Stamps, Phys. Rev. B 69,
144408 (2004).
[5] Y. B. Xu, E. T. M. Kernohan, D. J. Freeland, A. Ercole, M. Tselepi, and J. A. C. Bland,
Phys. Rev. B 58, 890 (1998).
[6] F. Bensch, G. Garreau, R. Moosbühler, G. Bayerheuther and E. Beaurepaire, J. Appl.
Phys. 89 (2001) 7133.
[7] E.M. Kneedler, B.T. Jonker, P.M. Thibado, R.J. Wagner, B.V. Shanabrook, L.J. Whitman,
Phys. Rev. B 56 (1997) 8163.
[8] P. M. Thibado, E. Kneedler, B. T. Jonker, B. R. Bennett, B. V. Shanabrook, and L. J.
Whitman, Phys. Rev. B 53, R10481 (1996).
[9] E. Kneedler, P. M. Thibado, B. T. Jonker, B. R. Bennett, B. V. Shanabrook, R. J. Wagner,
and L. J. Whitman, J. Vac. Sci. Technol. B 14(4), 3193 (1996).
[10] S. A. Chambers, F. Xu, H. W. Chen, I. M. Vitomirov, S. B. Anderson, and J. H. Weaver,
Phys. Rev. B 34, 6605 (1986).
[11] M. Brockmann, M. Zölfl, S. Miethaner, G. Bayreuther, J. Magn.Magn. Mat. 198-199,
384 (1999).
[12] M. Gester, C. Daboo, S. J. Gray, J. A. C. Bland, J. Magn. Magn. Mat. 165, 242 (1997).
[13] B.T. Jonker, G.A. Prinz, and Y. U. Idzerda, J. Vac. Sci. Technol. B 9, 2437 (1991).
[14] A. Stollo, Tesi di Laurea, University of Perugia, 2004.
73
[15] R. L. Stamps, A. Stollo, M.Madami, S. Tacchi, G. Carlotti, G. Gubbiotti, M. Fabrizioli,
J. Fujii, submitted to Phys. Rev. B.
[16] B. Lépine, C. Lallaizon, S. Ababou, A. Guivarc’h, S. Députier, A. Filipe, F. Nguyen Van
Dau, A. Schuhl, F. Abel, C. Cohen, J. Cryst. Growth 201/202, 702 (1999).
[17] S. Mirbt, S. Sanyal, C. Isheden, and B. Johansson, Phys. Rev. B 67, 155421 (2003).
[18] W. L. O’Brien and B. P. Tonner, Phys. Rev. B 50, 12672 (1994).
[19] E. Di Fabrizio, G. Mazzone, C. Petrillo, and F. Sacchetti, Phys. Rev. B 40, 9502 (1989).
[20] C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E.
Pellegrin, and F. Sette, Phys. Rev. Lett. 75, 152 (1995).
[21] P . Ryan, R. P. Winarski, D. J. Keavney, J. W. Freeland, and R. A. Rosenberg, S. Park,
C. M. Falco, Phys. Rev. B 69, 054416 (2004).
[22] R. Nakajima, J. Stohr and Y. U. Idzerda, Phys. Rev. B 59, 6421 (1999).
[23] J.S. Claydon, Y. B. Xu, M. Tselepi, J.A.C. Bland, G. van der Laan, Phys. Rev. Lett. 93,
037206 (2004).
[24] F. Gustavsson, E. Nordström, V. H. Etgens, M. Eddrief, E. Sjöstedt, R. Wäppling, and J.M. George, Phys. Rev. B 66, 24405 (2002).
[25] To find a discussion of recent surface sensitive magnetic techniques see: K. Amemiya, S.
Kitagawa, D. Matsumura, T. Yokoyama and T. Ohta, J. Phys.: Condens. Matter 15 (2003)
S561–S571.
[26] Y. B. Xu, M. Tselepi, C. M. Guertler, C. A. F. Vaz, G. Wastlbauer, J. A. C. Bland, E.
Dudzik and G. van der Laan, J. Appl. Phys. 89, 7156 (2001).
[27] Y. Wu, J. Stöhr, B. D. Hermsmeier, M. G. Samant and D. Weller,Phys. Rev. Lett. 69 230
(1992).
[28] M. Tischer, O. Hjortstam, D. Arvanitis, J. H. Dunn, F. May, K. Baberschke, J. Trygg, J.
M. Wills, B. Johansson and O. Eriksson, Phys. Rev. Lett. 75, 1602 (1995).
[29] J. Vogel and M. Sacchi, Phys. Rev. B 53, 3409 (1996) .
[30] M. Kosuth, V. Popescu, H. Ebert, private communication. Details on the calculations
based on LSDA (local spin density approximation) can be found in the reference quoted in
[31].
[31] Previous calculations had been performed by the same authors for a more conventional
nFe/GaAs(001) system (n = 1-7) and published as: M. Kosuth, V. Popescu, H. Ebert, and G.
Bayreuther, Europhys. Lett., 72 (5), pp. 816–822 (2005). Between the unpublished results
(private communication) there was the non-reduction of the Fe magnetic moment at the
interface.
74
Chapter 5
Magnetic patterned samples prepared by nanolithography techniques
The understanding of the magnetic-field-dependent correlations within an array of
submicrometric objects is important both fundamentally and practically.
In the following chapters (5, 6, 7 and 8) we report mainly on the analysis of a matrix of
rectangular dots of polycrystalline permalloy (Ni81Fe19) measuring 1000 nm × 250 nm:
different samples with variable thickness in the range 10 ÷ 125 nm were prepared by means of
X-ray lithography. We used resonant scattering of polarized soft X-rays to investigate their
magnetic behaviour as a function of the applied field. The main goal is to address the
potentialities of this technique called XRMS (X-ray resonant magnetic scattering), that
combines structural and spectroscopic analysis. Micromagnetic simulations are also discussed
as a valuable tool of comparison with scattering results.
We start from introducing in this chapter the lithographic fabrication techniques used for
the sample preparation. We choose an array of rectangular dots, as the shape anisotropy of
such systems allows an easier alignment of the magnetisation along the longer side of the
rectangle.
5.1 Fabrication of arrays of nanostructures
Central to nanofabrication is lithography, a multi-process, including resist coating,
exposure, and development. Lithography recalls the procedure of transferring a template
design over a specific sample. Although extensive literature exists on the basic lithography
processes,[1] a brief review helps to better illustrate the techniques used in the specific
preparation of our samples.
The work piece, an unpatterned film or a substrate, is first spin-coated with a uniform
75
layer of resist dissolved in organic liquid solvent. The resist thickness is typically a few
thousand angstroms to a micron, depending on the spinning speed and the resist viscosity. A
soft-bake of the resist is necessary to remove the resist solvent and promote adhesion.
Selected areas of the resist are then exposed to a radiation source, generally through a mask
(Fig. 5.1). The exposed polymer chains in the resist are either broken (positive resist), or
become cross-linked (negative resist, poorer resolving power). The exposed resist can be
further treated with a post-exposure bake to promote homogeneity, before being developed to
form a positive or negative image of the mask. As the lithography process transforms a twodimensional (2D) pattern into a three-dimensional (3D) structure in the resist and eventually
in the unpatterned film, the depth profiles in both layers are important. By choosing the right
developer, temperature and developing time, one can obtain straight, round-off or undercut
depth profiles in the resist.
Figure 5.1. Schematics of lithography processes for (a) positive and (b) negative resists in
conjunction with (a), (b) etching, (c) lift-off, and (d) electrodeposition.
Pattern transfer can be realized in two general processes: from the resist to an unpatterned
film by wet or dry etching; or post-deposition onto patterned resist by lift-off and/or
electrodeposition (Fig. 5.1).
76
For etching, the developed resist is usually hardened by a hard-bake before this process.
Wet etching uses chemical or electrochemical processes to dissolve the materials. It is
intrinsically isotropic and causes sloped pattern edges. Therefore the resolution is generally
limited by the thickness of the film to be patterned. However, anisotropic etching may be
achieved in oriented crystalline materials. In dry etching, physical processes such as ion
milling and sputter etching use ion bombardment to remove the unwanted materials; chemical
processes such as plasma etching use active species to react with surface material and form
volatile products; a combination of both processes, such as reactive ion etching (RIE), takes
advantage of both principles. These dry etching processes can produce straight and sharp
pattern edges, thus better resolution for a given film thickness. They are more desirable for
patterning ultrafine nanostructures. At the end of the process, the remaining resist is striped
away, for instance in a warm ultrasonic acetone bath.
Alternatively, nanostructures can be fabricated by post-lithography depositions. Lift-off
utilizes the height of a developed resist to break apart a subsequently deposited, much thinner,
layer of material (Fig. 5.1). The film deposited on top of the resist is lifted off during resist
striping, leaving behind only the portions directly deposited onto the substrate. It is crucial to
have a clean break-off of the film at the pattern edges of the resist. Therefore resists
developed with undercut edge profiles, as well as directional deposition techniques, are
preferred. One method to realize the undercut profile is to slowdown the development at the
resist surface relative to the bulk by, e.g., immersing the resist in chlorobenzene to harden the
surface. Note that the height of the lift-off structures is usually much smaller than the resist
thickness (Fig. 5.1).
Electrodeposition, or electroplating, is a general growth technique and is particularly
useful for post-lithography depositions. It refers to the deposition of materials from an
electrolyte by the passage of an electrical current. Unlike high-vacuum deposition techniques,
such as sputtering or evaporation, electrodeposition is an ambient temperature and pressure
process. It has the attractive features of cost-effectiveness, simplicity of operation, and the
ability to deposit onto substrates with complex geometries. Differing from lift-off, the
electrodeposited elements can have heights up to the resist thickness, therefore better vertical
aspect ratio
The lithography resolution limit is ultimately determined by the radiation wavelength.
Hence lithography is usually categorized by the radiation source as optical, electron-beam (ebeam), ion beam, and X-ray lithography. The fabrication of patterned arrays of dots, antidots
and wires on the submicrometric scale, with resolutions down to a few tens of nanometers,
77
can be carried out by both e-beam and X-ray lithography.
Electron-beam lithography (EBL) uses a beam of electrons to write directly on the resist
the desired pattern in a sequential way, so that it is heavily time-consuming for large area
patterning. On the contrary, X-ray lithography (XRL) is a parallel writing technique which
can be implemented at synchrotron radiation facilities for deep and large area patterning, by
using masks. The masks are fabricated by e-beam lithography just once, and then they are
used repeatedly in the X-ray process. The main advantage of using both types of lithography
is the possibility to design new processes with high resolution, higher resist aspect ratio and
large exposure areas.
We used an X-ray mask, which was previously built by means of EBL and electrolytical
growth,[2, 3] in order to fabricate magnetic patterns by X-ray lithography at the LILIT
beamline[4] of TASC-INFM[5] on the ELETTRA storage ring, in combination with a lift-off
process.
We now briefly concentrate on the basic aspects of these two lithographic techniques. By
presenting EBL we also introduce the scanning electron microscope, which is also the main
tool used to control the geometrical results of the lithographic process.
5.1.1 E-beam lithography with scanning electron microscopes
The e-beam lithography technique uses an electron beam to expose an electron-sensitive
resist. The exposure is usually done using the e-beam in a scanning electron microscope
(SEM) apparatus. The scheme of such apparatus is shown in Fig. 5.2 consisting of a
monoenergetic beam of electons which is collimated and controlled by a system of
electromagnetic lenses. The instrument is conventionally used to perform simple imaging of
surface topography by scanning the focused electron beam (deflection is induced by magnetic
scanning coils) and simultaneously detecting electrons emitted from the surface: for this
purpose the primary energy is typically 2÷10 keV and the beam can be focused into a spot
size of about 10 Å. Usually a TV screen displays the resulting image.
To convert the apparatus into a lithographic facility, the e-beam is controlled by a
computer through a position generator interface which allows to write any computer-defined
patterns on the resist, subsequently developed to form the desired structure. Typically
required energies for electron lithography are around 20 to 50 keV, which increases the size
of the beam spot. For instance, in the preparation of the X-ray mask used for the preparation
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of our samples, the exposure was carried out using a Leica EBMF-10 120 cs operating at 50
keV with a measured beam diameter of 50 nm:[3] the latter parameter limits the lateral
resolution of the writing process and as a consequence the step of exposure was set to 20 nm.
Figure 5.2. Schematic set-up of a scanning electron microscope (SEM).
