Static and dynamic X-ray resonant magnetic scattering studies on

Transcription

Static and dynamic
X-ray resonant magnetic scattering studies
on magnetic domains
Static and dynamic
X-ray resonant magnetic scattering studies
on magnetic domains
ACADEMISCH PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR
U NIVERSITEIT VAN A MSTERDAM
OP GEZAG VAN DE R ECTOR M AGNIFICUS
P ROF. MR . P.F. VAN DER H EIJDEN
AAN DE
TEN OVERSTAAN VAN EEN DOOR HET COLLEGE VOOR PROMOTIES
INGESTELDE COMMISSIE , IN HET OPENBAAR TE VERDEDIGEN
IN DE
A ULA DER U NIVERSITEIT
5 JULI 2005, TE 10.00 UUR
OP DINSDAG
DOOR
Jorge Miguel Soriano
geboren te Zaragoza, Spanje
Promotiecommissie
Promotor
Prof. dr. M.S. Golden
Co-promotor Dr. J.B. Goedkoop
Overige leden Dr. E. Brück
Prof. dr. K.H.J. Buschow
Prof. dr. T. Gregorkiewicz
Prof. dr. W. Kuch
Prof. dr. Th. Rasing
Prof. dr. G. Wegdam
Cover: word scattering from the history of a Ph.D. student’s life.
ISBN 90-5776-142-4
The work described in this thesis was carried out partly at the European Synchrotron
Radiation Facility (Grenoble, France) and at the Van der Waals-Zeeman Instituut of
the University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam. The work
is part of the Research Program 39 of the Stichting voor the Fundamenteel Onderzoek
der Materie (FOM) and was made possible by financial support from the Nederlandse
Organisatie voor Wetenschappelijk Onderzoek (NWO).
No sé si estoy en lo cierto,
lo cierto es que estoy aquı́,
otros por menos se han muerto,
maneras de vivir.
R. Mercado
a mi familia
a Marı́a
C ONTENTS
1. Introduction
1.1. Thin film magnetism . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. X-ray resonant magnetic scattering . . . . . . . . . . . . . . . . . .
1.3. This thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2. Magneto-optical constants at the rare-earth M4,5 absorption edges
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Optical constants in the soft X-ray range . . . . . . . . . . . . .
2.3. Resonant cross sections of the RE M4,5 edges . . . . . . . . . .
2.3.1. Calculation of atomic absorption spectra . . . . . . . .
2.3.2. Gd3+ experimental spectra . . . . . . . . . . . . . . . .
2.4. Calculated RE M4,5 magneto-optical constants . . . . . . . . .
2.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1. Calculated spectra . . . . . . . . . . . . . . . . . . . . .
2.5.2. Applications . . . . . . . . . . . . . . . . . . . . . . . . .
2.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3. An XRMS study of disordered magnetic stripe domains in a-GdFe thin
films
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1. Magnetism of amorphous GdFe thin films . . . . . . . . .
3.2. Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1. Samples: a-GdFe thin films . . . . . . . . . . . . . . . . . .
3.2.2. Small-angle X-ray scattering setup . . . . . . . . . . . . . .
3.3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1. Scattering curves at remanence . . . . . . . . . . . . . . . .
3.3.2. Field-dependent scattering curves . . . . . . . . . . . . . .
3.3.3. Stripe diffraction patterns in the small-angle limit . . . . .
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CONTENTS
5
3.3.4. Field dependence of total scattered intensity
3.3.5. Interpretation of scattering curves . . . . . .
3.3.6. The effect of disorder . . . . . . . . . . . . . .
3.3.7. Domain period and magnetization . . . . . .
3.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . .
4. Study of magnetization dynamics of GdFe thin films
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . .
4.2. Magnetic pulse generation . . . . . . . . . . . . . .
4.3. Magnetic reversal in Gd0.19 Fe0.81 films . . . . . . .
4.3.1. Time-resolved MOKE . . . . . . . . . . . .
4.3.2. Time-resolved XRMS . . . . . . . . . . . . .
4.3.3. Discussion . . . . . . . . . . . . . . . . . . .
4.4. Magnetic reversal in GdFe5 . . . . . . . . . . . . .
4.4.1. Time-resolved XRMS . . . . . . . . . . . . .
4.5. Conclusions and outlook . . . . . . . . . . . . . . .
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5. An XRMS study of ion-beam-patterned a-GdTbFe thin films
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Experimental . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1. Samples . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2. Focused-ion-beam irradiation . . . . . . . . . . . .
5.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .
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6. An X-ray magneto-optical study of magnetic reversal in perpendicular
exchange-coupled [Pt/Co]n /FeMn multilayers
101
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2. The [Pt/Co]n /FeMn perpendicular exchange bias system . . . . . 103
6.3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.3.1. XMCD spectroscopy . . . . . . . . . . . . . . . . . . . . . . 105
6.3.2. Element-specific hysteresis loops . . . . . . . . . . . . . . . 107
6.3.3. Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7. Conclusion and Outlook
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7.1. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6
CONTENTS
A. Sensitivity of the Gd3+ optical constants to the calculation parameters117
A.1. Atomic multiplet calculation . . . . . . . . . . . . . . . . . . . . . . 117
References
120
Summary
137
Samenvatting
139
Resumen
141
Acknowledgements
144
To my friends
145
1
I NTRODUCTION
1.1.
Thin film magnetism
Many devices of the current information technology era are based on
magnetic thin films. For example, hard disks, read/write heads and magnetic
sensors are ubiquitous in the day to day life of any citizen of a high technology and information centred society. These magnetic devices play host to, or
interact with, the main protagonist in this thesis: the magnetic domain. These
are tiny areas of the thin film that are uniformly magnetized in a given direction [1, 2]. In simple words, the magnetization inside a domain is given by the
size of the atomic spins and their degree of mutual alignment. In the so-called
domain wall - the region between two oppositely aligned domains - the spins
gradually change direction, so that the magnetization (for instance) turns from
pointing up to pointing down. Thus when a device sensitive to the direction of
the magnetization flies above the thin film (as is the case in a computer’s hard
disk), it feels these changes in magnetization and its signal is interpreted as ones
and zeros, thus rendering the bits containing the information.
In order to keep pace with our ever-increasing demands for more information (for example in the form of multimedia), the recording industry faces the
challenge of realizing a tireless growth in information storage density. The current bit width is approximately 25 nanometers, about a thousand times smaller
than the diameter of a human hair and a few hundred times the diameter of
an atom. Further reductions will bring us closer to the atomic limit. Thus, an
important question remains: what is the minimum stable domain size?
8
C HAPTER 1
a
b
c
d
e
Figure 1.1: Schematic diagram on the formation of stripe domains in magnetic thin
films with perpendicular anisotropy. Cross sections of a film with dominant dipolar
energy (a) and perpendicular magnetic anisotropy (b). The formation of out-of-plane
stripe domains (orange and blue), domain walls with magnetization perpendicular to
the plane of the figure (grey) and closure domains (green and violet) is illustrated respectively in (c), (d) and (e).
To resolve this question, new tools need to be added to the toolkit of domain characterization methods. Such a new tool is used in this thesis to study a
number of domain structures in thin films. In order to provide the background
for our investigations, we have first to describe the origin and the properties
of magnetic domains in thin films [3, 4]. The domains are the result of several
competing energies: on one hand, the exchange energy between the spins tends
to align them with respect to each other. Secondly, a preference for the spins to
be oriented in a certain direction, usually called easy axis, may be displayed. In
crystalline materials, this anisotropy direction is linked to the crystallographic
axes. The consequence of these two terms for ferromagnetic systems is that the
minimum energy state is reached when all spins are parallel and pointing along
the easy axis, and the whole system can be seen as a huge single spin or dipole.
The energy potential created by such dipole is described commonly in terms
of flux lines and magnetic charges, giving rise to another contribution to the
total energy, the demagnetization or dipolar energy. Unlike the exchange and
anisotropy energy terms, the dipolar energy is non-local, so that each spin is
Introduction
9
affected by any other spin in the system.
When the system is uniformly magnetized, the dipolar energy will be
maximal. To reduce it the system can break up in domains, at the cost of having
to form a domain wall. Within the domain wall, the spins of adjacent atoms are
no longer parallel and they will not point along the easy axis, locally increasing
the exchange and anisotropy energies. The detailed domain structure depends
on the balance between dipolar energy gain and the cost of making domain
walls, and on the history of the magnetic fields that were applied to the sample.
In thin films the dipolar energy causes the magnetization to have a strong
preference to lie in the film of the plane, as depicted in the first example in
Fig. 1.1. However, a second effect of the surfaces is the crystallographic symmetry is broken there, so that the surface atoms can have a completely different
anisotropy direction. Many elements will take on a perpendicular magnetic
anisotropy which can affect the anisotropy of the film as a whole or even, as
in the amorphous thin films studied here, it can be ’grown into’ the film during
deposition, causing the whole film to have a perpendicular magnetic anisotropy
(Fig. 1.1-b).
A very interesting situation occurs when the shape and surface anisotropy
energies are roughly equal. In this case the system breaks up in a regular series
of up and down stripe domains, decreasing in this way the number and extent
of the flux lines [2, 5] (see Fig. 1.1-c). In this situation, the dipolar energy is
minimized, but at the cost of the formation of domain walls, where the magnetization direction rotates from up to down or viceversa. Crudely speaking, the
period of such stripe lattices results from the interplay between these two factors. However, the detailed shape of the domain wall is important, as depicted
in a more realistic way in panel d. The detailed shape of the magnetization in
stripe systems cannot be calculated analytically as it depends on the interplay
between all the energy terms involved, which depend on material parameters
such as the saturation magnetization, the perpendicular anisotropy and the exchange constant, but also on the physical dimensions of the film. For instance,
the dipolar energy can be further reduced by the formation of closure domains
at the film surfaces (panel e). Again there is a price to pay, this time in the form
of a higher anisotropy energy in these domains. A vast range of domain configurations is possible, as shown in Ref. [2].