There is also an intrinsic process deteriorating the lateral resolution of the lithographic
technique, i.e. the so-called proximity effect. The high energy electrons in the resist may be
laterally scattered and so the exposed area is bigger than the spot size: the main contribution
comes from the primary electrons elastically scattered, as the secondary electrons have much
smaller penetration length. As a consequence the exposure dose (expressed as amount of
charge delivered over surface unit, i.e. typically
C/cm2), which must be sufficient to
overcome the activation threshold for the used resist, must also be as limited as possible in
order to reduce the size of the undesired extra-volume exposed through this effect. At the
same time, low penetration depth of electrons may require high doses to fully expose the
whole profile of the resist, whose thickness can not be indefinitely reduced without
compromising the efficiency of the final lithographic steps (see discussion on etching or liftoff). Thus, it is clear how the success in the lithographic process rises from a delicate balance
of different parameters and requires calibrating tests in resist solution, thickness, exposure and
development.
79
5.1.2 X-ray Lithography
The exposure of a resist to X-ray radiation in a parallel replication process is the basis for
this technique. In general, a synchrotron radiation facility is used to expose the samples.
Similarly to the e-beam lithography method, the sample is covered by a resist layer with high
sensitivity in the X-ray wavelength region: for instance, PMMA (polymethylmethacrilate)
resin is used in this method with excellent resolution.
Between the radiation source and the sample, at a distance g (‘gap’) of few micrometers
above the resist layer, a mask is placed to define the pattern. It is generally agreed that the
mask is the most crucial element of this technique. The X-ray masks are often made of small
thickness (around 2 m) silicon carbide membranes (the ‘transparent’ support), covered by a
metallic pattern with the desired geometry fabricated by e-beam lithography. A high-Z
absorber material (such as gold, tungsten or tantalum) is used to prevent X-ray exposure of
the sample.
The choice of the energy range typically used (soft X-rays of 1-2 keV) in this technique
comes from a compromise between the possibility of uniformly expose the resist thickness
(the penetrating power of the photons increase with their energy) and the control on the
blurring in releasing the energy through photoemitted electrons, which, analogously to
proximity effects, increases with photoelectrons energy, i.e. with photon energy, affecting the
spatial resolution in transferring the mask design: higher energies (> 5 keV) are so used only
in deep lithography, when thick resist layers (> 5 m) need to be exposed. What’s more,
another lower limit comes from considering the diffractive effects which cannot be neglected
in this wavelength range using submicrometric apertures: these cause a spread of the beam in
the shadow region, which can be estimated to be
100 nm with
( g)1/2 in the Fraunhofer limit, i.e. about
= 1 nm and a typical value for g = 10 m, dissuading from the use of longer
wavelengths.
Integrating the here discussed limitations on the spatial resolutions with the respective
considerations done for the electron lithography, which is involved in the construction of the
X-ray mask, it is clear that the achievement of high lithographic resolution (< 100 nm) for our
samples requires big care in the mask design and calibration of all processes.
For the case of Au, using a photon of about 1.5 keV results in an absorption coefficient of
about 5 m-1 and a thickness of 280 nm is calculated to provide a contrast (∼0.6) useful for an
efficient X-ray exposure. Au is very easy to grow through electrolysis and so is often chosen
for the fabrication of high-resolution X-ray masks by means of electron lithography. It was
80
also the case of our X-ray mask, whose image is reported in Fig. 5.3: a silicon nitride (Si3N4)
membrane of 100 nm thickness, framed by a silicon wafer, was coated with a 30-nm-thick
base plating of Cr-Au in order to allow the successive electrolytic growth process of 350-nmthick gold, after the pattern transferring on the resist by means of electron lithography
exposure and subsequent development.[3] The mask is designed to obtain a matrix of
rectangular elements measuring about 1000 nm × 250 nm, with an interdot distance in both
directions of 250 nm. The area of the grid (see Fig. 5.3) is about 750 × 750 m2 and is
surrounded by the uncovered membrane: this implies that the final result (after X-ray
exposure of a positive resist through the mask, development, metal deposition and lift-off)
will be a square matrix of rectangular dots surrounded by a continuous film of the same
chemical composition and thickness. This may be an advantage, as the presence of an
equivalent unpatterned film is often desirable for reference measurements, but also a
disadvantage, when the magnetic probe cannot easily distinguish from patterned and
unpatterned contribution (as is the case of a probing spot size bigger than the patterned area).
Figure 5.3 A SEM image of the X-ray mask used for the replication of magnetic patterned
arrays: the Au grid is well visible.[3]
5.2 Sample preparation
As mentioned above, the fabrication of magnetic patterns was carried out at LILIT
beamline exploiting X-ray lithography in combination with a lift-off process. The main
feature of the L.I.Lit (Laboratory for Interdisciplinary Lithography) beamline, devoted to the
fabrication of structures at micro and nano resolution level by means of X-ray lithography, is
81
the wide lithografic window achieved by combining high-pass (berillum window) and lowpass (mirrors at increasing angle of incidence) filters; this allows the continuous change of the
spectral range of interest from the soft to hard X-ray region. The interfaced X-ray stepper (i.e.
the equipment for the alignment and the movement of the samples during the exposures)
allows the loading of a 6 inches wafer.
In the following we report in details the lithographic processes followed for the magnetic
samples preparation. Actually the values reported for the different parameters have been
slightly varied from sample to sample, in order to optimize the results of the process and also
to tackle the different conditions rising from one sample to the other: for instance the total
development time (subsequent intermediate controls of the resist aperture at the optical
microscope can be performed on non-chemically-amplified resists, like PMMA, which allow
to avoid underdeveloped or overdeveloped conditions) changed for each sample, possibly as a
function of the different exposure time.
A Si(100) naturally oxidized substrate is uniformly coated, by a spinning machine at 4000
rpm (rounds per minute), with a resist layer of about 400 nm (checked with profilometer). The
deposited resist is PMMA in a 2:1 solution with chlorobenzene and is then baked for 1 minute
at 170 °C, putting the substrate on a hot-plate. The resist-coated substrate is then coupled with
the mask, using a 10 m Al separator lain on the Si frame of the mask, in order to avoid
mechanical stress on the very delicate membrane. The whole object is mounted on the X-ray
stepper and exposed through a 1.5 keV X-ray beam with a nominal dose of 4000 mJ/cm2.
After exposure, resist is developed for 1 minute in MIBK:IPA=1:3 solution at room
temperature and rinsed in de-ionized water: the pattern formation on the resist is continuously
checked by means of the optical microscope. A final more accurate check is done by means of
a SEM apparatus and in Fig. 5.4 we report one of these images of the patterned resist.
Before permalloy deposition, a cleaning process of the resist apertures was performed by
means of remove ion etching (RIE), with 02 at 0.1 Torr, RF power of 50 W at 70 V of bias for
a 10 s interval: this should guarantee a good adhesion between the substrate and the permalloy
structures. Subsequently a layer of polycrystalline permalloy (Ni81Fe19) was evaporated over
the resist pattern in a HV chamber with the pressure in the range 3÷5 × 10-6 Torr: the nominal
deposited thickness was estimated by means of a quartz microbalance and is reported in the
Table 5.1 for different samples. In the same chamber a capping layer of Ge was also
evaporated on the top, in order to reduce in-air oxidation of the structures. Finally a lift-off
process was performed in a warm ultra-sonic acetone bath, thus removing all the residual
resist and releasing the isolated magnetic structures.
82
Figure 5.4 SEM image of the result of the development of the expose resist. The
transferring of the pattern seems good, even if the shape of the rectangles results smoothed
at the corners. SEM estimations for the size are in good agreement with mask design.
Samplea
Nominal
Thickness
Profilometer
b
measurement
c
X-ray scattering
estimation (θ-2θ
scan) d
(Py + Ge)
A
10 + 2.5
11
12
I
25 + 2.5
35
32
B
50 + 2.5
65
65
S (II)
80 + 2.5
110
-
C
100 + 2.5
125
-
Table 5.1. a) The samples are ordered with increasing thickness. The ‘non-homogeneous’
nomenclature comes from the fact that they have been prepared in 3 different ‘steps’ but
with analogous process: 1. I is the first (thin) sample; 2. S is prepared in a second moment
(S stands for ‘second’) to dispose of a higher thickness; 3. A, B and C are prepared together
to obtain intermediate thickness steps. b) This is the nominal thickness (nm) as monitored
by the quartz microbalance in the evaporation chamber: permalloy deposition and capping
Ge layer are reported separately. c) This is the total thickness as measured in air by a
profilometer (± 5 nm of accuracy) on the continuous part of the film. d) This is the
thickness estimated (± 5 nm) by X-rays scattered intensities modulation in the specular
condition, as explained in section 7.1.
The table summarises the different thickness (nominal and measured) of the prepared
samples. The results of different techniques are quite consistent and we may conclude that the
83
real thickness is about 15 % larger than the nominal one, leaving the samples in the expected
thickness order.
In Fig 5.5 we show the final lithographic result for the sample B: a large area and a small
area SEM images are presented. The former confirms that the uniformity over a quite large
area is preserved, while the latter shows some lithographic defects: the irregular edges of the
dots as well as some nanoparticles deposition, whose regular position in the matrix suggests
that their presence could be related to some X-ray diffractive effects due to overexposure.
Figure 5.5. SEM images of the permalloy rectangles of sample B at the end of the
lithographic process. A large area and a more-resolved small one are scanned.
In Fig. 5.6 SEM images of the sample A are reported as well. The interdot defects are
disappeared but the edge of the rectangles is still irregular and smoothed at the corners.
Finally in Fig. 5.7 at the left, we show the border of the patterned area, which indicates the
close presence of the continuous film. One can note how these rectangular elements have a
different aspect ratio from our rectangles. There are actually three distinct areas realised on
the same mask, each one providing a different submicrometric geometry: the other two
consist respectively of rectangles of 750 nm × 500 nm (left image), with 250 nm of interdot
distance, and of anti-triangles (i.e. triangles on the mask instead of the grid) of equilateral
shape and 1- m-period (right image). These two geometries are not discussed in this work
thesis, where we mainly concentrate on the high aspect ratio rectangles.
84
Figure 5.6. SEM images of the sample A.
Figure 5.7. SEM images of the other two areas of the sample provided with nanostructured
arrays. In the left image, the edge of the patterned area is scanned showing the presence of
the continuous film. In the third geometry (right image) the empty parts are the isolated
ones: these anti-dot geometries have also attracted interest as possible candidates for
ultrahigh density storage.[6]
[1] J.R. Sheats, B.W. Smith (Eds.), Microlithography Science and Technology, Marcel
Dekker, NewYork, 1998, and references therein.
[2] P. Candeloro, A. Gerardino, E. Di Fabrizio, S. Cabrini, G. Giannini, L. Mastrogiacomo,
M. Ciria, R. C. O’Handley, G. Gubbiotti, and G. Carlotti, Jpn. J. Appl. Phys., Part 1 41, 5149
(2002).
[3] A. Gerardino, E. Di Fabrizio, A. Nottola, S. Cabrini, G. Giannini, L. Mastrogiacomo, G.
Gubbiotti, P. Candeloro, and G. Carlotti, Microelectron. Eng. 57-58, 931 (2001).
[4] http://www.elettra.trieste.it/experiments/beamlines/lilit/index.html
[5] http://www.TASC.INFM.IT
[6] L. J. Heyderman, F. Nolting and C. Quitmann, Appl. Phys. Lett. 83, 1797 (2003).
85
86
Chapter 6
Computational and experimental techniques for
the study of magnetic patterns
In this chapter we describe both a computational and an experimental technique for the
study of arrays of magnetic elements. These are the tools that have been used to characterize
the magnetic structures described in the previous chapter. The results are then discussed in
chapter 7.
We start with the micromagnetic theoretical approach which has proven to be a valuable
method to predict the detailed magnetic configuration for geometrically defined magnetic
structures immersed in an external field.
Then we describe the features of resonant scattering of polarized soft X-rays as a possible
tool to investigate the magnetisation reversal in a matrix of dots. This technique couples the
advantages of structural analysis to sensitivity to electronic structure. The former is inherent
to X-ray scattering, the latter the consequence of a spectroscopic response to resonant coreelectron excitations where optical constants depend on the local magnetic moment of the
scattering ion if polarized light is used. In a magnetic structure with an appropriate order
parameter, one can match Bragg's law at a photon energy that resonantly excites an inner shell
electron, simultaneously probing structural and magnetic properties, element selectively.
Magnetic contributions to the scattering amplitude are enhanced when the electron excitation
directly involves those orbitals that define the magnetic properties of the absorbing ion, as is
the case for the 2p to 3d excitations in 3d transition metals, in analogy with the already
discussed magnetic dichroism in absorption (see chapter 2).
6.1 Micromagnetic simulations
The ability of micromagnetics[1] to obtain a theoretical and computational approach to
87
understand the magnetic behaviour of magnetic materials has been widely used to address the
magnetization reversal in patterned dots or elements with submicrometric dimensions, with
particular emphasis on the effects of the shape, size, or material of the elements. In these
studies, each magnetic element is usually divided into a Cartesian array of parallelepiped
cells, and a magnetization vector Mi at the center of each cell is defined (with |Mi| = MS, the
saturation magnetization of the material). The equilibrium distribution of magnetization for a
given value of the applied magnetic field is then found by numerically integrating the coupled
Landau–Lifschitz–Gilbert equations of each discrete cell (denoted by i), that govern the
magnetization dynamics:
dM i
γα
i
i
= −γM i × [H eff ] − (
)M i × (M i × [H eff ] )
dt
MS
(6.1)
where
is the electron gyromagnetic ratio,
is a damping constant, and Heff is the pointwise
effective magnetic field. The latter is defined as [Heff]i = energy density and
0
0
-1
E/ Mi, where E is the average
the vacuum permeability. Heff includes all relevant sources of magnetic
field, such as exchange, crystalline anisotropy, demagnetization (self-magnetostatic), and
Zeeman (applied field) energy terms, which are evaluated within each particular case. For a
given applied field, the integration continues until a control point is reached. A control
point event is usually fixed as a threshold value for the point-torque |M × Heff |/MS2, under
which an equilibrium state is considered to be reached.
In order to consider |Mi| = MS within each cell, the size of each individual cell is usually
taken to be of the order of the exchange length. The exchange length, lex = (A/ 0MS2)1/2, is the
distance where atomic exchange interactions dominate the magnetostatic fields (A being the
exchange constant), and is rather similar for most magnetic materials (few nanometers). Thus,
a nanostructure with a size of the order of lex should have a uniform magnetization state, i.e. a
‘‘true’’ single domain state.
The simulations to be discussed in this thesis were performed using the NIST OOMMF
software,[2] which is an extensible public domain project: a list of the numerous scientific
publications using the code is available on the web site.
We run the stable 1.1b2 release, where the micromagnetic problem is impressed upon a
regular 2D grid of squares, with 3D magnetization spins positioned at the centers of the cells.
Note that the constraint that the grid be composed of square elements takes priority over the
requested size of the grid. The actual size of the grid used in the computation will be the
nearest integral multiple of the grid's cell size to the requested size. So the magnetic dot is
88
mapped as a grid of parallelepipeds whose height corresponds to the thickness of the sample.
The square basis corresponds to the size of cell, which is a parameter to be set in simulations:
we keep it lower than (or equal to) 10 nm for exchange length considerations. So the
approximation of using a constant magnetization inside each parallelepiped, whose height
could considerably exceed the exchange length for some of our dots, is introduced.
The shape of particle to be simulated is determined as a 2-color bitmap file by OOMMF
(white corresponds to the void and non-white corresponds to the magnetic material), where
each pixel of map represents a single cell. The program offers the possibility of designing
simple shapes, but it can also be fed with external bitmap files. Thus we use directly the SEM
images, properly modulated in colour and rescaled, to better account the dot geometry as well
as the presence of lithographic defects on the edges of the particle, so improving the quality of
the simulation.
The used material parameters are saturation magnetisation MS = 8 × 105 A/m, exchange
constant A = 8 × 1012 J/m, zero magnetocrystalline anisotropy (due to the polycrystalline
nature of the dots) and damping parameter
= 0.5, which determines the relaxation of the
magnetization into its local effective equilibrium field direction. These values for the
permalloy were found to give good agreement with MOKE measurements in Ref. [3], where
the authors used our same permalloy target for deposition. The mesh size and the torque value
are chosen to be respectively 5 nm and 10-5 in early single dot calculations, and then 10 nm
and 10-4 for multiple-dots time-demanding ones, after a check that such relaxed constraints
did not affect significantly the results.
For each investigated sample, the equilibrium magnetization configuration is calculated
and saved for different values of the applied field covering the range of magnetization
reversal and saturation. The hysteresis loop, corresponding to the average magnetization
(actually the distinct averages of the three components of M), is provided directly by the
OOMMF program.
6.2 X-ray resonant scattering: principles and experimental
concerns
6.2.1 XRMS
In this section we introduce the soft X-ray resonant magnetic scattering technique without
89
providing an in-depth theoretical introduction (for which one can refer to Ref. [4, 5] and
references therein), but simply underlining the main physical concepts and finally coming to
the formula of Hannon useful to interpret the magnetization dependence of the scattered
intensity.
Besides the XMCD and XMLD techniques discussed in the second chapter and based on
X-ray absorption, also X-ray scattering experiments, both non-resonant and resonant, are used
to obtain magnetic information.[6] In radiation scattering one photon exists in both the initial,
|i, ωin>, and final state, |f, ωsc> - where |i> and |f> represent the initial and final electronic
states of the scattering ion and ωin and ωsc the energies of the incident and scattered photon
- and we are dealing with second-order optical processes because two interactions are
required: the transition from |i, ωin> to an excited intermediate electronic state |I> and deexcitation of this state to |f, ωsc>, where the intermediate state may contain no photon (in this
case the incoming photon is absorbed in the excitation process and the scattered photon is
emitted in the de-excitation) or two photons (in this case the scattered photon is created
already in the excitation and the incoming photon is annihilated only in the de-excitation).
Through a perturbative calculation it may be found that the matrix element yields for the
scattering probability a term responsible for anomalous dispersion
T fi =
2π
f H' I I H' i
I
ε I − εi
2
δ (ε f − ε i )
(6.2)
where ε is the energy of the (electron + photon) system (namely εi = Ei + ωin, εf = Ef + ωsc,
and εI = EI or EI + ωin,+ ωsc whether the intermediate state contains zero or two photons)
and H' stands for H'em or H'ab, i.e. the perturbation in the Hamiltonian for the emission or
absorption processes, depending on the intermediate state.
The non-resonant magnetic X-ray scattering arises directly from the interaction of the
electromagnetic field of radiation with the spin moment of uncompensated electrons: its
amplitude is almost independent from the binding energy of the electrons, since the name of
non-resonant magnetic term, and it is much weaker than conventional charge scattering
mostly in the soft x-ray region, with a reduction factor of ( ω/mc2) compared to that. A
pioneering experiment by De Bergevin and Brunel,[7] using a conventional source,
demonstrated in 1972 this magnetic dependence of X-ray scattering, taking advantage of the
fact that in an antiferromagnetic system as NiO the peak of magnetic origin is separated by
the charge peak and so easily identified: in fact the antiferromagnetic order results in a
90
superstructure of double periodicity.
On the other hand, the resonant magnetic scattering happens when the energy of photon is
tuned for the excitation of a core electron into an empty valence state: the resonant effect is
readily seen by the presence of the energy terms in the denominator of Eq. (6.2) and in this
case the magnetic effect can be of the same magnitude compared to the charge effect, in
analogy to what happens for XMCD in absorption, as the transition probabilities between the
states |i>, |I> and |f> may depend upon the relative orientation of the local magnetic moments
and of the polarization of the incident and scattered photons. In the dipole approximation
(labelled E1), the resonant scattering additional component to the scattering amplitude is
given to the Hannon's notation[8]
(
)
f E1res ∝ eˆ ∗f ⋅ eˆ i [F11 + F1−1 ]
− i (eˆ ∗f × eˆ i ) ⋅ m[F11 − F1−1 ]
+ (eˆ ∗f ⋅ m )(eˆ i ⋅ m )[2 F10 − F11 − F1−1 ] ,
(6.3)
where m is the unit vector of the quantization axis defined by the atomic magnetic moment, ei
and ef are the polarization vectors of the incoming and outgoing photon. The F1∆M are made of
an energy-resonant denominator and of matrix elements which couple, via the dipole operator
D, the ground state |0> to the excited state |η∆M > with a change ∆M of the magnetic quantum
number of (+1, 0, -1):
F1M ∝
0 Dη
η
2
Eη − E 0 − ω − iΓη / 2
.
(6.4)
So F11 and F1-1 describe the excitation provided by a circularly polarized photon (positive
or negative elicity) which propagates along the quantization axis, and F10 the case of a photon
with the linear polarization parallel to the quantisation axis, as discussed in dipole
approximation selection rules [see Eq. (2.5)] for absorption. Hence the presence of large
magnetic effects at core resonances located in the soft X-ray region is obtained by the direct
involvement, as intermediate states of the process, of the orbitals which define the magnetic
properties of the atom, which means the use of p
3d resonances for the magnetic transition
metals, which completes the analogy with the magnetic dichroism in absorption.
The first term of Eq. (6.3) is independent of magnetization and gives the resonant
contribution to the charge scattering amplitude. It produces strong variations of the scattering
91
intensity when the photon energy is scanned across a resonance and is sometimes called
anomalous scattering. The second and third terms depend on the relative orientation of light
polarization and magnetization and vanish if the latter is randomly oriented. The second term
consists of a polarization dependent geometrical factor (eˆ ∗f × eˆ i ) ⋅ m multiplying the
difference (F11 - F1-1) between the resonant optical responses of the medium for opposite
magnetization-to-elicity orientation. We will discuss later the conditions for the geometrical
factor to be non-vanishing. The linearity in m indicates the sensitivity of this term to the
orientation of the magnetization which can be useful to probe the ferromagnetic order. The
third term is quadratic in m, and so it is sensitive to the direction of the magnetization but not
to its sign, making its contribution observable for antiferromagnetic order. Anyway this term
contains the difference [2F10 - (F11 + F1-1)] which is directly related to the observation of
dichroism in the absorption of linearly polarized x-rays and it can be neglected in the case of
metallic transition metals.
Since the discovery of these strong magneto-optical effects, soft X-rays experiments have
been performed in both the specular reflectivity mode and the Bragg diffraction mode:[9] the
latter experiments are performed on multilayers where the chemical modulation has an
appropriate period in the nanometer range (see for instance Ref. [5]). In fact, while soft Xrays have prohibitively long wavelengths for Bragg diffraction from a crystal lattice, they
match perfectly with the nanometer length scale of such magnetic multilayers and of periodic
domain structures.
6.2.2 Experimental scattering geometries
The intensity of X-rays elastic scattering as a function of the incident and scattering angle
is conventionally used to analyse the structural properties of a system. The equation (6.3)
shows for a magnetic sample how the relative orientation between the polarization of the
incoming and outgoing photon determines the components of the magnetization contributing
to the scattering amplitude. We want now to describe the geometry of our measurements
where all these ingredients play a significant role.
A sketch of the experimental geometry is given in Fig. 6.1: we will identify the z axis as
the normal to the sample surface (xy plane), and xz as the incidence plane (containing the
incoming photon momentum and the sample normal). The scattering geometry is coplanar,
i.e., the scattering plane coincides with the incidence plane. In such conditions for an elastic
scattering process the modulus and the components of the momentum transfer vector q = Kout
92
– Kin, where Kin,out are the wave vectors of the incoming and outgoing photons of wavelength
λ, are
4π
sin (θ ),
λ
4π
q x = q sin(∆θ ) =
sin (θ )sin( ∆θ ),
λ
4π
q z = q cos(∆θ ) =
sin (θ ) cos(∆θ ).
λ
q = K out − K in =
(6.5)
where θ = θD/2 and ∆θ = θS - θ (qy = 0, i.e., coplanar condition). The specular conditions are
satisfied by θS = θD/2 = θ : the angle ∆θ, representing the deviation from the specular
condition, is zero and the momentum transfer vector is oriented along the normal to the
surface plane.
Figure 6.1. Sketch of the X-ray scattering set up. The measurements are performed in
coplanar geometry, applying the magnetic field either parallel (longitudinal geometry) or
perpendicular (transverse geometry) to the scattering plane.
The control of the incident and scattering angles is achieved by a two-circle reflectometer:
the concentric arms rotate independently the sample surface around the y axis, so determining
θS, and the detector position, i.e. θD. Every q = (qx, 0, qz) point of the reciprocal space
93
corresponds univocally to the choice of θS and θD. Different type of scans can be performed
by accessing different paths of the reciprocal space. In our measurements two particular types
of scans are performed: the specular reflectivity measurement and, more often, the scan of θS
with constant θD (fixed detector). In the first case θD and θS are scanned with the condition θS
= θD/2, the so-called θ-2θ scan, which results in varying qz holding qx = 0, so probing the
vertical modulations of the system: in fact one can find in the case of multilayers the Bragg
peaks originating from the constructive interference of the radiation scattered by the different
layers. In the second case, the so-called rocking scan, only the sample is rotated and holding
θD constant fixes the vector q during the scan: as qx and qz are equal respectively to q⋅sin(∆θ)
and q⋅cos(∆θ), small variations around the specular condition can be seen as a scan of qx
keeping qz constant and so the Bragg condition is satisfied when the sample provides a lateral
periodicity in the surface plane along the x axis, as can be the case for our samples made of
periodical arrays of dots if we align a symmetry axis with x direction. As for a diffraction
grating, n-th order peaks correspond to qx = 2nπ/d, where n can take positive and negative
integer values and d is the order parameter in the x direction. Measuring the angle for the first
Bragg peak (n = 1), and using equation (6.5) for qx, one can easily find the relation for the
order parameter d:
d=
λ
1
.