10
C HAPTER 1
With regard to the foregoing discussion of magnetic recording media,
another technologically important aspect concerns the speed of the writing process, in which the magnetization direction is reversed. This affects the dynamics
of the domain magnetization, and thus poses the following question: how fast
can a magnetic domain be switched? In today’s hard disks, it takes some nanoseconds to write a bit.
The reversal time scale in magnetic research ranges from years down to
nanoseconds, and lately even femtoseconds. Above a few picosecond switching times, reversal is thermally assisted, involving nucleation of a domain in the
new direction and its subsequent growth by domain wall motion.
When the excitation time scale lies well within the picosecond range or
faster, the magnetic system does not have enough time to adapt by displacing the domain walls and magnetic reversal involves coherent rotation of many
spins that behave as a single spin under the driving field. Ultimately, when the
excitation is very fast - on the femtosecond time scale - the non-linear character
of spin precession is able to bring the system out of thermodynamic equilibrium
as regards the electronic, crystal lattice and spin degrees of freedom (a review
on spin dynamics and magnetic reversal can be found in Ref. [6]). Also, the intrinsic non-linear character of spin precession can cause this macrospin to break
up, generating spin waves that rapidly decay into phonons, a situation that we
encounter in this thesis.
A different class of magnetic thin film systems relevant for applications
are the exchange-biased systems [7]. They basically contain a ferromagnetic and
an antiferromagnetic layer, the main effect of the latter being to shift the hysteresis curve of the former in the magnetic field axis. This exchange-bias effect is
central to the fledgling field of magnetoelectronics, and as such is the subject of
many ongoing investigations [8, 9].
From the discussion thus far it is clear that magnetic domains, their dimensions and behavior in thin film systems are important topics, attracting a
large degree of interest from academia and industry alike. It then follows that
experimental techniques able to give local information on magnetic domains
and their dynamical behavior are important players in the characterization and
Introduction
11
the development of tomorrow’s magnetic storage media. In this context, techniques based on microscopy are obvious front-runners, such as Lorentz, Kerr or
magnetic force microscopy. Each of these has its own strengths and weaknesses.
From technique to technique the latter could be argued to include limited spatial resolution, difficulty in applying high magnetic fields or the necessity for
long acquisition times. Given this backdrop, we argue that it would be valuable
to explore the possibility of using X rays to answer some of the open questions currently limiting our understanding of the magnetization dynamics in
thin film systems. X rays possess the positive attributes of providing a maximum resolution of several angstroms in almost any condition of temperature
and field. Unfortunately, the current status as regards the development and
availability of high-resolution X-ray lenses means that rather than using direct
X ray microscopy, we have chosen to explore the merits (and thus also identify
the drawbacks) of X ray scattering as a probe of thin film magnetization and its
dynamics on nanometer and nanosecond timescales.
1.2.
X-ray resonant magnetic scattering
The X-ray methods described in this thesis are still under development,
having only been introduced somewhat more than a decade ago. They are
based on the strong magnetic resonances between core electrons and the spinpolarized valence states of magnetic solids. This means that when an X-ray
wavefront travels through a solid, it excites the orbital motion of the electrons
in the constituent atoms. These electrons then start oscillating in the plane of the
light polarization [10]. This excitation is consequently relaxed by the emission
of a spherically symmetric wave centered at the nucleus of the atom in question.
If the photon energy E of the incoming X-ray photon matches the energy
difference between two atomic levels }ω0 = E f − Ei , the electrons occupying
the lower level absorb the photon and are promoted to the higher level which,
naturally, needs be initially at most partially unoccupied in order to allow the
transition to take place. So, how does magnetism come into this? The absorbtion and re-emission of the X ray is only sensitive to the magnetic state of the
atom if the spin-orbit interaction plays an important role. When an atom is magnetized, it has more valance electrons with spin in one direction than in other,
resulting in a net total magnetic moment. This occupancy difference also means
that the number of empty states available for the electron to be excited into de-
12
C HAPTER 1
M4
ω
q = 0,
1
M5
ω’
q’ = 0,
1
Initial state:
Intermediate:
Final state:
3d 10 4f N
3d 9 4f N+1
3d 10 4f N
|JM
|J’M’
|JM
Figure 1.2: Schematic resonant X-ray absorption process in the atomic multiplet description applicable to the RE M4,5 edges. The incident X-ray photon with energy h̄ω
and polarization state q (0: linear, ±1 circular) causes a resonance to occur between the
Hund’s rule ground state level | J M i of the initial 4 f N configuration multiplet with the
multiplet levels | J 0 M0 i of the excited configuration 3d9 4 f N +1 . The scattered photon can
have a different polarization state q0 .
pends on its spin. Typically the spin-orbit interaction is large for core levels such
as the 2p and 3d levels of the transition-metal and rare-earth elements, respectively. As these elements are the main players in the magnetic game, this opens
up the prospect of resonantly tuning the incoming X-ray beam to a core-level
threshold, exploiting the spin-orbit interaction to give a strongly magnetizationsensitive absorption of the X-ray beam. This basic process results in the strong
magnetic sensitivity of the refractive index when dealing with the interaction
of soft X rays with magnetic matter, as it is in this photon energy regime that
the characteristic absorption edges of the 2p and 3d levels of the transition metals and rare earths are located. Naturally, the fact that the corresponding X-ray
wavelengths are of the order of the typical size of magnetic domains for interesting thin film magnetic systems is a nice bonus.
In fact, the two strongest aspects of these soft X ray-based methods are
Introduction
13
(i) that the spectroscopy can give access to an independent measure of the spin
and orbital magnetic moments of systems ranging in thickness from much less
than a monolayer [11] to the bulk and (ii) that they also possess elemental and
chemical sensitivity, since the resonances for different elements appear at different energies. An additional benefit - shared by all photon-in, photon-out
techniques - is that the application of high fields and the use of low temperatures are straightforward.
Up to now it sounds as though soft X rays should have already conquered the world of thin film magnetism. That this has not yet occurred is due
to two main factors. Firstly: they are not (yet) available as a table-top source,
and secondly that the current quality of X-ray optics (Fresnel zone plate or hollow lenses) is limited, causing the current spatial resolution to be from one to
three orders of magnitude larger than the diffraction limit. We have taken this
latter drawback as part of our motivation to explore the possibilities of lensless
techniques such as X-ray resonant magnetic scattering as a useful alternative
since the spatial resolution in the scattering case simply scales with the maximum scattering angles intercepted. The price one pays is that - in measuring
the scattered intensity - one loses the phase information carried by the X rays
coming from the sample. This phase problem - well known from diffraction can be partially overcome by using coherent beams in combination with phase
reconstruction algorithms [12], although it seems unlikely that the resolution
will be better than that of a zone plate microscope in the soft X-ray range. In
this thesis, we limit ourselves to incoherent diffraction, and we show what spatial magnetic information is indeed extractable from this technique.
As regards the history of the technique, X-ray resonant magnetic scattering (XRMS) has been exploited in the soft X-ray range only since the late
nineties. This energy range is host to the largest magnetic resonances of the
magnetically important transition-metal and rare-earth series. The wavelength
at these resonances is between 1 and 2 nm, larger than the atomic lattice spacing
so that atomic resolution cannot be obtained, but highly suitable for magnetic
domain studies. For example, it was utilized to study the internal magnetic
structure of stripe domain lattices in thin film surfaces [13]. Beyond element
specificity, the advantages of XRMS are that it gives information of the collective
behaviour of the domains, showing in a very natural way the size distribution
and correlations between domains.
14
1.3.
C HAPTER 1
This thesis
The main goal of this thesis is to explore the possibilities of XRMS in the
study of the domain structure and dynamics of thin magnetic films. A variety
of pilot experiments have been carried out, and in order to simplify as much
as possible the scientific case, we have extensively used amorphous rare earthtransition metal (RE-TM) alloys. Such films, which are used in magneto-optical
storage devices, are devoid of grain structure. This homogeneity, in combination with the perpendicular magnetic anisotropy, makes them an attractive test
bed for domain studies.
As has already been pointed out, the refractive index changes dramatically around the atomic resonant energies, and thus prior knowledge of these
spectra is needed to conduct XRMS experiments. Chapter 2 is devoted to the
calculation of the magneto-optical constants of the RE M4,5 absorption edges.
In Chapter 3, we investigate the evolution of the disordered domain pattern of amorphous GdFe thin films in out-of-plane fields. The period, correlation length, size of the reversed domain and total scattered intensity are followed as function of the external field along the hysteresis loop. A general
rule relating the scattered intensity from films with perpendicular easy-axis to
the out-of-plane component of the magnetization is derived. Finally, a domain
model is used to calculate the period of the stripe lattice from the shape of the
hysteresis loop.
As a further step, the dynamical response of the same GdFe films is investigated in Chapter 4. By using very powerful magnetic field pulses and
combining the information from time-dependent magneto-optical Kerr effect (tMOKE) measurements and time-dependent XRMS, we find that the magnetic
pulse is so strong as to decouple the magnetization of the constituent Gd/Fe
subnetworks. This phenomenon is explained as the dynamical analogue of the
spin-flop transition observed in other intermetallic compounds.
In an attempt to control the sites of domain nucleation, perpendicular
anisotropic GdTbFe thin films were locally modified by focused-ion-beam irradiation. As shown in Chapter 5, rather than influencing the nucleation process,
these damage arrays affect the morphology of the domain pattern during re-
Introduction
15
versal. With the help of magnetic force microscopy (MFM), we were able to
qualitatively explain the scattering patterns obtained with XRMS. The domains
in the irradiated areas present three effects as compared to the pristine sample:
positional, orientational and size lock-in, depending on the different ion doses
and dot spacings.
On a slightly different note, a study of the coupling between the ferromagnetic (F) and antiferromagnetic (AF) layers of two room-temperature, perpendicular exchange-bias systems is reported in Chapter 6. Our X-ray magnetic
circular dichroism (XMCD) results prove the existence of a small number of uncompensated AF spins at the interface, that rotate along with the F layer. The
relative number of pinned and unpinned AF spins indicate that models developed for low-temperature, in-plane coupled systems are applicable. Furthermore, the domain correlation length and total scattered intensity were followed
along the hysteresis loop with XRMS. Although nucleation and domain-wall
propagation are the two leading reversal mechanisms for both samples, clear
differences appear between the two branches of the system showing exchange
bias, caused by the different activation energies.
In the final chapter, we will look back on what we have learned from this
work and evaluate the usefulness of the XRMS technique.
16
C HAPTER 1
2
M AGNETO - OPTICAL
CONSTANTS AT THE
RARE - EARTH
M 4,5
ABSORPTION
EDGES
For the interpretation of X-ray resonant magnetic scattering and absorption, good knowledge of the magneto-optical constants is extremely useful. In the case of the rare-earth
M4,5 absorption edges, the absorptive part has been predicted accurately on the basis of
atomic multiplet theory. Here we use such calculations with slightly more optimized parameters to obtain the dispersive part via Kramers-Kronig transformation. The complete
dataset should represent realistic values for the complete magneto-optical constants, including the Faraday and Voigt constants which are given explicitly. We shortly discuss
another possible application in X-ray sources based on the Cherenkov effect.
2.1.
Introduction
The increasing use of resonant X-ray techniques in magnetic research
would greatly benefit from good prior knowledge of the magneto-optical constants involved. In general, these can not be calculated ab initio since the dipole
transition matrix element involved contains the unoccupied valence states. A
notable exception form the important M4,5 edges of the rare-earth elements,
where the 3d electrons resonates with the partly filled 4 f shell. The atomic nature of the 4 f shell allows one to describe the 3d-4 f resonance in a purely atomic
18
C HAPTER 2
model.
This was realized first by Thole et al. [14], who predicted the existence of X-ray
magnetic circular dichroism (XMCD) in the absorption spectra M4,5 of Dysprosium. After the successful experimental confirmation of this model in measurements on Terbium garnets by van der Laan et al. [15], calculations for all rare
earths were published by Goedkoop et al. [16]. The influence of crystal field effects on the 4 f shell was described in detail by Vogel [17].
These papers showed that effects of the embedding of the rare-earth atom in
a solid (screening, hybridization, etc.), can be effectively included by applying
small reductions to the two-particle Slater integrals involved in the atomic theory.
In a previous paper [18], we made a detailed analysis of the Gd M4,5
absorption cross sections (unpolarized, circularly and linearly polarized). Using Kramers-Kronig transformations to obtain the real part of the spectra we
showed that these the complete complex optical constants thus obtained accurately describe the energy dependence of the magnetic scattering cross section.
This leads us to expect that the calculated atomic spectra can be used to obtain the optical constants and scattering cross sections for all the rare earth M4,5
edges, and forms the motivation for this chapter.
The structure of this chapter is as follows: Sect. 2.2 gives a brief theoretical description of the resonant absorptive and dispersive corrections to the
refractive index. Sect. 2.3 discusses the experimental methods to obtain the optical constants and the atomic multiplet calculation for the RE M4,5 absorption
cross sections and their comparison for the case of Gd. In Sect. 2.4, the calculated optical constants and resonant scattering cross sections and Faraday and
Voigt rotation are presented for all rare-earth elements. Sect. 2.5 discusses the
results and the possible applications, and Sect. 2.6 presents the conclusions. The
sensitivity of the calculated spectra to variations in the calculational parameters
is investigated in Appendix A.
Magneto-optical constants at the rare-earth M4,5 absorption edges
2.2.
19
Optical constants in the soft X-ray range
The interaction of X rays of energy }ω with matter is described by the
complex refractive index n or equivalently the complex dielectric constant e:
√
n(ω ) = e = 1 − δ(ω ) + iβ(ω ).
(2.1)
Here δ(ω ) is the refractive index decrement and β(ω ) is the absorption index which account respectively for dispersive and absorptive processes. These
two corrections to the refractive index are bound via the Kramers-Kronig transforms [19]:
Z
∞ ω 0 β(ω 0 )
2
dω 0
P
(2.2)
0
2 − ω2
π
ω
0
Z ∞
2ω
δ(ω 0 )
β(ω ) =
P
dω 0 ,
(2.3)
02
2
π
0 ω −ω
so that knowledge of one of the two magnitudes is sufficient to obtain the refractive index n. The P before the integrals stands for principal value [10, 20].
δ(ω ) = −
The complex refractive index is related to the X-ray scattering factor f (q, ω )
that describes the X-ray/matter interaction as [21]:
2πρ a re
f (q, ω ),
(2.4)
k2
where ρ a is the atomic number density, re is the Thomson scattering length and
k is the wavenumber.
The atomic elastic-scattering factor reads
n(ω ) = 1 −
f (q, ω ) = f 0 (q) + f 0 (ω ) + i f 00 (ω ),
(2.5)
where q = k f − ki is the wavevector transfer. The first term f 0 (q) is the Thomson charge scattering, given by the Fourier transform of the electron density
with relativistic corrections ( f 0 (0) = Z ∗ = Z − ( Z /82.5)2.37 ), and is independent of the photon energy. The dispersion corrections f 0 (ω ) and f 00 (ω ) account
for the fact that the atomic electrons are bound, and depend very strongly on the
photon energy. When the photon energy matches the energy difference between
two atomic levels ω0 = ( E f − Ei )/}, the probability of electronic transition between the two levels greatly increases, and so does the total absorption cross
section σa (ω ). The relation between the imaginary part of the atomic elasticscattering factor f 00 (ω ) and the atomic absorption cross section is:
β(ω ) = −
ρa
2πρ a re 00
f
(
ω
)
=
σa (ω ),
2k
k2
(2.6)
20
C HAPTER 2
where f 00 (ω ) and σa (ω ) are respectively measured in electrons per atom and
Å2 . Analogously, we can write for the dispersive part
δ(ω ) =
2πρ a re
[ f 0 (q) + f 0 (ω )].
k2
(2.7)
When the medium through which the incoming radiation travels is magnetized,
the time-reversal symmetry of the entire system is broken. In this case the most
important solution of the wave equation are eigenmodes with well defined polarizations. If the light propagation k and magnetization m are parallel, the eigenmodes are left and right circularly polarized waves propagating in a medium
with refractive indexes n+(−) . If k is perpendicular to m, the eigenmodes are
linearly polarized parallel and perpendicular to m with a corresponding refractive index nk(⊥) .
Just to complete our terminology, we recall that the differences in absorption
( β + − β − ) and dispersion (δ+ − δ− ) are respectively called circular dichroism
and birefringence, scale with the magnetization m, and are directly related to
the imaginary and real parts of the complex Faraday angle. Correspondingly,
( β k − β ⊥ ) and (δk − δ⊥ ) are called linear dichroism and birefringence, which
are the imaginary and real parts of the complex Voigt angle. These linear effects
are proportional to |m|2 .
Although both the electric and magnetic multipole transitions contribute
to the corrections of the refractive index, for the M4,5 absorption edges only the
dipole E1 transitions need to be taken into account. Following the notation of
res = f 0 + i f 00 to the
Hannon and Trammell [22], the resonant contribution f E1
elastic-scattering amplitude can be written as
res
f E1
(ω ) = (ê0∗ · ê) F (0) (ω ) − i (ê0∗ × ê)mF (1) (ω ) + (ê0∗ · m)(ê · m) F (2) (ω ), (2.8)
where ê, ê0 are the polarization vectors of the incoming and outgoing beams,
and m is the direction of the local magnetic moment of the ion. The energy
dependent factors F (0,1,2) (ω ) are linear combinations of the atomic oscillator
1 ( ω ) for electric dipole transitions:
strengths FM
3 1
[ F + F−1 1 ]
4k 1
3 1
[ F − F−1 1 ]
F (1) (ω ) =
4k 1
3
F (2) (ω ) =
[2F01 − F11 − F−1 1 ],
4k
F (0) (ω ) =
(2.9)
with
µ
1
FM
(ω )
=∑
α,η
pα pα (η )Γ x (αMη )/Γ(η )
x (α, η ) − i
21
¶
.
(2.10)
Here pα is the probability to find the ion in the initial state |αi and pα (η ) is
the probability that the excited state |η i is vacant for a transition from |αi. Γ x
gives the partial line width for dipole radiative decay from |η i to |αi and Γ(η )
is the total line width, determined by all (radiative and non-radiative) decay
processes. In the resonance denominator x (α, η ) = ( Eη − Eα − }ω )/[Γ(η )/2]
is the deviation from the resonance in units of Γ(η )/2. For photon energy
}ω = Eη − Eα this term diverges, resulting in a strong enhancement of the
scattering amplitude.
We thus obtain the expressions for the circular and linear dichroism [19,
23] to the imaginary part of the resonant scattering amplitudes F (0,1,2) (ω ):
σ0 (ω ) = 1/3[σ+ + σ− + σk ] = −2λre Im[ F (0) (ω )]
σc (ω ) = σ+ − σ− = 4λre Im[ F (1) (ω )]
(2.11)
σl (ω ) = σk − σ⊥ = −2λre Im[ F (2) (ω )],
where σ+ (σ− ) are respectively the absorption cross sections measured with left(right-) circularly polarized light.
The X-ray resonant complex Faraday [24] and Voigt [25, 26] specific rotations are defined as:
n+ − n−
e F = θ F + iα F =
k
(2.12)
2
nk − n⊥
eV = θV − iαV =
k
(2.13)
2i
The relation between the specific rotation angles and the atomic resonant scattering amplitudes F (1,2) is given by:
θ F (ω ) = −λre ρ a Re[ F (1) (ω )]
α F (ω ) = −λre ρ a Im[ F (1) (ω )] = −
θV (ω ) = −λre ρ a Im[ F (2) (ω )] =
αV (ω ) = −λre ρ a Re[ F (2) (ω )].