2 sin (θ )sin (∆θ )
(6.6)
Due to the sensitivity of XRMS also to the magnetic modulations and not only to the
structural ones, diffraction peaks can exist which are of pure magnetic origin. For example, in
the case of specular reflectivity from magnetoresistive multilayers, antiparallel magnetic (or
AF = antiferromagnetic) coupling appears as an extra intensity in the half-order position,[10]
as the vertical superstructure has a parameter d which is double compared to the chemical
period; on the contrary, the chemical period equals the magnetic period in the case of parallel
(FM = ferromagnetic) coupling and the magnetic peak results superimposed to the charge
peak. Moving to the lateral periodicity, analogously we can pick up correlation lengths within
the array other than the structural ones, by properly varying qx: a way of probing magnetic
correlations between pairs of rectangles, for instance, is to set qx at half the value of the first
order peak of the rocking scan, so that
94
qx=
1
(2π / d ) = π / d = 2π / d ' ;
2
d ' = 2d .
(6.7)
This corresponds to introducing a new order parameter d’ = 2d, or, as often said, to taking
n = ½ in the equation qx =2nπ/d (half order position with respect to the order parameter d).
Once the Bragg conditions for the FM or the AF coupling are found, an external magnetic
field can be applied to record the evolution of the scattered intensity, so tracing the field
dependence of the magnetic order. When the field is applied along the x direction (H parallel
to the scattering plane) we speak of longitudinal geometry and of transverse geometry for the
field applied along the y direction.
6.2.3 Instrumentation and polarization selection with synchrotron
radiation
The prepared samples have been measured by use of XRMS technique on two different
beamlines equipped with two distinct reflectometer end-stations. One is the X-ray metrology
beamline 6.3.2 at the Advanced Light Source (ALS) synchrotron radiation facility
(Berkeley),[11] and the other is the Circular Polarisation beamline at ELETTRA synchrotron
(Trieste).[12] In the second case the used reflectometer is the one developed by M. Sacchi and
co-workers[13], from whose collaboration this research activity arises. The magnetic fields
are applied by means of a horseshow electromagnet, calibrated in air and supplying up to
~1000 Oe. Conventional photodiodes are used with different slits aperture and then angular
acceptance.
By making use of the synchrotron radiation source, we have the possibility to perform
measurements with photons of different polarization, so determining which components (Mx,
My) of the magnetization contributes to the scattered intensity following equation (6.3): we
neglect the Mz component of the magnetization out of plane as the magnetization prefers to lie
in the thin film plane, mostly when the magnetic field is applied within it, as we do.
•
Linear polarization
In agreement with the longitudinal Kerr effect for visible light, the scattering from a
magnetic medium of linearly polarized X-rays with the electric vector normal to the incident
plane (s-polarization) provides a rotation of the polarization direction of an angle proportional
95
to Mx. In this way the scattered radiation has a non-zero component of the polarization in the
scattering plane, whose amplitude is related to the value of the magnetisation projection along
the vector (eˆ ∗f × eˆ i ) (channel s p of the magnetic scattering) and the Kerr effect consists in
monitoring this polarization rotation by means of a polarization analyser.
In the case of magnetic multilayers, each layer of magnetic material can contribute to the
s
p channel with a phase yielding the sum of an optical path term and of a term ±π, where
the sign depends on the relative orientation of the magnetization of the layer: so the case of
AF coupling defines a superstructure resulting in a AF Bragg peak.
Carrying the analogy to the in-plane periodicity, we will try to use the s-polarization to
probe the AF order along the x direction, with the sensitivity to the Mx component of the
magnetization.
Similar considerations can be made for the p-polarization (where the electric vector is
inside the incident plane), with the p s channel sensitive to the AF order for Mx. But in this
case the situation is complicated by the fact that one should also consider the p
p channel,
which results in a non-zero component of the vector (eˆ ∗f × eˆ i ) along y axis, i.e., a contribution
of the scattering intensity depending on the sign and value of My.
•
Circular polarization
Third generation synchrotrons are equipped with insertion devices which can provide
photons of elliptical polarisation: this can be decomposed into a circular polarisation part and
a linear polarisation part. By analysing the geometrical factor (eˆ ∗f × eˆ i ) ⋅ m , a measurement
making use of the circular polarization is sensitive to the value of the magnetization and to the
magnetic order (AF and FM) along x.
[1] A. Aharoni, Introduction to the Theory of Ferromagnetism, (Oxford, New York, 1996).
[2] http://math.nist.gov/oommf/
[3] http://www.elettra.trieste.it/science/highlights/2001-2002/elettra_highlights_2001-2002pg035.pdf. P. Candeloro, L. Businaro, E. Di Fabrizio, M. Conti, G. Gubbiotti, G. Carlotti, A.
Gerardino, ELETTRA Research Highlights 2001 - 2002, 35, Magnetic Systems.
[4] J. M. Mariot and C. Brouder, Magnetism and Sinchrotron Radiation, Springer, Lecture
Notes in Physics, Vol. 565 24-59 (Eds. E. Beaurepaire, F. Scheurer, G. Krill and J.-P.
Kappler, 2001).
[5] C. Spezzani, Ph.D. Thesis, Diffusion résonante des rayons X polarisés et couplage
magnétique dans les multicouches Co/Cu, Université Paris XI, 2003.
96
[6] D. Gibbs, Synchrotron Radiation News 5 (5), 18 (1992).
[7] F. De Bergevin and M. Brunel, Phys. Lett. A39, 141 (1972).
[8] J. P. Hannon, G. T. Trammell, M. Blume and D. Gibbs, Phys. Rev. Lett. 61, 1245 (1998).
[9] M. Sacchi and C. Hague, Surf. Rev. Lett., 9, 811 (2002).
[10] J. M. Tonnere, L. Sève, D. Raoux, G. Souillié, B. Rodmacq, and P. Wolfers, Phys. Rev.
Lett. 75, 740 (1995).
[11] J. H. Underwood, E. M. Gullikson, M. Koike, P. C. Batson, P. E. Denham and R. Steele,
Rev. Sci. Instru. 67, 3343 (1996).
[12] http://www.elettra.trieste.it/experiments/beamlines/polar/index.html
[13] M. Sacchi, C. Spezzani, P. Torelli, A. Avila, R. Delaunay and C. F. Hague, Rev. Sci.
Instr. 74, 2791 (2003).
97
98
Chapter 7
XRMS results: structural analysis, magnetic
response and comparison with computation
In this chapter we report the main experimental results obtained on the matrix of
rectangular permalloy dots by means of XRMS. We start with a brief summary of the
technique, and then show, for different geometries, the obtained field dependent results. The
results of micromagnetic calculations are discussed in comparison with the experimental data.
7.1 Energy and angular dependence of the diffuse scattering
All the experiments discussed here were done with circularly polarized light, unless
otherwise specified. The convention for axis identification is the one used in Fig. 6.1.
Figure 7.1 shows an example of energy dependent specular reflectivity measured for two
opposite values of the applied field (H = ±300 Oe, longitudinal geometry) with the photon
beam illuminating the continuous unpatterned area of the permalloy film: the permalloy is
known to be a soft magnetic material and for thin polycrystalline films the magnetization can
be easily and isotropically aligned in-plane under the influence of a small external field (few
Oe). The energy range covers both the Fe 2p (700–730 eV) and Ni 2p (850–880 eV)
resonances. The corresponding magnetic signal (difference between the two curves for
opposite magnetizations) is given by the dashed line at the bottom and comes from the
different magnetization-to-elicity orientation, the former being inverted by the field while the
latter is kept fixed.
From this measurement it is evident that resonant X-ray scattering technique offers
interesting features like element selectivity and sensitivity to electronic properties: in fact the
energy dependent excitation promoted at the resonance from core shell levels to empty
99
conduction states makes it a spectroscopic tool of investigation, sensitive at the magnetic
properties of these final states as well. In this work we are mainly interested in monitoring the
magnetization of homogeneous magnetic dots of permalloy, where the magnetic moments of
neighbouring Fe and Ni atoms are known to have the same orientation due to ferromagnetic
coupling: so, from now on, we decide to fix the photon energy at 707.5 eV, corresponding to
the maximum magnetic signal of the Fe L3 edge region (see Fig. 7.1). Anyway it must be
underlined that for patterns of heterogeneous multilayers, which may be interesting structures
for the magnetoresistive applications, the element selectivity through the proper photon
energy could add the capability of monitoring the layer-dependent magnetization.
Figure 7.1. Specular reflectivity (θS = 9°) of elliptically polarized X-rays as a function of
their energy over the range including the 2p resonances of Fe and Ni. A field of 300 Oe
(positive and negative) is applied along the x axis. The difference observed for opposite
orientations of the field is shown as a dashed line.
Figure 7.2(a) shows the result of a θS scan at fixed θD = 12.5° (rocking scan), with the
long side of the rectangles oriented along x. By making use of equation (6.5) the intensity is
plotted versus qx, and one can observe the n-th order Bragg peaks, rising from the in-plane
charge modulation along x. Both positive and negative (n < 0) peaks are shown up to the 9th
100
order, with their symmetrical position around the specular reflection. The position of the first
order peak is qx = 5.036 µm−1, corresponding to d = 1.247 µm, in excellent agreement with
the structural parameters given in chapter 5.
a
Figure 7.2. Diffuse intensity versus qx (rocking scan, see text). In (a) rectangles are aligned
with their longer side parallel to the scattering plane: the position of the first order peak
corresponds to d = 2π/qx = 1.247 µm. In (b) rectangles are aligned with their shorter side
parallel to the scattering plane and d = 0.53 µm.
We have performed a similar measurement by aligning the rectangles with their short side
in the scattering plane. The rocking scan in Fig. 7.2(b) gives the first order peak at qx = 11.897
µm−1, corresponding to a horizontal order parameter of 530 nm, to be compared to the
nominal 550 nm of the pattern design. The appearance of weak structures right in between
Bragg peaks of the grating deserves some comments. We have verified, by introducing
appropriate filters in the beam path, that they originate from second order light from the
monochromator, i.e., in this case, a contamination at 1415 eV photon energy. This implies
that, calculating qx for 707.5 eV, they appear at half of the correct value.
In Figure 7.3 we show the effect of the magnetization on the diffused scattering: two
rocking scans are measured with the long side of the rectangles parallel to x and θD = 10° and
with opposite magnetic field applied along x. Both the calculated difference and asymmetry
(difference of the two curves divided by their sum) show that the magnetic contributions to
the scattering intensity hold the same features of the rocking scan, which is not surprising as
the magnetisation modulates like the structure, once it is aligned inside the dots.
101
b
Scattered Intensity (a. u.)
Asymmetry
H = +240 Oe
H = -240 Oe
difference
100
10
1
0.1
4.0
4.5
5.0
θS
5.5
6.0
4.0
4.5
5.0
θS
5.5
6.0
0.3
0.2
0.1
Figure 7.3. Diffused intensity versus θS at fixed θD = 10°. A difference is found for two
opposite values of the magnetic field (H= ±240 Oe, longitudinal geometry). In the bottom
we report the asymmetry.
Figure 7.4 shows the result of an energy scan like that of Fig. 7.1, but with the sample
angle set to match the first order peak of the diffuse scattering at 707.5 eV. The shape of the
energy dependent scattered intensity is quite different from the specular reflectivity curves. In
particular, the intensity variation across the edge region is much stronger (more than two
orders of magnitude in Fig. 7.4, compared to a factor 5 in Fig. 7.1), reflecting the fact that, for
fixed values of both θD and θS, the Bragg condition qx = 2π/d is satisfied exactly only at one
wavelength. The shape of the magnetic contribution, however, is similar to that of Fig. 7.1.
Up to now, we have firstly illustrated the effect of the magnetization on the energy scan
(fixed geometry, varying the energy), so to choose a good energy to enhance such effect
(707.5 eV, i.e. Fe L3 edge). Then we have shown the effect of the structural modulation on the
scattered intensity (fixed energy, varying θS) in order to check the position of the Bragg order
peaks. In the following we will monitor the scattered intensity scanning the magnetic field at a
proper fixed energy and for different fixed scattering geometries as, for example, the n-th
order Bragg peaks, which can yield a strong magnetic contribution (Fig. 7.3).