ρa
σc (ω )
4
ρa
σ (ω )
2 l
(2.14)
22
C HAPTER 2
2.3.
Resonant cross sections of the RE M4,5 edges
2.3.1.
Calculation of atomic absorption spectra
In the atomic picture, the 3d → 4 f absorption process involves the electronic excitation 3d10 4 f N → 3d9 4 f N +1 , where all the other shells are either filled
or empty (see Fig. 1.2). Both the initial and final configurations are split in
multiplets of states with energies EαJ and wavefunctions denoted by |αJ M i (α
labels all quantum numbers other than J and M needed to completely specify the state). The final-state configuration 3d9 4 f N +1 contains two open shells
and, consequently, its multiplet is more complicated, comprising in the middle
of the Lanthanide series several thousands of levels |α0 J 0 M0 i (primes indicate
final-state quantum numbers). The strongest final-state multiplet interaction is
the spin-orbit coupling of the 3d hole, which splits the multiplet in two parts
which, to a first-order approximation, may be labelled 3d 5/ and 3d 3/ , or M5
2
2
and M4 respectively. In the X-ray absorption spectrum, only those states of the
excited multiplet that can be reached from the Hund’s rule ground-state |αJ M i
under the optical selection rules ∆J=0, ±1, are present. According to Fermi’s
Golden Rule and after using the Wigner-Eckart theorem, the absorption cross
section in the dipole approximation can be written as:
Ã
σαJ M→α0 J 0 M0 (ω ) = 4π 2 α0 }ω SαJα0 J 0 ∑
q
J
1 J0
− M q M0
!2
,
(2.15)
where SαJα0 J 0 = |hαJ ||P||α0 J 0 i|2 is the square of the reduced matrix element of
the dipole operator P, known as linestrength. The element between brackets is
the Wigner 3-j symbol, that dictates the distribution of the linestrength of the
αJ → α0 J 0 line over its different M → M0 components.
Transitions to the unoccupied np-states are also allowed, but, due to the
small spatial overlap, have much smaller cross section compared to the 4 f resonance [27]. The difference in excitation energy between the 4 f resonance and
the continuum edge results from the very efficient screening of the hole by the
4 f N +1 final state.
The 4 f electronic orbital is very efficiently screened by the electrons of
more external orbitals. Owing to this, the effect of the interaction of its electrons with the electronic cloud of the surrounding atoms, i.e. the crystal electric
23
field (CEF) effects, become secondary as compared to the spin-orbit interaction.
As a result, the M4,5 absorption edges can be described with an atomic model
and calculated with atomic multiplet programs. The theory of atomic spectra is
quite involved in the multiplet calculation, and a full explanation of the procedure can be found in Refs. [28, 29, 30]. Various computer programs [31, 32, 33]
have been developed, and we have used Cowan’s atomic Hartree-Fock program
with relativistic corrections [28, 31], which has been applied extensively in the
past [27, 34, 35].
The complete atomic multiplet calculations in intermediate coupling, including all the states of the initial and final configurations, have already been
performed for all rare-earth M4,5 edges [27]. They calculated the relative energy of the different terms of the initial and final states, obtaining the radial
part of the direct and indirect Coulomb repulsion and the Coulomb exchange
parameters, i.e., Ffk f , Fdk f and Gdk f , also called Slater parameters. Together with
the spin-orbit parameters ζ d and ζ f , they determine the energies of the different
terms within the initial and final atomic configurations 4 f N and 3d9 4 f N +1 .
The electrostatic and exchange parameters have typically to be scaled to
80% of their atomic value to account for the solid-state surrounding of the ion
that leads to hybridization and charge transfer with the adjacent ions. These
downscaling factor will be later referred to as κ1,2,3 , corresponding respectively
to Ffk f , Fdk f and Gdk f . The lifetime of all final states is taken to be the same, and all
dipole transitions are convoluted with a Lorentzian line shape of width 2Γ 5/
2
full width at half maximum (FWHM) for the M5 peaks and by a Fano line
shape [36] of 2Γ 3/ FWHM and asymmetry parameter q 3/ for the M4 peaks.
2
2
This difference in line shapes reflects the stronger Coulomb interaction of the
3d 3/ with the nucleus, and therefore the more damped oscillator. The result2
ing spectrum is finally convoluted with a Gaussian line shape with standard
deviation σg to account for the instrumental resolution. In summary, seven free
parameters are needed in the calculation: three reduction factor of the Slater
parameters, two Lorentzian line widths, a Fano asymmetry parameter and the
Gaussian standard deviation.
Large surface crystal electric field (CEF) effects have been found in M4,5
spectra of RE overlayers [34]. For bulk systems, it was also shown that CEF
effects could induce linear dichroism when the atomic symmetry was lower
24
C HAPTER 2
than cubic. For the case of our amorphous thin films, we do not consider the
CEF effects in the calculated absorption spectra, although the atomic multiplet
program allows one to include this extra term of the Hamiltonian.
2.3.2.
Gd3+ experimental spectra
As was mentioned in the introduction, we seek to obtain the complete
set of magneto-optical constants by measuring the resonant absorption cross
sections which directly yield the imaginary part of the scattering amplitudes.
Subsequently, the real parts are calculated by means of the Kramers-Kronig
transforms. This approach requires detailed knowledge of the absorption cross
section over a sufficiently large photon energy range. Since for the rare-earth
M4,5 the atomic resonances are only a few eV wide and the next absorption
lines are at least 50 eV away, such an approach has been found to work satisfactorily, as shown in previous determinations of the RE M4,5 magneto-optical
constants [18, 21, 34, 37, 38, 39, 40, 41].
The required polarized rare-earth M4,5 absorption spectra can be measured in two different ways. The most common one is total electron yield, where
one measures the amount of photoelectrons excited by the incoming X-ray beam
as function of the photon energy [42, 43, 44, 45]. This method does not give absolute cross sections, and is also susceptible to saturation effects caused by the
photon absorption length being longer than the electron escape length. Similar
problems affect total fluarescence yield measurements [46, 47].
These problems are absent in the classical transmission method which
is however not common because it requires sample thicknesses of less than
100 nm on ultrathin supports. Earlier, we measured the Gd M4,5 magnetooptical constants in transmission geometry [18]. Fig. 2.1, reproduced from that
work, shows the measured absolute cross sections of a non-magnetic sample Gd
film giving the non-magnetic resonant contribution and the circular and linear
dichroism of thin GdFe films saturated in field at T = 20 K.
Also shown are the best obtained fits of the calculated spectra for T = 0 K, assuming the Gd3+ angular momentum J = S = 7/2 to be completely saturated.
The optimal parameters obtained from this fit were found to be κ1 = 0.83, κ2 =
0.95 and κ3 = 0.85 as scaling factors for the Slater parameters Ffk f , Fdk f and Gdk f .
The width of the lifetime and experimental broadening were Γ 5/ = 0.3 eV, Γ 3/
2
2
25
Figure 2.1: Comparison of the experimental (symbols) and calculated (full lines) Gd
M4,5 X-ray absorption cross sections. From top to bottom, isotropic, circular and linear
dichroic spectra.
= 0.4 eV, q 3/ = 12 and σg = 0.3 eV.
2
Since these parameters are based on data obtained from an amorphous
material, they are only strictly valid for systems with structural spherical symmetry. However, similar values of κn have been obtained in a monocrystalline
Tb thin film with hexagonal close-packed structure [15, 48]: κ1 = 0.84, κ2 = 1.0
and κ3 = 0.80.
A more detailed study, given in Appendix A, shows that variations of the
width of the lifetime and experimental broadening around the optimal values
do not lead to significant changes in σ0,c,l and F (0,1,2) . Overall, it demonstrates
the validity of the calculated RE M4,5 magneto-optical constants.
Unfortunately, although the experimental and theoretical spectral line
shapes match up very well, the calculated isotropic cross section had to be mul-
26
C HAPTER 2
tiplied by a factor 1.5 to obtain a quantitative fit with the experimental data.
Errors in the nominal thickness and density of the different samples used in
the experiment could also explain this discrepancy. Still, the quantitative agreement is good enough to expect that the calculated cross sections will provide
good predictions for the optical constants for all RE M4,5 spectra.
2.4.
Calculated RE M4,5 magneto-optical constants
The calculated magneto-optical constants for all trivalent RE ions are
shown in the top panels of Fig. 2.2, beginning with the isotropic spectra of
the non-magnetic La3+ and Eu3+ ions. In each case, the top panel shows the
imaginary part of the resonant scattering factors F (0,1,2) (ω ) as obtained from the
atomic calculation and the corresponding real part obtained by Kramers-Kronig
transformation of the imaginary parts extended to a 100 eV range around the
spectral center of mass, which was tested to be wide enough to assure the correctness of the Kramers-Kronig transforms.
Our imaginary-part spectra show more structure than earlier calculations [16, 35]. The new real parts show the dispersion of single absorption lines
in the case of La and Yb, and correspondingly more complicated line shapes
for ions with more extended multiplets. Although the charge contributions F 0
completely dominate the spectra around the resonance energies, at 10 eV away
from them, the contributions of other absorption channels, such as the 3d to unoccupied 4sp and the surrounding absorption edges, become important. The
general trends in these contributions away from resonances are predicted well
by Ref. [49]. Since these backgrounds are non-dichroic, they are not important
for the dichroic spectra listed here. The dispersive parts of the latter do not have
the long tails seen in the F 0 spectra.
The bottom panels of Fig. 2.2 show the scattering cross sections calculated as the squared moduli of the F (0,1,2) . The non-resonant isotropic scattering contribution Z ∗ is indicated by a horizontal dash-dotted line, and has been
added to the isotropic part | F (0) |2 . It is seen that the circular dichroic | F (1) |2
parts and linear dichroic | F (2) |2 parts peak at different energy, which allows one
to change the polarization contrast just by changing the photon energy, which
greatly helps in separating different scattering channels in domain studies (see
for example Sect. 3.3.3). Alternatively, these curves allow one to trade absorp-
27
Figure 2.2: Resonant scattering amplitudes at the RE M4,5 edges, starting with the two
non-magnetic ions. Top panel: Imaginary (top) and real (bottom) parts of the complex
charge F (0) (black), circular magnetic F (1) (red), and linear magnetic F (2) (blue) atomic
scattering factors as function of energy in units of re . Bottom panel: absolute value of the
scattering cross sections | f 0 (q) + F (0) (ω )|2 (black), | F (1) (ω )|2 (red) and | F (2) (ω )|2 (blue)
in logarithmic scale. The horizontal dash-dotted line gives the non-resonant scattering
cross section (continued on next pages, this page: only the two non-magnetic RE ions).
tion contrast to dispersive contrast.
Figs. 2.4-2.5 show the specific resonant Faraday and Voigt rotations as
calculated using Eqs. 2.14. The relative photon energy centers on the centroid
of the multiplet spectra [27].
In the remainder of the section we will discuss the parameter choice used
in the calculation of the imaginary parts. Most of the parameter values were
based on our fit of the Gd3+ spectra. The reduction factors for the Slater parameters were κ1 = 0.83, κ2 = 0.95 and κ3 = 0.85; the Fano asymmetry parameter q 3/
2
= 12 and the Gaussian line width σg = 0.3 eV.
28
C HAPTER 2
Figure 2.2: (Continued)
29
30
C HAPTER 2
31
Overall, these values are smaller than the ones used in an earlier calculation of the absorption spectra [16, 35], which are proportional to the imaginary
parts shown here. This is brought about by the improvement of the experimental resolution over the last two decades, that allows a much better fitting to the
more detailed experimental data. It also required the refinement of the values
for the lifetime broadenings which are summarized in Fig. 2.3. For the light rare
earths, Γ 5/ was chosen to increase monotonically from 0.2 to 0.3 eV, whereas
2
Γ 3/ was kept constant and equal to 0.4 eV. In the case of the heavy RE elements,
2
Γ 5/ = 0.3 eV and Γ 3/ linearly increased from 0.4 to 0.5 eV. This choice of values,
2
2
although admittedly not physically intuitive, is based on the detailed fit to the
Gd spectra, the overall decrease of the core-hole lifetime along the Lanthanide
series [27], and a fit to published electron yield data at the beginning and the
end of the series.
2.5.
Discussion
2.5.1.
Calculated spectra
The calculated cross sections | f 0 + F (0) |2 , | F (1) |2 and | F (2) |2 are very sensitive to the photon energy, displaying intensity changes of several orders of
magnitude in a few eV. At the edges, the cross sections are dominated by absorptive terms, while the long wings around the edges are produced by the real
parts of the F (0,1,2) . It is important to note that these wings are produced by
the Kramers-Kronig transforms and are not influenced by the lifetime and experimental broadenings. Furthermore, we find that the dichroic effects, needed
to perform magnetic studies, are important (and comparable to the charge scattering) only around the resonance energy. It is interesting to observe how, for
light rare earths, the intensity in the inter-edge energy range is only one or two
Figure 2.3: Lifetime values of the M5 (black) and M4 (red) absorption edges used in the
calculation, indicated respectively in the left and right axis.
32
C HAPTER 2
Figure 2.4: Specific resonant Faraday rotation θ F (red) and ellipticity α F (orange). Major
tick marks in the vertical axis correspond to 1 degree/nm.
33
Figure 2.5: Specific resonant Voigt rotation θV (blue) and ellipticity αV (cyan). Major
tick marks in the vertical axis correspond to 1 degree/nm.
34
C HAPTER 2
orders of magnitude smaller than the maximum values. This makes magnetic
studies feasible in a much wider energy range, in regions where absorption is
low, allowing studies of thicker samples.
The non-magnetic RE elements (J = 0 ground state), La3+ and Eu3+ ,
show no dichroic effects due to the spherical symmetry of their 4 f orbital, and
only F (0) is shown. This is mathematically reflected in the optical selection rules:
only the ∆J = 1 transitions contribute to the spectrum, and the 3-j symbols with
J = 0 and q = ± 1 are equal.
Regarding the predominance of circular over linear dichroism, no rule
exists, with the only exception of Gd3+ , where | F (1) (ω )|2 & | F (2) (ω )|2 for energies just below the M5 edge [18]. It should be stressed at this stage the factor
two difference in the relations between the circular and linear dichroism σc,l and
the imaginary parts of F (1,2) (Eq. 2.11): a relatively small linear dichroism may
result in a linear dichroic scattering contrast comparable to the circular counterpart, as can be clearly observed for Yb3+ , where σc = 2σl and | F (1) | = | F (2) |.
As the 4 f electronic occupancy increases along the Lanthanide series,
several trends can be detected in the energy dependence of the scattering amplitudes: firstly, there is a clear gradual intensity shift from the M4 to the M5
absorption edge, to the point that the M4 edge totally disappears for Yb3+ . This
shift is due to the increasing spin-orbit parameter ζ f that, in absence of CEF
effects, determines the branching ratio [50, 51] (ratio of the intensity at the M5
edge to the total). In simpler words, the 4 f occupied levels in the ground state
tend to have more 4 f 5/ character than the empty states [27]. This decreasing
2
intensity of the M4 absorption edge is obviously reflected in the real part and
the squared moduli of the scattering amplitudes. Secondly, | f 0 + F (0) |2 shows,
in semilogarithmic scale, a negative peak-positive peak dispersive shape in all
cases, whereas | F (1) |2 and | F (2) |2 display a more complex pattern, which is very
strongly depending on the internal structure of the multiplets, but not on the
line broadenings (see Appendix A).
Unfortunately, quantitative comparison with literature is nontrivial, since
most of the studies used total electron yield or photoemission, so that one would
need tabulated cross sections well below and above the edges to use as a reference for quantitative analysis. Furthermore, these studies are frequently af-
35
fected by saturation effects. Overall, the peak features and relative height of
the RE calculated spectra are reproduced in the corresponding literature cited
in Sect. 2.3.2.
From Eqs. 2.12-2.14, it is clear that the main features of e F,V come from
the
which have already been discussed. However, larger values found
for the linear dichroic effect as compared to the circular one stress again that it
should not be discarded.
F (1,2)
2.5.2.
Applications
The M4,5 magneto-optical constants are directly involved in a wide range
of studies. We name dichroism experiments, either in transmission [46, 47] or
total electron yield [42, 43, 44, 45]; photoemission experiments [48, 52, 53, 54];
X-ray reflectivity [55, 56, 57]; transmission X-ray microscopy [58, 59]; coherent
scattering experiments [60] and scattering experiments at phase transitions [61,
62].
As for small-angle scattering experiments in transmission geometry, the
knowledge of the resonant scattering factors is vital for planning experiments,
simulations and data analysis [13, 63, 64, 65, 66, 67, 68], especially if they involve non-negligible linear dichroic contrast. For the case of ordered stripedomain lattices, the possibility to switch between F (1) and F (2) contrasts allows
one to discern contributions from out-of-plane and in-plane magnetic domains,
already used for the Gd case [18]. This is also clearly possible at the trivalent
Nd, Pm, Sm, Tb and Dy M5 edges, and to a lesser extent for Ce, Pr, Ho, Er and
Tm.
In the case of transmission microscopy experiments, all the previous considerations can be applied to them, both for linear and circular dichroism, which
has been used to observe ferromagnetic [58]. On the other hand, the shown
spectra are the first ingredient for simulations of reflectivity experiments [56],
both in specular reflection mode and in diffuse scattering measurements.
Recently, in coherent small angle scattering experiments, phase retrieval
algorithms have been successfully applied [12] to recover the real-space image from the scattered speckle patterns. Here multiple scattering and polarization mixing are serious problems, requiring good knowledge of the optical
36
C HAPTER 2
constants. With the advent of the 4th -generation synchrotron sources during the
next decade, such experiments will be widely exploited, so that accurate knowledge of the scattering cross sections will be required.
Finally, a recent pioneering work used the Cherenkov effect to produce
to generate soft X rays by passing a moderate-energy electron bunch through
a foil [69, 70]. Such a source has potential for a laboratory-based X-ray microscope. The requirement for the Cherenkov effect is that the electrons move
faster than the group velocity of the light. Two conditions have to be fulfilled:
the electron should move with relativistic speeds (typically in the 5-25 MeV
range), and the real part of the refractive index must exceed unity. This happens at photon energies just below the absorption edge.
From the real parts of F (0,1,2) (Fig. 2.2), we observe that almost for all elements there exist energy ranges where this condition is fulfilled. The resonant
enhancements presented here are probably the largest that can be found, (with
the possible exception of the corresponding resonances in the actinides), and an
order of magnitude higher than those of the Si and Ni targets used in the original study. Moreover, in the case of target films that are magnetically saturated
along the electron propagation direction, the emitted X-rays will be circularly
polarized. The data presented here therefore are highly relevant for the further
development of soft X-ray Cherenkov radiation source.
2.6.
Conclusions
In a previous study, high-quality transmission Gd3+ M4,5 absorption cross
sections σ0,c,l (ω ) were compared with calculated atomic spectra. The parameters resulting from the best fitted curves (reduction of Slater integrals and line
broadenings), have been used here to obtain the charge, circular and linear
dichroic absorption cross sections for all trivalent-RE M4,5 absorption edges.
The application of the Kramers-Kronig transforms to these spectra provided
the real part of the atomic resonant scattering factors, i.e. the dispersive part
of the refractive index n(ω ). Finally, the total scattered intensity spectra and
the specific Faraday and Voigt rotation angles were given. The sensitivity of
the calculated spectra to the parameter choice is found to be only moderate.
We should also mention that our calculated spectra assume spherical symmetry
without any crystal field effects. Such crystal field effects are small for the 4 f
37
shell, but can change the absorption line shape [17] on the same scale as do the
parameter dependences discussed in the appendix. Such effects can be included
in the calculation once the symmetry of the ion is known.