102
Scattered intensity (arb. units)
400
350
300
st
1 order Bragg peak
Fe 2p resonance
250
200
H = + 360 Oe
H = - 360 Oe
Difference
150
100
50
0
-50
-100
660
680
700
720
740
Photon energy (eV)
Figure 7.4. Scattered intensity versus photon energy across the Fe 2p resonance. Conditions
are as in Fig. 7.1, but with qx = 2π/d (n = 1) instead of qx = 0.
In Fig. 7.5 we show the specular reflectivity measurement where the scattering intensity is
recorded as a function of the sample angle θS. In this case, instead of reversing the
magnetisation applying an opposite field, it was, equivalently, the elicity of the circularly
polarized photons to be changed. The difference of the two curves and the asymmetry are
plotted too. The intensity reduces at high angles and similarly does the magnetic contribution
(see ‘difference’ curve). This must be kept in mind when measuring the scattered intensity at
the Bragg peaks, whose value is already reduced compared to the specular reflectivity (e.g.
see Fig. 7.2): what’s more, going to high angles for θD means that the peaks in the rocking
scan get closer to one another and finally overlap due to their finite size, which is an
undesired effect. On the other hand, the more grazing is the incident angle the larger is the
part of the beam impinging outside our patterned area, therefore contributing to the
background but not to the magnetic signal. A typical beam size at the sample position is about
103
300 µm horizontal by 100 µm vertical. In these circumstances the photon spot could be placed
entirely onto the patterned area for a sample angle θS greater than 8°. A good compromise for
measuring our samples is the range θS = 4-10°, and looking at the modulation of the
magnetisation-related asymmetry (difference divided by sum) in Fig. 7.5, we often use θS =
5°.
Scattered intensity (arb. units)
1000
elicity +
elicity difference
sum
asymmetry
100
10
1
Scan θ/2θ
hν
ν = 707.5 eV
0.1
0.01
0.001
5
10
θS
15
Figure 7.5. Modulations in the scattered intensities in a θ/2θ scan, inverting the elicity of
the circularly polarized photons. The difference represents the magnetic contribution.
In analogy with the study of periodical multilayers, the oscillations in the scattering
intensity can be used to estimate the thickness of the deposited permalloy layer, as they come
from the interference between the waves scattered at the surface and the ones scattered at the
interface between the permalloy and the substrate: from the angular positions θn,n+1 of the
relative maxima of two consecutive oscillations, which satisfy (n + 1)λ = 2t sin θ n +1 and
nλ = 2t sin θ n , one can estimate the thickness t of the deposited layer:
t=
λ
1
.
2 sin θ n +1 − sin θ n
(7.1)
104
Whenever this estimate has been done we have reported the value in the table 5.1, to be
compared with the others. The different maxima positions of the oscillations in reversing the
elicity-to-magnetization orientation, show the effect of the magnetization on the dielectric
tensor and finally on the optical path of the light.
7.2 Magnetic field dependence of the scattered intensity
Scattered intensity at fixed θD, θS, and ω (707.5 eV) was measured as a function of the
applied field. Under these conditions, the variation of the scattered intensity with the applied
field gives a measure, on a relative scale, of the local magnetic moment of Fe projected along
the x axis when circularly polarized light is used.
7.2.1 Comparing first and zero order geometry
Figure 7.6 compares three examples of such measurements (θD = 18°) performed on the
sample I with the long side of the rectangles and the applied field both oriented along x. The
intensities have been arbitrarily rescaled between −100 and +100 for each curve.
The square symbols are the result of a specular reflectivity measurement (θS = 9°) on the
continuous permalloy film framing the patterned area. The measured coercive field Hc is 5±1
Oe and remanence is in the order of 60%. These values are typical of a thin polycrystalline
permalloy film, which can be considered a soft magnetic material: the magnetisation is easily
aligned (saturation is already reached at about 20 Oe) but it rearranges into domains when the
field is switched off, so to minimize the magnetostatic energy.
Open circles in Fig. 7.6 represent specular reflectivity from the patterned area (zero order
scattering, qx = 0), giving the average magnetization of Fe over the illuminated area.
Remanence in this case is close to unity, but two components can be clearly identified in the
hysteresis curve. We have modelled this and other similar curves by summing two almostsquare loops of adjustable width and height, in order to estimate the coercive field and the
relative importance of each component. The narrow loop represents roughly 30% of the total
intensity variation as a function of H and its coercive field is Hc = 11 ± 3 Oe. The second loop
105
has a larger Hc of about 90±10 Oe.
Scattered intensity (arb. units)
100
50
Sample I
Unpatterned Permalloy
θS = 9°
Pattern, zero-order
θS = 9°
st
Pattern, 1 -order
θS = 9.26°
0
hν = 707.5 eV
-50
θDetector = 18°
-100
-400
-200
0
200
400
Applied field (Oe)
Figure 7.6. Scattered intensity as a function of the applied field at the Fe 2p resonance. The
intensity has been arbitrarily rescaled between −100 and +100 for each curve. Squares:
specular reflectivity from the continuous permalloy film framing the patterned area. Open
circles: specular reflectivity (zero order) from the patterned area. Line: first order scattering
from the patterned area.
Finally, the continuous line was obtained by matching the first order peak (θS = 9.26° , qx
= 5.04 µm−1), with the long side of the rectangles oriented along x. The hysteresis curve
displays a single loop with almost complete remanence (90–95%) and a coercive field of 90 ±
3 Oe.
By comparing these curves, we can easily identify the hysteresis on the first order
scattering peak with the broader component measured at zero order. The sides of the
hysteresis loop are rather slanted, with a large difference between coercive (90 Oe) and
saturation (230 Oe) fields. Therefore, the magnetization reversal does not take place as an
abrupt switching as a function of field, but is characterized by intermediate magnetic
configurations. The hysteresis loop is measured at the first order scattering peak, which means
that these configurations repeat themselves in a regular way throughout the pattern and must
be related to the specific shape of the rectangles. The edges of the dots act as pinning centers
106
for magnetization reversal, determining an increased coercive field with respect to the
continuous film. Moreover, magnetic poles are likely to form at the edges of the rectangles,
particularly at the corners. The demagnetizing field associated to these poles can be large
enough to be responsible for the slanted sides of the hysteresis loop, indicating the difficulty
of reaching saturation in the patterned area compared to the continuous film. The high
remanence that we observe after saturation implies that, in our sample, the zero field state is
characterized by a rather homogeneous magnetization aligned along x within each dot,
excluding the formation of closure domain patterns: this may be explained by the fact that,
once the magnetization is forced along the longer side of the dot, its elongated shape may
favour the stability of such configuration even when the field is switched off. This is known
to happen for prolated ellipsoids, to which our rectangles can be roughly approximated,
mostly when the size is sufficiently reduced to neglect the possibility of domain formation.[1]
The hysteresis curve at zero order measures the field dependence of the average Fe
magnetization over the entire illuminated area, while at first order the hysteresis measures
only those changes which repeat regularly over the pattern. The presence of a narrow
component in the zero order, but not in first order, hysteresis curve (Fig. 7.6) indicates that
part of the illuminated sample behaves like the unpatterned film. The slight differences
(higher coercivity and remanence) are ascribable to the different geometry of the probed part
of the continuous film which is interrupted at the border of the patterned area. We conclude
that, although the sample angle was set at a relative high angle (θS = 9°), the zero order
measurement is affected by some of the photon beam spilling over the continuous permalloy
film framing the pattern.
As a straightforward confirmation to this we report in Fig. 7.7 the hysteresis loops
measured at specular conditions on the patterned area with increasing sample angles: as the
area illuminated by the beam spot reduces, the narrow component of the hysteresis decreases
and finally disappears at high angles. Also note the reduction of the recorded intensity and the
effect of the noise on the signal in last graph.
107
Sample A
Scattered intensity
Specular meas.
θS = 10°
θS = 5°
4000
11.4
θS = 17°
11.2
40
11.0
3000
35
-200 -100
0 100 200
Oe
-200 -100
0 100 200
Oe
-200 -100
0 100 200
Oe
Figure 7.7. Specular reflectivity as a function of the applied field: the relative intensity is
maintained between the different geometries.
To conclude, a result that comes out clearly from Fig. 7.6 is that, by choosing to work at
the first order Bragg peak, we automatically exclude all contributions that do not come from
the regular pattern, cleaning up the signal from spurious sources.
7.2.2 Demagnetizing field effects
In a magnetic medium with no magnetocrystalline anisotropy, two different fundamental
interactions must be considered in order to interpret the possible magnetic configurations: the
exchange interaction, which is the short range interatomic interaction responsible of
ferromagnetism, and the dipolar interaction which dominates on a long range dealing with the
energy of the magnetic dipoles immersed in the total field. To this field can contribute also
relevantly the magnetic field formed by the other magnetic dipoles in the medium, which is
called the demagnetizing field, as it is responsible of the domain formation.
We now investigate such effects on our dots recording the hysteresis at first order Bragg
peak to single out the contributions coming from the regular magnetic structure: compared to
previous measurements, we vary firstly the geometry of the experiment (the field is applied
along the short axis of the rectangles) and then increase the thickness of the dots.
•
Shape anisotropy
A different magnetic response is expected when the field is applied along one side or the
other of the rectangles because they are highly asymmetric. Figure 7.8 compares two
hysteresis curves for the sample I, both at the first order Bragg peak, obtained with the field
108
aligned along the major and minor sides of the rectangles always using longitudinal geometry
(field parallel to the scattering plane). The short side behaves as a hard axis for the sample
magnetization, and we are not able to reach magnetic saturation in this direction with a field
of up to 800 Oe (therefore remanence could not be evaluated from our measurements): a small
hysteresis loop is observed over the range ±100 Oe. Analogous result was previously found
using MOKE on a 30nm-thick permalloy sample obtained by identical preparation with the
same X-ray mask.[2]
This behaviour is not surprising: complete alignment of the magnetization along the short
side of the rectangle requires a number of uncompensated magnetic poles on the long lateral
edges of the sample. Opposite sign magnetic poles would face from these opposite lateral
edges which are closer than in the other configuration (field along the longer side) so resulting
in a much bigger demagnetizing field. That’s why this magnetic configuration is much harder
Scattered intensity (arb. units)
to establish and immediately rearranges when the field is switched off.
0,8
Sample I
hν = 707.5 eV
Longitudinal
geometry
(H // x)
0,0
H // minor side
-1
qx = 11.9 µm
H // major side
-1
qx = 5.04 µm
-0,8
-300
-200
-100
0
100
200
300
Applied field (Oe)
Figure 7.8. Field dependent scattering at the first order peak with the field applied along the
x axis. Line: longer side along x (same as in Fig. 7.6). Dots: shorter side along x.
•
Thickness effect
We prepared samples of different thickness of the patterned film from 10 up to 125 nm. In
Fig. 7.9 we show the hysteresis loops, rescaled between −1 and +1, recorded for all the
109
samples by matching the first order peak with the long side of the rectangles oriented along x
(qx = 5.04 µm−1).
The first striking evidence is that the hysteresis shapes of the thickest samples (II, that is
S, and C) show zero remanence resulting completely different from the ones of the thinnest
samples (A, I and B), which yield a remanence higher than 90 %. Starting from the thinnest
sample A and growing with thickness, the visible trend is that the almost squared loop
becomes less pronounced, i.e., the reversal is more slanted, the remanence decreased and the
saturation field higher. This is also an effect of the dipolar interaction inside the dot: in fact,
due to the extensive nature of this magnetic energy term, the bigger is the volume of the dot
the harder is to obtain a single domain configuration. This effect finally becomes
‘catastrophic’ for a critical thickness comprised between 65 and 110 nm: the hysteresis of
sample II results completely upset with a shape resembling the one observed for
submicrometric circular dots where stable magnetic vortex states form.[3] This change with
thickness has already been observed in analogous systems.[4] A trend analogous to the one of
the thinnest samples is observed by comparing sample C with sample II: at higher thickness
the open lobes, representing the irreversible path of the hysteresis, move toward higher field
values, and the saturation field increases.
Scattered intensity (a. u.)
1.0
0.5
Samples - (nm)
A - 10
I - 30
B - 65
II - 110
C - 125
H // major side
θD = 10°
0.0
First Bragg peak:
-1
qx = 5.04 µm
-0.5
-1.0
-600
-400
-200
0
200
400
600
Oe
Figure 7.9. Field dependent scattering at the first order peak with the field and the longer
side parallel to the x axis. All the prepared samples are measured and two different
hysteresis shapes may be distinguished depending on the thickness range.
110
•
A comparison with OOMMF single dot results
We attempt to compare these experimental findings with micromagnetic predictions. In
Fig. 7.10 we show the OOMMF hysteresis calculated for an isolated dot, whose image,
randomly chosen from SEM images, is reported together with the field application geometry,
parallel to the long side of the rectangle. The different loops correspond to different thickness
values (nm), as indicated in the figure together with other calculation parameters, torque and
cell size (nm). In the main graph the average x component of the magnetization, parallel to the
applied field, is shown, while in the inset the out-of-plane z component is reported.