We expect that these magneto-optical constants will be useful in absorption, scattering and microscopy experiments, and to a lesser degree, photoelectron emission microscopy. Furthermore, they may contribute to the development of a Cherenkov effect X-ray source. The calculated optical constants can
be downloaded from http://www.science.uva.nl/∼ miguel/
38
C HAPTER 2
3
A N XRMS STUDY OF
DISORDERED MAGNETIC STRIPE
DOMAINS IN
a-G D F E THIN
FILMS
X-ray resonant magnetic scattering (XRMS) has been used to investigate the structure
of magnetic stripe domain patterns in thin amorphous GdFe films. Under the influence
of a perpendicular magnetic field, the scattered intensity displays a smooth transition
from a structure factor of correlated stripes to the form factor of isolated domains. We
derive an expression that relates the total scattered intensity of XRMS to the absolute
value of the magnetization. Furthermore, we show how the strong circular dichroism
in the scattered intensity can be used to probe the domain wall structure. Finally, we
find that domain theory is applicable to pre-aligned stripes, but loses relevance with
increasing orientational disorder of the stripe system.
3.1.
Introduction
Magnetization reversal in thin films is a subject that is rich in physics [2]
and highly relevant for the data recording industry. For switching timescales
down to nanoseconds, magnetic reversal involves the field-driven, thermallyassisted nucleation of incipient domains which then grow via domain wall propagation [71]. The dynamics of this process depends strongly on the film thickness and the properties of the magnetic material in question. Furthermore, the
40
C HAPTER 3
film homogeneity determines the density of nucleation centers and the strength
of domain wall pinning. The interplay between these factors leads to a profusion of possible domain structures [2].
Among these, one of the most studied are stripe domains found in thin
films displaying perpendicular anisotropy [5, 13, 72, 73, 74, 75, 76, 77, 78]. In
these cases, the local exchange and anisotropy interactions favor a single domain state with the magnetization saturated perpendicular to the film plane.
The resulting long-range demagnetizing field leads to a break up of this single domain, at the cost of the creation of domain walls. Given the right combination of thickness and magnetic properties, highly correlated alternating
bands of up and down magnetization form. Such stripe systems can have quite
complex structures, the alternating up-down strips being separated by Bloch
walls, possibly capped with closure domains that further minimize the dipolar energy [79]. Additionally, the two-dimensional domain pattern depends on
the magnetic history of the system. After demagnetization in a perpendicular
field, the stripe pattern is disordered, looking much like a human fingerprint,
whereas after in-plane saturation highly aligned stripes appear, oriented in the
saturating field direction.
Since the seminal work of Kooy and Enz [5] the theoretical description
of magnetic stripe domains in applied fields has steadily improved, both for
in-plane [72], and out-of-plane [73, 75, 76, 77, 80] magnetization loops. Such
theoretical approaches, dubbed domain theory models, use a Fourier expansion
of the magnetic structure to calculate the dipolar energy. Furthermore, they assume perfect translational order. However, these models rely on an estimation
of the domain wall energy and do not describe wall structures precisely. Alternatively, the true domain structure can be calculated accurately using micromagnetic finite element methods [74, 81, 82], which however require the stripe
period as an input parameter. The smallest domain period is roughly twice the
domain wall width, which scales with the square root of the film thickness.
In order to test domain models in thin films, experimental methods are
required that give access to the three-dimensional magnetic structure with nanometer resolution. In this context, magnetic stripe morphology has been studied extensively using Magneto-Optical Kerr Effect microscopy (MOKE) [5, 83], which
is the most suitable technique for the study of the evolution of stripe patterns
An XRMS study of disordered magnetic stripe domains in a-GdFe thin films 41
a
b
Figure 3.1: Schematic view of aligned stripe domains (a) and reversed domain (b). The
up (blue) and down domains (orange), Bloch walls (yellow) and closure domains (green
and violet) are depicted.
in external fields. More recently, Magnetic Force Microscopy (MFM) has enabled much higher resolution studies in zero or moderate fields [84, 85, 86, 87].
Another new technique, transmission X-ray microscopy (TXM) [88, 89, 90], exploits the strong magneto-optical contrast at certain X-ray absorption transitions. Since the resolution of the zone plate lenses is still limited, resulting in a
lateral resolution of 25 nm, X-ray resonant magnetic scattering (XRMS) [13, 22,
38, 60, 61, 63, 65, 66, 67, 68, 91, 92, 93, 94, 95, 96, 97] is an interesting and simpler
alternative that could potentially give higher resolution.
In scattering experiments one loses the phase information of the wave
field coming from the sample, thus obtaining - by definition - ensemble averaged information. In this chapter we show that despite this phase problem,
XRMS is a powerful tool for the study of domain structures, especially when
these are periodic.
Data from two 42 nm thick GdFe films are compared here, whereby the
films themselves differ mainly in their saturation magnetization. We show that
the resulting change in dipolar interactions leads to a quite different domain
42
C HAPTER 3
width and magnetization loop. Furthermore, for the sample with the smallest
stripe period, we compare the differences in behavior starting from either the
aligned or the disordered initial stripe structure. We find that the behavior of the
aligned case is described quite well by a domain theory model [76], in contrast
to a recent similar study [63]. This is ascribed to the absence of strong pinning
centers in the flat and structureless amorphous layers that are considered here.
Furthermore, in the case of aligned stripes, we show that the scattered intensity
displays strong circular dichroism, which can be used to estimate the size of the
Bloch wall magnetization surrounding isolated stripes. In addition, we derive a
general relation between the total scattered intensity and the absolute value of
the magnetization.
The layout of the chapter is as follows: after introducing the magnetism
in rare-earth transition-metal thin films, Section 3.2 introduces the magnetic system under investigation and describes the experimental details. In Section 3.3,
we relate the experimental results and their discussion, split into sub-sections
dealing with scattering results (A) for the zero-magnetization state and fielddependent scattering curves (B), the theoretical description of stripe diffraction
patters in the small-angle limit (C) and the field dependence of the total scattering intensity (D), interpretation of the scattering curves (E), the effect of disorder
(F) and domain period and magnetization (G). Finally, we close with conclusions in Section 3.4.
3.1.1.
Magnetism of amorphous GdFe thin films
Amorphous GdFe films have been described [98, 99, 100] both as ferrimagnets (e.g. Gd) and as sperimagnets (magnetic structure of a two-subnetwork
amorphous magnet where the moments of one or both subnetworks are dispersed over a range of angles around the magnetization direction).
For the case of RE-Fe amorphous alloys, ferromagnetic (F) and antiferromagnetic (AF) interactions were deduced from susceptibility, magnetization
and specific heat data within the Fe subnetwork due to different interatomic
Fe-Fe distances [4, 101]. These competing interactions provoke the creation of
two sets of Fe spins within the Fe subnetwork, the F and AF Fe subnetworks.
The number of nearest neighbours in bcc and fcc Fe is respectively 8 and 12, and
they are ferro- and antiferromagnetic. Since the number of adjacent atoms in-
creases with the disorder in the atomic positions, so will do the AF subnetwork.
A non-collinear structure in the Fe-subnetwork spins was observed for
a-GdFe thin films [102], with typical apex half angles of 40◦ . This spin structure
can be understood as a visualization of the F/AF Fe subnetworks, as a result of
the short-range exchange interactions of different signs. A plethora of different
values for the exchange interactions is found in the literature [4, 98, 102, 103].
Despite this, all of them coincide in giving | JFeFe | one order of magnitude larger
than | JGdFe |, and an almost negligible Gd-Gd exchange coupling [102].
a-GdFe was firstly assumed to be a pure ferrimagnet due to the S = 0 character of the Gd3+ ion [104, 105]. However, it was later pointed out that, close to
the ferrimagnetic compensation composition xc (the composition where the Fe
and Gd subnetwork magnetization cancel each other), GdFe may be sperimagnetic [98], with the Gd spins no longer collinear but distributed in a cone-like
shape.
Amorphous GdFe films are structurally highly disordered on a length
scale of several interatomic separations, while being extremely flat and defectfree on a length scale larger than a few nanometers [4]. In our samples, these
properties are reflected in a particularly high degree of perfection of the aligned
stripe systems.
3.2.
Experimental
3.2.1.
Samples: a-GdFe thin films
Gd1− x Fex magnetic thin films with x = 0.83 (sample A) and 0.81 (sample B) were grown by electron beam evaporation on a rotating sample holder
at 1×10−9 mbar. The two selected compositions lie on the Fe-rich side of the
ferrimagnetic compensation composition xc ' 0.76 [106]. A thickness of 42 nm
was chosen to give approximately 1/e absorption at the Gd M5 resonance using
the calculated cross sections due to Thole et al. [27]. As supports we used 100
nm thick commercially available Si3 N4 windows, which have a transmission of
∼95% at the Gd M5 resonance energy. The magnetic films were capped with a
2 nm Al protection layer in order to prevent oxidation. X-ray diffraction scans
showed no trace of structural order in the GdFe films. Rutherford back scattering was used to determine the film thicknesses, as well as to check composition
44
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Table 3.1: Magnetic properties of the Gd1− x Fex films.
Sample
A
B
x
(%Fe)
0.83
0.81
Ms
(kA/m)
221
150
k
Bnuc
(mT )
160.3
228.6
⊥
Bnuc
(mT )
89
7.4
Ku
5
(10 J /m3 )
0.18
0.17
and homogeneity. Atomic force microscopy (AFM) measurements showed that
the surfaces were free of pinholes, flat and structureless on the 1 nm scale.
Figure 3.2: Perpendicular-field magnetization loops of Gd1− x Fex with x = 0.81 (sample
A, top) and x = 0.83 (sample B, bottom). Insets: schematic cross section of magnetic
flux patterns at remanence and close to saturation showing principal stripe magnetization (blue and orange) with their stray field (ellipses), Bloch walls (¯) and closure
magnetization (green and violet).
Table 3.2: Magnetic properties used and obtained from the model explained in
Sect. 3.3.7.
Q
0.58
1.21
µ∗
2.73
1.82
χr0
2.5
12.3
lc
(nm)
13.9
33.2
γw
−
(10 4 J /m2 )
8.5
9.3
δ
(nm)
37.2
42.9
A
λc
(10−12 J /m)
2.6
3.2
0.33
0.79
The magnetization loops of both samples as measured with vibrating
sample magnetometry (VSM) are shown in Fig. 3.2. Their form is typical for
stripe domain samples: a low-field hysteresis-free region separating two triangular hysteretic regions. The insets represent typical low and high field cross
sections of the magnetic flux pattern. The values of the saturation magnetization Ms and the anisotropy constant Ku estimated from the in-plane nucleation
k
field Bnuc are listed in Table 3.1. The main distinction between the samples are
the much smaller perpendicular nucleation field B⊥
nuc and the 33% smaller saturation magnetization of sample B due to it being closer to the compensation
composition xc .
The remanent domain states were imaged with Magnetic Force Microscopy
(MFM). The MFM images were affected to some extent by tip-domain interactions, visible as horizontal discontinuities. Stable images appeared typically
only after a few sweeps over the field of view even when using low moment
tips, indicating low domain wall pinning, and illustrating a limitation of MFM
for domain characterization. The measured periods are listed in Table 3.3.
3.2.2.
Small-angle X-ray scattering setup
The X-ray experiments reported here were carried out at the soft X-ray
beamline ID08 at the European Synchrotron Radiation Facility [107]. The Apple
II undulator source offers complete control over the polarization. The experiments were performed with modest energy resolution ∆E/ E ≤ 10−3 and a
beam size of 100 µm.
Fig. 3.3 shows the layout of the experimental setup. The incident intensity I0 was monitored by reading the drain current from the refocusing mirror.
Either a horizontal 1 mm wire (Fig. 3.4-d, e) or a knife edge (panel f) were used
as beamstops. The scattered intensity was recorded 50 cm behind the sample.
46
C HAPTER 3
Table 3.3: Stripe periods as obtained from MFM and XRMS, and correlation length to
period ratio from XRMS.
Sample
A dis
A ord
B dis
τ( MFM)
(nm)
232
160
835
τ(XRMS)
(nm)
253
162
934
ξ /τ
2
8
1.2
As a detector we used a P20 phosphor-coated (5 µm thick, 1 µm grain size) vacuum window with a 12 bit CCD camera. For the present experiments, a TV lens
combined with a 5 mm macro-ring was used, giving a field of view of ∼15 mm
and a 10 µm resolution.
The co-ordinate system employed here is such that ( x̂, ŷ) define the sample plane and ẑ is parallel to the light propagation direction k. In the longitudinal geometry, the field B = µ0 H is applied parallel to k, while in transverse
geometry B is parallel to x̂. The sample was mounted in a room-temperature
rotatable holder, allowing us to preset the initial alignment of the stripe lattice
to an ordered or disordered lattice by saturating the sample in-plane or out-ofplane respectively.
Beamstop
CCD
Phosphor
screen or
diode
Sample Pinholes
Slits
Figure 3.3: Layout of the scattering experiments. The incoming synchrotron beam is defined with the help of slits and pinholes. The sample could be magnetized transversely
to the beam with a yoked horizontal magnet (not shown). The beamstop eliminates
the straight-through beam allowing the scattered intensity to be measured either with a
photodiode or with a fluorescent layer on a vacuum window, imaged by a visible-light
CCD camera.
Figure 3.4: Left: MFM images of the remanent magnetic domain patterns of sample A
(a) and B (c) after out-of-plane saturation. (b) Id. of the aligned pattern obtained after
in-plane magnetization for sample B. Right: corresponding measured 2D diffraction
patterns.
48
C HAPTER 3
3.3.
Results and discussion
3.3.1.
Scattering curves at remanence
In order to make a connection between the real space domain patterns
as measured with MFM and the reciprocal space scattering data, we compare
three important domain patterns in Fig. 3.4. After out-of-plane magnetic saturation, both samples have a remanent domain pattern (panels a, c) that consists of
completely disordered meandering bands with appreciable domain branching
and truncation. On the other hand, after saturation in an in-plane field, sample
A shows a remarkably perfect aligned stripe system (panel b).
On the right of these MFM images we show the corresponding XRMS
scattering patterns. The disordered stripe patterns produce diffuse rings of scattered intensity [13, 108, 109] (panels d, f), while the aligned stripe system produces very sharp and intense diffraction peaks (panel e), which at the Gd M5
resonance contain even 5% of the transmitted primary beam. The used beam
stops gave scattering vector ranges of (0.004-0.05) and (0.01-0.20) nm−1 for sample A and B respectively. The diffuse background was eliminated before further
data processing by subtraction of exposures taken at magnetic saturation.
Angular integration of these images gives the dependence of the scattered intensity on the scattering wavevector transfer qr , reproduced in Fig. 3.5.
The disordered pattern of sample A (panel a) shows clear first and third diffraction orders, whereas sample B in this case only displays a very broad maximum.
The ordered lattice of sample A, shown in Fig. 3.5-b, produces a series of very
pronounced diffraction peaks, shown here up to the fifth order and marked
with small arrows. The peak width increases linearly with the diffraction order
due to residual disorder in the stripe lattice [110].
From the peak position of these curves, the average domain period τ
can be obtained, while the width gives the correlation length ξ, i.e. the distance
over which the periodicity exists. As shown in Table 3.3, the period values from
XRMS are up to 10% larger than the MFM values, the difference being mainly
due to calibration errors. Also, in sample A the period of the aligned lattice is
30% smaller than in the disordered lattice, due to the absence of branchings and
other lattice faults.
Figure 3.5: XRMS intensity curves obtained by azimuthal integration of the 2D patterns. (a) and (c): the disordered remanent magnetic domains of samples A and B. (b)
Id. for the aligned case for sample A taken with left- (black) and right-circular (red)
polarization.
3.3.2.
Field-dependent scattering curves
Field-dependent XRMS is a convenient and direct way to monitor the
evolution of the domain pattern over these magnetization loops. In general,
the scattered intensity consists of a series of concentric rings, the higher orders showing up more strongly in systems in which the stripe period is better
defined. This is exemplified in Fig. 3.6-a-b, which shows the evolution of the
angularly integrated scattered intensity between the nucleation and saturation
50
C HAPTER 3
Figure 3.6: Field-dependent evolution of the scattered intensity for the disordered domains of samples B (a) and A (b) and for the aligned stripes in sample A (c), taken with
left- (black) and right-(red) circularly polarized beams. Data are displayed on a logaI−
rithmic scale. The asymmetry II++ −
+ I− for the ordered case of sample A is shown using a
linear scale in (d). The value of the applied field in mT is shown next to the traces.
points for both samples. For the sake of clarity not all curves are given. In both
cases we observe a clear evolution of the peak positions and intensities. Sample
A shows more higher order peaks, reflecting the larger correlation length in the
stripe lattice. In both cases the peaks disappear at high fields and ultimately
the curves develop into a broad structure with intensity minima that move to
higher qr . Later on we will identify this structure with the form factor of the
remaining reversed domains as shown in Fig. 3.1-b.
Fig. 3.6-c shows the field dependence for sample A when starting from
the aligned stripe lattice. In this case the initial diffraction spots of Fig. 3.4-e
remain well defined up to saturation, with a constant angular width of 5◦ . This
implies that the reversed stripes are pushed apart, but remain grosso modo parallel. Also, in this case the scattered intensity observed for left and right circularly
beams I+ and I− show a pronounced circular dichroism. The circular dichroic
I−
asymmetry ratio, defined as II++ −
+ I− , is shown in Fig. 3.6-d. Initially the asymmetry curve is strong only at the even diffraction orders, but towards high fields a
broad structure develops with a zero crossing that is located at the qr position
of the minima in the corresponding diffraction curves in Fig. 3.6-c.
In Fig. 3.7 we compile the field dependent data for both samples: the
reduced magnetization mz = Mz / Ms , the domain period τ obtained from the
wave vector of the first order peak, the correlation length of the stripe lattice
obtained from the peak width, normalized to the period ξ /τ and the total scattered intensity. The width of the reversed domain wd given in panel (c) will be
discussed later.
3.3.3.
Stripe diffraction patterns in the small-angle limit
In Sect. 2.2 we showed how the polarization dependence of resonant
magnetic scattering at the RE M4,5 edges could be expanded as function of the
charge, circular and linear dichroic scattering cross sections (Eq. 2.8).
We can rewrite this equation in the form of a simple Jones matrix, first introduced by Hill and McMorrow [111]. In the small angle scattering limit, which
is applicable since the domain sizes are at least 150 times the wavelength, this
gives the simple expression
"Ã
!
Ã
!
#
2
m
m
m
0 −imz
x y
x
Escat =
F (1) +
F (2) E0 .
(3.1)
2
m x my
my
imz
0
Here we choose as an orthogonal basis two polarization directions x̂, ŷ lying in
the plane of the sample and the light propagation direction along the normal
direction, k//ẑ.
If a domain structure m(r) is present in the sample, the resonant terms F (i) will
cause part of the incoming plane waves E0 to be scattered out of the incident
beam, where the far field scattered amplitude is the Fourier transform of the
wave field Eout (r) just after the sample. For samples thinner than one absorption
length, the latter is given to good approximation by taking the integral of Eq. 3.1
over the sample thickness (i.e. we neglect the distortion of the wavefront as it
is travelling through the sample). Introducing the contrast functions gz (y) =
Rt
Rt
0 mz ( y, z ) dz and gij ( y ) = 0 mi ( y, z ) m j ( y, z ) dz (i, j = x, y), where t is the film
thickness, we obtain
#
!
Ã
!
"Ã
g
g
0 −igz
xx
xy
F (2) E0 .