1.0
Thickness, Torque, Cell size
0.0
remanence
XRMS
100, 1.0E-4, 5
150, 1.0E-4, 10
200, 1.0E-4, 10 zero
200, 1.0E-5, 5 remanence
OOMMF
Mz/|Ms|
5
x10
-3
Mx/|Ms|
0.5
10, 1.0E-4, 10
10, 1.0E-5, 5
30, 1.0E-4, 10
50, 1.0E-5, 5
-0.5
0
H // x
-5
-1.0
-1000
-1000
-500
0
Oe
-500
0
500
500
1000
1000
Figure 7.10. OOMMF simulations for different thickness, torque and cell size of a
permalloy dot chosen as a representative sample of our pattern: the dot image and the
direction of applied field are shown. In the main graph the hysteresis of the average
magnetisation component parallel to the field are reported: they may be distinguished in
remanent and non-remanent ones. In the small inset the relative loops of the average out-ofplane component, normalized to MS, show very small values, with the ones of the remanent
hysteresis much lower than the others. Finally in the smallest inset a comparison between
simulation (30-nm-thick) and measurement (sample I, hysteresis from Fig. 7.9) is shown.
The thickness dependence for Mx results in very good agreement with the measurements
of Fig. 7.9. The trend of the shapes is reproduced and the smoother character of the
111
measurements comes from its averaging thousands of similar, but not perfectly identical, dots:
in the smallest inset we compare the calculated hysteresis for a 30-nm-thick dot with the one
measured for the sample I (coming from Fig.7.9), finding a reasonable match of the coercive
field and the shape. The dashed lines correspond to simulation runs on the same thickness, but
with some parameters set to more restrictive values (smaller cell size, 5 nm, and smaller
torque, 10-5), resulting in much longer and more accurate calculations: in both cases (a thin
and a thick sample) the loop is not seen to shift considerably and the shape of hysteresis is
essentially the same. So we conclude that reliable simulations can be carried out also with
looser parameters allowing a faster convergence. This is a relevant advantage when
simulating a matrix of dots (see following sections), where the computational grid is much
more extended and the calculation time increases exponentially with the number of cells,
becoming a long-demanding task (several days) for a standard PC (2 GHz processor and 512
MB RAM).
In an inset of Fig. 7.9 we also report the calculated loops for the average of the out-ofplane component (always normalized with MS), which show quite low values (less than 1 %)
suggesting that the magnetisation lies in plane: however, one can note how the curves
corresponding to the non-remanent hysteresis have values much higher than the others (an
order of magnitude 102 – 104 higher). This could be an evidence of the formation of vortices,
where the magnetisation points out-of-plane in the center. This is also predicted by the
magnetic configurations calculated by OOMMF, as it is shown in Fig. 7.11 for the illustrative
case of the 100-nm-thick dot.
The figure reports the 2D distribution of the 3D magnetization vector inside the dot at
different positions along the hysteresis loop. The magnetic vector was calculated for each cell
and is represented here with coloured arrows, each arrow averaging a group of cells for a
clearer visualization. Blue arrows correspond to Mx > 0 and red to Mx < 0, with black
standing for low values of Mx, i.e. the magnetisation mainly along y. The same convention is
used for the average value of Mx (i.e. the coloured hysteresis). The background colour inside
the dot is chosen to represent the Mz component, through a black-grey-white colour map,
where the black and white areas coincide with a tilt of the magnetisation vector out-of-plane:
it can be observed that the magnetisation lies in the sample plane with the main exception of
some black spots (M entering the plane) inside the vortices.
112
a)
Mx (x > 0)
H
b)
e)
c)
d)
Mx (x < 0)
H
Figure 7.11 Hysteresis loop (at the centre) and magnetic configuration at its different
position, calculated by OOMMF. Nucleation and annihilation of vortices take part in
magnetisation reversal. Blue and red colours stand for positive and negative Mx values
(both for spins inside the dot and for their average, i.e. the hysteresis).
In the figure one can follow the evolution of the magnetisation as a function of the
hysteresis position (continuous line for the ‘backward’ H range, from +10000 to -10000 Oe,
and dashed line for the opposite ‘forward’ range). Moving from a positive-field saturation (we
reduce the images of the dot in representing the saturated states) to the configuration (a), two
vortices have already nucleated close to the edges of the two ends of the dot, favoured by the
rounded shape, resulting in a decrease of the magnetization alignment. Then an abrupt jump is
found in the hysteresis, as the fingerprint of the nucleation of a third central dot, visible in
configuration (b): there begins the reversible part of the hysteresis, positioned around the
zero, where the centers of the vortices move perpendicularly to the applied field in order to
give, in average, a positive or negative value for Mx, depending on the sign of the applied
field. The configuration (c) results from another sharp change in the hysteresis corresponding
113
to the annihilation of the central vortex, resulting in re-alignment of most of the spins with the
increasing negative field. Then the saturation occurs again with the expulsion of the lateral
vortices and we have run through half the hysteresis: the ‘forward’ part is symmetric, and we
just mention the configuration (e), which illustrates the condition of the central vortex before
being expelled.
Finally we report in Fig. 7.12 the scattering measurements, and the corresponding
OOMMF calculations, with the field applied along the short (and hard) axis of the rectangles,
always in longitudinal geometry, circular polarization and at first order Bragg peak of the
scattered diffusion: samples A and I are measured (the curve for I is the one already reported
in Fig. 7.8) and the comparison with micromagnetic simulations shows a good agreement.
The effect of the increased thickness makes the spins very hard to align, whereas the
saturation is reached for the thinnest sample A.
1.0
0.5
H // minor side
Scattering at First Bragg peak:
θD = 10°, qx = 11.9 µm-1
sample A (10 nm)
sample I (30 nm)
9
8
OOMMF:
10 nm (1.0E-4, 10)
30 nm (1.0E-4, 10)
0.0
7
-0.5
6
-1.0
-400
-200
0
Oe
200
400
Figure 7.12. Field dependent scattering at the first order peak with the field and the shorter
side parallel to the x axis. Samples A and I are shown, with the relative parallel-to-field
component of the magnetization found in OOMMF simulations for the same geometry.
As a conclusion, we found that the simulated hysteresis of one particle match quite well
the XMCD signals of the collection of dots.
114
Up to now, we have reported about the magnetic field dependence at first order Bragg
peak, which resulted useful in monitoring the average magnetization of the collection of dots:
this can as well be done by means of other standard techniques, for example MOKE in
specular reflectivity (paying attention to focus all the beam on the patterned area), or XMCD.
From now on, we will try to explore other capabilities of the technique related to the
diffractive nature of the experiment.
7.2.3 Probing correlations between dots at half order parameter
As mentioned in section 6.2.2, by fixing the geometry at the half order position we may
probe correlations over a distance which is double the period of the pattern, i.e., a periodic
structure which implies pairs of rectangles: such a superstructure, if any, can only be of
magnetic origin, for example a systematic antiparallel coupling of the magnetization in
neighbouring. In this section we try to investigate these correlations by making use of the spolarized light.
We report a first result in Fig. 7.13 for the sample A (about 10 nm thick), comparing it
with the already discussed hysteresis measured at first order. A strong enhancement of the
measured signal is observed at ±100 Oe, the sign depending on the direction of the field
variation. Outside the ±200 Oe region, the scattered intensity is extremely weak and displays
no field dependence, confirming the purely magnetic origin of the peaks. The scattered
intensity peaks in correspondence with the magnetisation reversal, i.e., around the coercive
field of the hysteresis loop for the long side of the rectangles. This field dependence compares
very well to the derivative of the hysteresis curve at the first order peak as it shown in the
graph of inset (a).
We also report in the inset (b) of Fig. 7.13 the field dependent scattered intensity at the
first order peak using s-polarized light: the loss of intensity at the coercive field is a
fingerprint of the loss of ferromagnetic order during reversal. In fact s-polarization at this
geometry is sensitive to the FM order of the x component of the magnetization, but cannot
distinguish the sign (that’s why it is constant at opposite saturation fields).
115
13.8
160
a)
140
13.4
13.2
13.0
1st order:
Circular polarization
-1
qx = 5.04 µm
Half order:
S-polarized light
-1
qx = 2.52 µm
-200
0
200
b)
120
12.8
-200
0
200
Scattered intensity (a.u.)
Scattered intensity (a.u.)
13.6
Derivative of 1st order curve
Sample A
H, x // major side
θD = 10°
100
12.6
-400
-200
0
Oe
200
400
Figure 7.13. Field dependent scattering measured on the sample A at the first order peak (qx
= 5.04 µm-1) and at the so-called half order peak (qx = 2.52 µm-1): for this second curve spolarization is used and sharp extra-intensities are found in correspondence with the
magnetization reversal. In the inset (a) we compare it with the derivative (taken as absolute
value) of the one measured at the first order peak. In the inset (b) we report the loop at first
order peak but using s-polarization: again some features are found at the coercive field, but
with opposite sign (loss of intensity).
At a first glance, this experimental evidence could suggest that the magnetisation reverses
inside the collection of dots through a transient magnetic configuration where an antiparallel
coupling is established between pairs of neighbouring rectangles along x direction. Actually,
we must point out that this effect can be observed, with varying intensity, over a fairly large
range of qx values around the half order position (see subsequent discussion of Fig. 7.14), i.e.,
it is not strictly related to a distinguishable presence of AF order peak, maybe indicating that
the supposed order repeats over a limited number of periods only. So we conclude that the
scattered intensity at the half order position is indicative of a non zero probability that an
antiparallel coupling sets up between neighbouring rectangles during the magnetisation
reversal, that is, the zero average magnetization is obtained with a certain degree of
antiparallel alignment between the magnetization in one rectangle and in its neighbours, and
that this alignment repeats itself in an ordered manner only over a limited extent of the
pattern.
116
To extend this discussion on the AF peak as a side effect of the loss of ferromagnetic
order, we report in Fig. 7.14 the effect of a demagnetization-like procedure on the scattered
intensity using such configuration (half order position and s-polarized light): starting from
saturating value H = 500 Oe, the field is made to oscillate between positive and negative
values and its amplitude is reduced progressively to zero (from step 0 to step 70). Two further
complete hysteretic loops follow, with amplitude of 500 Oe. As the field amplitude decrease
during demagnetization process no effect is seen on the scattered amplitude as the
magnetisation is completely aligned till the coercive field is reached (a blue line is traced as a
view guide at ±100 Oe): in this region an extra-intensity arises reaching a value which is
twice the one, recorded always at coercive field, in the two following loops.
H (Oe)
Half order:
S-polarized light
-1
qx = 2.52 µm
400
200
12.5
0
12.0
-200
11.5
-400
100
steps
Scattered intensity (a.u.)
0
200
300
At remanence
After
demagnetization
10
500
Rocking scan,
S-polarized light
θD = 10°
order +1
order -1
1
400
0.1
half order
4.4
4.6
4.8
5.0
θS
5.2
5.4
5.6
Figure 7.14. Top. Scattered intensity (black curve) measured on the sample A at the socalled half order peak (qx = 2.52 µm-1) using s-polarization: the corresponding applied field
is represented by red dots. The first 70 steps represent a demagnetization procedure where
the applied field oscillates between positive and negative values of progressively reduced
amplitude; the other steps represent two consecutive typical loops. Bottom. Rocking scan
around specular condition: even after the demagnetization no half order peak arises.
117
External field (Oe)
Scttered intensity (a.u.)
13.0
This amplification of the effect suggests that the demagnetization-like procedure results in
a further recovery of antiparallel magnetic coupling of adjacent dots. This is still not enough
to talk of a real order in AF coupling as it is shown in the bottom graph of the figure, where
the rocking scan recorded after the demagnetization-like procedure is compared to the one
recorded at remanence (after the application of a saturation field): no peak at half order
position is visible, but rather the intensity is increased all along the angular interval between
the specular condition and the first order peaks (both positive and negative).
The same ‘half-order’ behaviour is shown in Fig. 7.15 for the samples B and C. The extrapeaks are larger in sample B then in sample A, as the original hysteresis has a more slanted
switching of the magnetization (effect of increased thickness). Concerning C, there is only an
wide extra-peak underlying the complete reversal process; also the related anti-peak of the sscattered intensity at first order shows the same effect. The extra(anti)-peak starts at a lower
value of the field, coming from saturation, in agreement with its relationship to the loss of
ferromagnetic order: to understand the evolution compare the continuous arrows between
them (going towards saturation) and then the dashed ones (reversing from saturation).
H, x // major side, θD = 10°
-1
Sample B
-500
Sample C
1st order: qx = 5.04 µm
Circular polarization
S-linear polarization
-1
Half order: qx = 2.52 µm
S-linear polarization
0
500
-500
0
500
Figure 7.15 The same results of Fig. 7.13 for the case of thicker samples, B and C.
Comparison between hysteresis recorded at first order with circularly polarized light (red FM order), hysteresis at first order with s-polarization (blue – loss of FM order) and the
hysteresis at ‘half-order’ with s-polarization (black – sensitive to AF order).
118
•
OOMMF results on a matrix of dots
In order to check the likelihood of antiparallel magnetic order between neighbouring
rectangles, we take advantage of the ‘real space’ micromagnetic calculations by performing
simulations on a matrix of elements. The issue of ‘coupling’ between neighbouring particles
is a non-trivial problem for the micromagnetic simulations. For an array of well-spaced
particles it can be argued that the coupling (dipolar) will be small and the micromagnetic
simulations of a single particle are adequate. Otherwise, if the particles are in close proximity
it is necessary to simulate an array of particles to take into account the reciprocal coupling
effects. This could be our case as in Ref. [3] it was found that circular particles of analogous
size, thickness and interdot separation undergo dipolar coupling which affects the values of
the annihilation and nucleation of vortices inside the dots.
We report in Fig. 7.16 the OOMMF results for a 3 × 3 matrix of 50-nm-thick rectangles.
The image map is always recovered from SEM images, in order to introduce real defects in
the simulation. We also show the hysteresis calculated separately for each single dot of the
matrix; it is important to note how their behaviour seems quite dispersed, for example the
coercive field may lie in a wide range (60 – 160 Oe), indicating that the defects along the
borders of the dots significantly affect the magnetisation reversal. One can also compare the
average of these single-dot hysteresis with the average signal coming from simulating all the
nine dots together: the slight disagreement can be ascribed to the effect of dipolar coupling
between dots.
Finally we checked, in the simulation of the matrix, the magnetic configurations
corresponding to positions of the hysteresis very close to the coercive field, where the extraintensities of scattering are measured at the half-order peak: no relevant evidence of some
antiparallel order in the magnetization is found, as it shown in the representative image at
bottom of Fig. 7.16 (the teal-white-red colour is referred to the Mx component parallel to the
field). One can also check how the state of the magnetisation reversal appears quite different
in each dot, as expected from considerations on the hysteresis shape.
119
1.0
Matrix
Single Dots
1
2
3
4
5
6
7
8
9
Average
0.5
0.0
H
-0.5
-1.0
-500
0
Oe
500
Figure 7.16. Micromagnetic simulations for a 3 × 3 matrix of 50-nm-thick rectangles: the
dots image and the direction of applied field are shown. In the top graph the hysteresis of
the average magnetisation component parallel to the field are reported for the matrix
simulated as a whole (‘Matrix’) and for each single dot simulated separately: from the nine
separated dots also an ‘Average’ hysteresis is calculated to be compared with the matrix
one. In the bottom, the magnetic configuration at the coercive field is reported for the
matrix simulation.
7.2.4 Hysteresis at nth order peak
In Fig. 7.17 we show the hysteresis loops measured at different order peaks - 1st, 2nd and
3rd of the rocking scan – using circularly polarized light. A thin and a thick sample (B and C
120
respectively) are represented: it is quite evident that in both cases the shapes of the hysteresis
change between different orders. For the sample B the almost square loop of the first order
becomes rounded at the second order, where the signal saturates at higher values of the field;
at the third order the shape changes again. Analogous considerations hold for sample C: here
the well open lobes of the first order become narrower and again higher values of the field are
required to saturate the signal.
1.0
Scattered intensity (a.u.)
Sample B
0.5
0.0
-0.5
nd
st
1 order
-1.0
-400
0
400
2
-400
0
rd
order
400
3 order
-400
0
400
Oe
1.0
Scattered intensity (a.u.)
Sample C
0.5
0.0
-0.5
nd
2
st
1 order
-1.0
-400
0
400
-400
0
order
400
rd
3 order
-400
0
400
Oe
Figure 7.17. Field dependent XRMS data for two samples (B and C) recorded at different
geometries corresponding to 1st, 2nd and 3rd Bragg peaks of the rocking scan.
These data indicate that there is magnetic information in the diffracted beams and this
121
information is not identical to that carried in the reflected beam. So an interesting question
arises about the origin of these differences: is it possibly related to the detailed magnetic
configuration which, in average, occurs inside each dot during the magnetization reversal? In
fact, as well as at the half order peak we sense the possible magnetic order concerning pairs of
dots, at higher order peaks we should deal with possible insights concerning the magnetic
configurations of the single dot.
To investigate more deeply this issue, we carry out the analogy with another technique
which offers similar capabilities of XRMS, that is the diffracted magneto-optic Kerr effect
(D-MOKE),[5] which investigates the possibility of obtaining magnetic information from the
laser beams diffracted from an array of microsized objects. Strict analogies can be found even
in the theoretical description of the two measurements, both dealing with magneto-optic
effects.
Vavassori, Grimsditch and co-workers found a method to compare the micromagnetic
simulations with the D-MOKE loops recorded at different order, so studying with this
crosscheck procedure a great number of magnetic patterned structures (see Ref. [6] and
references therein): the method states that the diffracted MOKE loops are proportional to the
magnetic form factor or, equivalently, to the Fourier component of the magnetization
corresponding to the reciprocal lattice vector of the diffracted beam. In a summarizing
review[6] they develop step by step the used formalism but they warned that the resulting
simple equations should be treated with some caution as derived by approximations and
‘reasonable’ generalizations. In their works they insert the magnetic configurations, obtained
from micromagnetic simulations at different fields, into these equations in order to predict the
observed D-MOKE loops: the most interesting part happens when the prediction is not
correct, as they show how the re-evaluations of the assumptions that enter the micromagnetic
simulations may lead to a different calculated configuration which gives much better
agreement with measured signals, so allowing the discovery of intermediate and metastable
states during reversal.[7] The D-MOKE loops may be a valuable instrument for confirming
the micromagnetic simulations in laterally resolving the details of magnetization. The inverted
procedure, of predicting the magnetic configuration from the scattered intensity signals of the
different nth Bragg peaks, is the next highly challenging goal, requiring an amount of data in
the reciprocal space as large as possible, i.e., n to be accessible up to high integers, which is
an achievable task only within the wavelengths of the X-rays region (see equations of chapter
122
6, qx = 2nπ/d = 4π/ ·sin sin
).
Inspired by the developments of D-MOKE , we also attempted to deepen our
understanding on the actual magnetic information that can be retrieved from the hysteresis
loops recorded at nth order peaks. The first step was to run micromagnetic simulations. Then
we decided to follow an alternative calculation method, overcoming the crude approximations
on the magnetic form factor. The proposed method for the scattered intensities calculations is
the direct derivation of a code that was successfully used for resonant magnetic scattering in
order to predict the field dependent diffused scattered intensities in magnetoresistive Co/Cu
multilayers[8], also allowing to estimate the in-plane size of the antiferromagnetically coupled
domains. Very promising preliminary results were obtained by this code as implemented by
Carlo Spezzani in order to receive as input the magnetic confurations calculated by OOMMF
over a collection of elements. The results are not discussed here but we want to stress that
when the scattered intensities calculated from micromagnetic simulations do reproduce the
XRMS results, all the other predictions from these simulations can be accepted with
considerably more confidence.
Finally, in comparing XRMS versus D-MOKE it must be noted that, apart from adding
element selectivity (intrinsic to resonant X-ray spectroscopies), working with X-rays implies
that shorter wavelengths are employed which means that it is possible to investigate higher
diffraction orders, as mentioned above, and/or shorter lateral periods (lower than 100 nm),
which is a crucial requirement related to the natural technological trend.
7.3 Conclusions
We have used resonant scattering of polarized soft x-rays to analyze the field dependence
of the magnetization in an array of submicrometric rectangles patterned into a polycrystalline
permalloy film of varying thickness from 10 to 125 nm. Sensitivity of x-ray scattering to
magnetization was obtained by using elliptically polarized light and by tuning the photon
energy at the Fe 2p resonance.
As for a diffraction grating, the lateral modulation of the pattern produces sharp peaks in
the diffuse scattering that we used to single out contributions coming from a regular magnetic
structure. This allowed us to filter out other contributions from, e.g., unpatterned areas and/or
nonregular patches, while illuminating and measuring the entire sample. The hysteresis curves
123
obtained at the first order scattering peak measure the collective magnetization rotation in the
array. When the field is applied along the long side of the rectangles, the hysteresis is
characterized by almost complete remanence and by a coercive field Hc of about 90 Oe for the
thinnest samples, while thickest ones had zero remanence. On the other hand, the short side is
a hard axis for the magnetization of the rectangles: a very small hysteresis loop was observed
also for the thin samples, and saturation could not be reached at the maximum field available
in our experiment. These results have been discussed in connection with the action of
demagnetizing fields and compared to predictions obtained by micromagnetic calculations.
We have measured also the scattered intensity at half-order position, corresponding to an
order parameter that involves pairs of rectangles. We have shown that this scattering channel
is of purely magnetic origin, since its intensity can be made negligible as a function of the
applied field.
In the hysteresis curve, the scattered intensity sharply peaks around the
coercive field value, indicating that a high degree of antiparallel alignment between
neighbuoring rectangles is reached only at Hc. As in the case of specular scattering from
magnetoresistive multilayers, antiparallel magnetic coupling appears as extra intensity in the
half-order scattering channel. From the field and angular dependence, though, we conclude
that the antiparallel alignment is rather a local property that does not extend in a regular way
throughout the entire array.
Also the additional information which potentially resides on the hysteresis loops recorded
at different Bragg orders has been analysed and discussed as a validating approach of
micromagnetic simulations in analogy with D-MOKE techniques.
As a conclusion, our experiment pointed out the interest of using soft x-ray resonant
scattering for the analysis of arrays of submicrometric particles. Resonant scattering analyzes
in reciprocal space a collection of objects, offering a complementary approach with respect to
microscopy techniques that deal more directly with single objects in real space.
Both x-ray (photoemission microscopy, see Ref. [9]) and electron (Lorentz microscopy,
see Ref. [10]) based techniques have been used in the past to image the remanent magnetic
properties of permalloy dots. The importance of combining microscopy and scattering
techniques for the analysis of magnetic structures was pointed out in a study of the formation
of magnetic domains in multilayers,[11] as well in the mentioned D-MOKE experiments.[6]
The combination in a single technique of structural and magnetic sensitivity together with
element selectivity makes resonant scattering a remarkable tool in this field. Also, its photon124
in/photon-out character makes it possible to work in the presence of time dependent magnetic
fields, which is an unavoidable requirement for magnetisation switching studies, and also
opens new opportunities in the investigation of collective dynamics in magnetic
microstructures.
Soft X-ray wavelengths ideally match the vertical period of typical multilayer structures,
as well as the ever-increasing reduction of the lateral size of magnetic structures. Patterning
multilayers in general and magneto-resistive multilayers in particular is interesting for
spintronics applications. Magnetoresistive multilayers display distinct vertical order
parameters for ferromagnetic and antiferromagnetic coupling. Therefore, a peculiar feature of
resonant x-ray scattering is that it makes it possible to match simultaneously lateral and
vertical periods of a patterned multilayer, probing correlated magnetic order in both
directions.
[1] A. Aharoni, Introduction to the Theory of Ferromagnetism, (Oxford, New York, 1996).
[2] http://www.elettra.trieste.it/science/highlights/2001-2002/elettra_highlights_2001-2002pg035.pdf. P. Candeloro, L. Businaro, E. Di Fabrizio, M. Conti, G. Gubbiotti, G. Carlotti, A.
Gerardino, ELETTRA Research Highlights 2001 - 2002, 35, Magnetic Systems.
[3] M. Natali, I. L. Prejbeanu, A. Lebib, L. D. Buda, K. Ounadjela, and Y. Chen, Phys. Rev.
Lett. 88, 157203 (2002).
[4] Gianluca Gubbiotti, Olga Kazakova, Giovanni Carlotti, Maj Hanson, and Paolo Vavassori,
IEEE TRANSACTIONS ON MAGNETICS 39, NO. 5, 2750 (2003).
[5] A. Vial and D. van Labeke, Opt. Commun. 153, 125 (1998).
[6] M. Grimsditch and P. Vavassori, J. Phys.: Condens. Matter 16 (2004) R275–R294.
[7] As an example, see: P. Vavassori, M. Grimsditch, V. Novosad, V. Metlushko and B. Ilic,
Phys. Rev. B 67, 134429 (2003).
[8] C. Spezzani, Ph.D. Thesis, Diffusion résonante des rayons X polarisés et couplage
magnétique dans les multicouches Co/Cu, Université Paris XI, 2003.
[9] C. M. Schneider and G. Schönhense, Rep. Prog. Phys. 65, R1785 (2002).
[10] R. D. Gomez, T. V. Luu, A. O. Pak, K. J. Kirk, and J. N. Chapman, J. Appl. Phys. 85,
6163 (1999).
[11] C. Spezzani, P. Torelli, R. Delaunay, C. F. Hague, F. Petroff, A. Scholl, E. M. Gullikson,
and M. Sacchi, Physica B 345, 153 (2004).
125
126
Conclusions and perspectives
The results reported in this thesis embrace two different model nanostructured systems
which are both prototypical for the study of low dimensionality magnetism and for the field of
spintronic technology. In both studies we remark the use of synchrotron light in the range of
soft X-rays which cover the excitations of the 2p core levels where the magneto-optic effects
are particularly strong for the 3d transition ferromagnets (Fe, Co, Ni) which are involved in
the formation of most ferromagnetic materials.
We now summarise briefly the most interesting results and the descending perspectives
respectively for the two cases and then discuss in the ‘Perspectives’ section the development
of an in-situ method for growing systems with the peculiar characteristics of both of them.
The first study consisted in a surface science experiment where a 6 ML bcc Fe film was
grown in UHV on an atomically clean GaAs(001)-(4 × 6) reconstruction and nanostructured
by the presence of 0.5-ML-equivalent Co atoms embedded in the Fe matrix at different
distances from the interface up to the surface. The sample preparation and control required the
use of a wide set of surface science techniques (MBE, LEED, AES, MOKE, XPS) and finally
ended with a layer-by-layer magnetisation profiling by exploiting the element selectivity of
XMCD to sense the Co atoms acting as magnetic local probes: through the application of the
magneto-optic sum rules it was possible to follow the profile of spin and orbital magnetic
moments separately. Here follow the main conclusions.
The film is found to be magnetically active down to the interface, ruling out the presence
of a magnetically dead layer: such a presence was suggested by the first studies of the
Fe/GaAs(001) interface and is considered to be of crucial relevance for the injection of
spin-polarized electrons through the FM/SC interface, which is a fundamental issue in
spintronics technology.
The reduction of Fe crystal symmetry at the interfaces resulted in the enhancement of the
orbital magnetic moment of Co atoms in direct contact with GaAs. The values were
roughly constant in the inner layers and unexpectedly reduced at the surface.
127
The profile of the spin magnetic moments of Co atoms showed a maximum for the
middle layers and a progressive reduction of about 30% at both interface and surface. The
reduction at the interface can be related to the bonding and intermixing with the
semiconductor atoms, where especially the influence of As on Fe is expected to be a
possible deteriorating factor of the magnetisation. Similarly, the As is monitored to
segregate up to the surface and LSDA calculations have shown how its presence strongly
reduces the otherwise surface-enhanced spin moments. The agreement with theory of this
local detail adds validation to our original approach and, as a consequence, to all its
results.
We demonstrated the validity of such method in the magnetisation profiling of magnetic
interfaces: it could be applied whenever a layer of the FM, usually at the very interface, is
suggested to be magnetically dead or suppressed. For example, interesting results could
be obtained by applying it at the study of Fe/GaAs(001) interfaces where specific GaAs
reconstructions or the growth conditions are known to favour such deteriorating effects
on the magnetic state. Such kind of studies requires controlled conditions of preparation
and must be performed in UHV systems.
The second subject concerned the preparation of a dense array of submicrometric
permalloy dots in a regular matrix and its study with soft X-rays scattering. The shape of the
dots was chosen to be rectangular, so to enhance the stability of the magnetisation due to its
elongated shape (1000 × 250 nm2): in fact such systems are of particular interest in the field of
magnetic storage devices where the detailed control and switch of the magnetic state must be
carefully tailored. Generally speaking the lateral reduction of the FM films to nanometric
dimensions follows the natural trend of high integration in solid state devices.
The samples were prepared with varying thickness from 10 to 125 nm by X-ray
lithography followed by a post-lithographic deposition of polycrystalline permalloy in HV
conditions and a final lift-off process. The use of such techniques allows to obtain
submicrometric structures with good resolution, but the disadvantage compared to the first
surface science study is that no detailed control of the interface with the substrate is possible
due to the ex-situ nature of some of the processes involved.
The samples were then transferred to a UHV chamber equipped with a reflectometer so to
be characterized by means of polarized soft X-rays scattering which, at 2p
3d resonance, is
sensitive to the magnetisation of the scattering elements as well as to the structural analysis
related to diffraction. Actually, the experiments were also aimed to illustrate the capabilities
of XRMS in investigating such periodical magnetic nano-systems: it must be stressed that the
technique is well suited to magnetisation reversal studies (external applied field) with the
further add-in of the element sensitivity (even if this advantage is not exploited in our study).
128
We also run micromagnetic simulations to deepen the comprehension of the system and
integrate the measurements with theoretical predictions. We summarise here the main
conclusions.
We explored our ultra-high-density dots by XRMS and found that at small thickness (<
70 nm) they behave as reliable information storage bits when the field is applied along
the longer side of the rectangles, but increasing the thickness the hysteresis collapse and
no remanent net magnetisation is available at zero field: in fact the vortex nucleation
becomes relevant and dominates the magnetic configuration of the dots, as pointed out by
the consistent results of micromagnetic simulations.
We discussed the possibility of exploiting the diffractive nature of measurements, for
example probing correlations of magnetic origin between neighbouring dots using the
half order geometry. This could result in more interesting results for denser and closer
structures where effects like the dipolar coupling would play a significant role.
Always concerning the diffractive nature of the technique, the hysteresis recorded at
higher Bragg orders appear different one from the other and maybe carry additional
information on the magnetic configuration inside the single dot during the reversal, rather
than on the average magnetisation of the whole collection of dots. This has already been
proven to happen for D-MOKE loops on micrometric matrices. We also tried to
reproduce the measured loops by calculating the scattered intensities starting from the
detailed results of micromagnetic simulations. In Fig. 8.1 we present some promising
preliminary results with the courtesy of Carlo Spezzani who implemented the code to
calculate the diffused scattering: also the comparison for some s-polarization
measurements is reported. We want to conclude by underlining that when the scattered
intensities calculated from micromagnetic simulations do reproduce the XRMS results,
all the other predictions from these simulations, which are an invaluable tool for magnetic
investigation, can be accepted with considerably more confidence.
As a perspective work one can try to carry completely the analogy with the D-MOKE
(Diffraction in the Magneto-Optic Kerr Effect) technique: in fact, we wonder whether the
magnetic information contained in the hysteresis loop shape at different Bragg
diffraction orders is, in the case of our rectangles, relevant of some particular state for the
magnetic configuration inside the dot (states which would repeat coherently in the whole
collection at reversal), or is rather an averaging effect on the magnetic configurations
inside each dot, configurations which can also happen to be quite different from dot to
dot. The results of the micromagnetic simulations seem to reflect a quite dispersed
behaviour (see Fig. 7.16, for instance), making the second hypothesis more likely. In fact
the direct SEM images show visible and randomly positioned defects along the edges of
the structures anticipating their role of possible active centers during the reversal of
magnetisation (pinning centers or vortex nucleation centers). Also the small dipolar
coupling between dots can not be neglected: it complicates the behaviour of the system
and makes the OOMMF calculations heavier to be performed, requiring a larger
collection of elements to be simulated together. So efforts should be done in measuring
and simulating other nanostructured arrays of more uniform dots coherently behaving
under reversal (which needs the improvement of nanofabrication performances).
129
1.0
0.5
1.0
1
st
order
0.5
1.0
2
nd
rd
3
order
order
0.5
0.0
0.0
0.0
-0.5
-0.5
-0.5
-1.0
-1.0
-500
1.0
0.5
1
st
0
-1.0
500
-500
1.0
order
0.5
2
nd
0
500
Simulations
-500
3
order
rd
0
500
1.0
order
0.5
0.0
0.0
0.0
-0.5
-0.5
-0.5
-1.0
-500
0
500
-1.0
-500
0
500
Measurements
-500
0
500
Figure 8.1. Comparison between the calculated and measured scattered intensity.
Top: circular polarization. The 1st, 2nd and 3rd Bragg orders are shown, using the simulations
for a 50-nm-thick sample and the data of the sample B.
Bottom: s-polarization. The thickness for simulations (10 nm) is approximately the one of
the sample A, used for comparison: the agreement is good with the peaks centered at the
relative coercive field values.
130
-1.0
Perspectives
A third activity has been carried out in parallel with the two previous studies, concerning
the instrumental development of a peculiar evaporation stage in a UHV chamber at APE
beamline.
The idea consists in approaching a shadow mask with nanometric holes very close to the
substrate and then depositing with standard molecular beam epitaxy the desired material (in
our case Co or Fe) through the mask. This allows to grow arrays of epitaxial single-crystal
nano-dots in controlled UHV conditions over atomically clean substrates so to obtain
carefully prepared interfaces (as in our first study) which have a nanometric lateral size (as in
the second study): such structures have already shown interesting features[1] and can be seen
as prototypical constitutive elements of spintronic devices.
Here we report the first test results on the functionality of the home-built stage to
underline that the two different approaches used in the two subjects addressed in this thesis
can be integrated on the same samples in the future, allowing a first surface science approach
to check the quality of the grown interface and a further study by means of XRMS technique,
eventually ex-situ after sample capping to prevent oxidation. The APE HE beamline is being
equipped with a Fresnel zone-plate microscope which should focus the beam down to less
than 100 nm, allowing laterally resolved magnetic imaging of nanostructures.
Some technical difficulties must be overcome, as a parallel and close approach between
the mask and the substrate is necessary in order to control shadow effects at the border of the
grown structures, which are due to the divergence of the evaporation source: for our
prototypical system, the approach is purely mechanic and the mask frame is pushed by a
spring against the substrate and is separated from it at a fixed distance determined by the
presence of 12- m-thick Kapton stripes. This separator avoids the direct contact with the
fragile part of the mask where the holes are dug across a silicon-nitride (Si3N4) membrane of
100 nm thickness framed by a silicon wafer. In fact, the other challenging technical
requirement is the preparation of properly tailored mask with the desired shape and size of the
holes: usually the masks consist of thin foils, less than 1- m-thick, with microholes that have
been etched with a commercial focused ion beam (FIB) system.
In Fig.8.2 we show a SEM image of the used mask where a square matrix of circular holes
of about 400 nm diameter and 1 m period can be distinguished: the SEM image on the right
is the result of a test deposition through the mask, with circular dots of Co transferred on a asintroduced GaAs substrate in UHV conditions. The size of the dots is slightly more than 500
131
nm, as expected when using a 12 m separator with an evaporation source of about 2 mm size
distant 20 cm from the mask. The good quality of the deposited structures is also confirmed
by AFM (Atomic Force Microscope) measurements, not reported here, where the edges of the
dots are found to be smooth even if not sharp as one could desire.
Figure 8.1. SEM images of the mask (left) and of the Co 20-nm-thick dots (right)
evaporated through it in UHV conditions.
Finally one should remind that single-crystal 2D structures can also be obtained by
patterning a continuous epitaxial film by means of a more conventional multi-step
lithographic process,[2] with the disadvantage that the capping of the continuous film is often
required, or by means of FIB milling,[3] which is a slow direct-writing process with the need
of highly specialized equipment: usually the competition between magnetocrystalline and
shape anisotropy is studied in these systems.
[1] C. Stamm, F. Marty, A. Vaterlaus, V. Weich, S. Egger, U. Maier, U. Ramsperger, H.
Fuhrmann, D. Pescia, Science 282 (1998) 449.
[2] M. Zölfl, S. Kreuzer, D. Weiss, and G. Bayreuther, J. Appl. Phys. 87, 7016 (2000). R.
Pulwey, M. Zölfl, G. Bayreuther, and D. Weiss, J. Appl. Phys. 91, 7995 (2002). M. Hanson,
O. Kazakova, P. Blomquist, R. Wäppling, B. Nilsson, Phys. Rev. B 66, 144419 (2002). R.
Pulwey, M. Zölfl, G. Bayreuther, and D. Weiss, J. Appl. Phys. 93, 7432 (2003). C. A. F. Vaz,
L. Lopez-Diaz, M. Kläui, and J. A. C. Bland, T. L. Monchesky and J. Unguris, Z. Cui, Phys.
Rev. B 67, 140405(R) (2003).
[3] P. Vavassori, D. Bisero, F. Carace, A. di Bona, G. C. Gazzadi, M. Liberati, and S. Valeri,
Phys. Rev. B 72, 054405 (2005).
132