(3.2)
F (1) +
Eout (r) =
gxy gyy
igz
0
52
C HAPTER 3
Figure 3.7: From top to bottom, a) the VSM hysteresis loops (full line) together with
the magnetization value obtained from the scattering data (symbols), b) the period τ,
c) the reversed domain size, wd , estimated from the minima of the form factor, d) the
1st order peak FWHM to period ratio and e) the total integrated intensity (symbols),
together with the 1 − hmz i2 curves, calculated from the VSM data. Left panels: sample
A, right panels: sample B. • represents data obtained from the disordered state, N from
the aligned one. Black/red: increasing/decreasing field.
Notice we have left out the non-magnetic term of Eq. 3.1 as it only contributes
to the average attenuation. Since at any position in the sample, the Bloch wall
magnetization m x is symmetric with respect to the film midplane in ẑ, while the
closure domain magnetization my is antisymmetric, the contrast function gxy
vanishes. The Fourier transform of Eq. 3.2 is
"Ã
!
Ã
!
#
0
−iGz (q)
G
(
q
)
0
xx
E(q) = E0
F (1) +
F (2) ,
iGz (q)
0
0
Gyy (q)
where Gz (q), Gxx (q) and Gyy (q) are the Fourier transforms of the corresponding contrast functions. The far field scattered intensity I (q) = |E(q)|2 is then
given by the absolute square of this amplitude.
We will now narrow the discussion to the case of the aligned stripes in
sample A, which we will approximate by a perfectly periodic set of stripe domains magnetized along the ẑ direction, with translational symmetry in the ŷ
direction. The Bloch walls in this case are magnetized along the x̂ direction, and
can be capped with closure domains with magnetization in the ŷ direction, as
indicated in the insets of Fig. 3.2. Since the structure is invariant along the x̂
direction, the Fourier transform in this direction yields a trivial delta function.
If the incident X rays are linearly polarized along the x̂ direction, the total intensity is given by
½
¾
(1)
2
(2)
2
Ix = I0 | F Gz | + | F Gxx | ,
(3.3)
with a similar expression for ŷ polarization. For circularly polarized incident
light with helicity ±1, the total intensity is:
½
´
1 ³ (2)
2
(2)
2
(1)
2
I± = I0 | F Gz | +
| F Gxx | + | F Gyy |
2
h
i¾
(1)
∗ (2)
± Re ( F Gz ) F ( Gxx + Gyy ) .
(3.4)
The last helicity dependent term is an interference between the polarizationrotating F (1) term and the polarization-conserving F (2) term. It can give circular dichroism if it is non-zero, which happens if Gz (qy ) has the same spatial
frequencies as Gxx (qy ) or Gyy (qy ). The resulting asymmetry is:
h
i
(1) G )∗ F (2) ( G + G )
Re
(
F
z
xx
yy
I+ − I−
¢.
= (1) 2 1 ¡ (2)
(3.5)
I+ + I−
| F Gz | + 2 | F Gxx |2 + | F (2) Gyy |2
54
C HAPTER 3
Figure 3.8: Generic real space scattering contrast functions for a single up domain (A)
and an in-plane (Bloch or closure) magnetization component (B) as shown in Fig. 3.1
and their Fourier transforms (C) and (D). Corresponding form factor for circular and
linear polarized light for | F (2) / F (1) |2 = 0.164 (h̄ω=1184 eV) [18] are shown in (E) and
− I−
the asymmetry ratio II++ +
I− in (F). The domain wall to domain width ratio is 2:9.
It should be noted that at the transition metal L2,3 edges F (2) is small with respect to F (1) , making the linear dichroic effects hard to observe, while at the Gd
M4,5 resonance they can have similar amplitudes [16, 14] and the asymmetries
reach 25% in our circularly polarized data, as shown in Chapter 2. We will first
determine what information can be obtained from this dichroism.
Denoting the total period as τ = wu + wd , where wu and wd are the upand down-domain widths, the average reduced magnetization mz is equal to
Gz (0):
Mz
1
mz =
=
Ms
τ
Z τ
0
gz (y)dy = Gz (0).
(3.6)
For a periodic system, Gz (qy ) will have maxima at qy = 2πn/τ with n any integer. At remanence however hmz i = 0, so that wu = wd = τ/2 and the only
non-zero terms of Gz (qy ) are at qy = 2πn/τ with n odd, explaining the strong
odd numbered diffraction peaks in Fig. 3.5. Since at remanence the period of m2x
and m2y is half that of mz , Gxx (qy ) and Gyy (qy ) are non-zero only at qy = 2πn/τ
with n even, which show up as the second-order peak in Fig. 3.5-a-b. Therefore,
no interference between the in-plane and out-of-plane components exists at remanence. This is not true in out-of-plane fields, when Gz (qy ) contains terms
with any integer n, which will interfere with Gxx and Gyy giving rise to the
dichroic asymmetry observed in sample A in the ordered case. The absence of
dichroism in the disordered cases is not completely understood, although the
most likely explanation is the large disorder.
Clearly, the one-dimensional periodic model used so far is inappropriate
for the broad structure observed at high fields, which can be interpreted as the
sum of form factors of all the uncorrelated reversed domains. To illustrate this,
we show the contrast functions of an isolated reversed domain of width w and
their Fourier transforms in panels (A-B) and (C-D) of Fig. 3.8. Again, the interference between the scattering from the out-of-plane domain and the in-plane
magnetization components (Bloch wall and closure) surrounding it leads to a
helicity-dependent scattered intensity (panel E) and asymmetry ratio (panel F),
which closely resemble the observed line shapes. The position of the minima of
the form factor and the zero-crossings of the asymmetry curves are positioned
at multiples of ( 2π/w) and therefore are a simple means to determine the average size of the reversed domains.
3.3.4.
Field dependence of total scattered intensity
As shown in the bottom panels of Fig. 3.7, the normalized total scattered
intensity is approximated very well by the function 1 − |mz |2 , depicted by a full
line for the two field directions (red and black). Although this behaviour was
already present in recent work from other groups [92, 109], this agreement has
never been microscopically justified. It can be explained by applying Parseval’s
56
C HAPTER 3
theorem to the contrast function gz (y):
1
τ
Z τ
0
2
| gz (y)| dy =
Z ∞
−∞
Z
2
2
| Gz (qy )| dqy = | Gz (0)| +
qy 6=0
| Gz (qy )|2 dqy .
The term on the left side of the equation is the average of the squared reduced
magnetization hm2z i, which equals unity if the in-plane magnetization of the
domain walls can be neglected. According to Eq. 3.6, | Gz (0)|2 = hmz i2 while the
integral over qy 6= 0 is the integrated scattered intensity. Normalizing to the
maximum scattering at remanence, we find:
Iscat
' 1 − hmz i2 .
Iscat (B = 0)
(3.7)
The result implies that the scattered intensity can be used to measure the absolute value of the magnetization for any sample containing mainly out-of-plane
domains.
In the bottom panels of Fig. 3.7 the intensity predicted by this expression is compared to the measured intensity at the diode. A quite good match is
obtained and we have found the same agreement in many other samples. Especially, it is worth noting that the field dependence of the scattered intensity is
the same for the disordered and aligned cases of sample A, while the period for
the two cases is completely different.
3.3.5.
Interpretation of scattering curves
Kooy and Enz [5] found that the magnetization loop of stripe systems
has a reversible part at low fields, which is characterized by reversible adjustments of the relative width of the up and down domain without changes in the
overall pattern. This process continues until the reversed domains cannot be
compressed more, which happens when they reach a minimum width of about
two domain wall widths. From that point on, stripes are eliminated, causing an
increase of the domain period and a loss of long range correlation in stripe position. The stripes then break up into segments [77], which gradually shorten to
magnetic bubbles, located at favorable (i.e. low anisotropy) pinning sites, and
are eventually annihilated by progressively higher fields. On returning from
saturation, bubbles nucleate at much lower fields Bnuc and rapidly finger out
to fill the film surface. This difference in annihilation and creation leads to the
appearance of a distinctive hysteresis in the magnetization loop, characterized
by the triangular shape near magnetic saturation. The main difference between
the two samples considered here (Fig. 3.7-a) is the range of the reversible region
and the nucleation field, both larger in sample A.
This description, developed for MOKE data, can also be applied to the
present data. Starting with the aligned initial state of sample A (Fig. 3.7, left) the
diffraction curves show well-defined higher order peaks with an initial correlation length of eight stripes. In the reversible region, the system mainly adapts
to the field by increasing the up domain width wu with respect to wd while
keeping the lattice period more or less constant. This causes the appearance of
even orders in the Fourier transform of mz , which mix with the scattering of the
in-plane components, producing appreciable circular dichroism as discussed
above. The angular width (not shown) of the diffraction spots stays constant
with field over the whole field range, indicating that the stripes remain parallel
and that we do not reach the bubble state, which should scatter isotropically.
However, above ∼20 mT, the transverse correlation drops linearly with field
(see Fig. 3.7-d) to one stripe width, indicating the complete loss of correlation in
the position of the isolated stripes.
The scattering and asymmetry curves become gradually dominated by
the form-factor shape of the reversed domains with the intensity minima moving to higher q. The reversed domain width w, as estimated from the zerocrossing of the dichroic asymmetry (Eq. 3.5), displays a gradual decrease from
the half-period to 50 nm, with a trend to much smaller sizes. For an ideal stripe
system, the magnetization can be calculated from the reversed domain size and
the period. The result is compared with the reduced magnetization in Fig. 3.7-a,
the agreement being quite satisfactory for lower fields, proving the correctness
of the average reversed domain size obtained this way. Clearly, in the bubble
regime this approach is no longer valid.
By fitting the measured asymmetry curves with a model as in Fig. 3.8F, and neglecting possible closure, we obtain a domain wall width of about 30
nm. With data extending over a more extended range and by using linearly
polarized light it should also be possible to get very precise information on the
reversed domain and the spin structure of the adjacent Bloch wall and closure
magnetization [112].
58
3.3.6.
C HAPTER 3
The effect of disorder
Although the aligned stripes can be qualitatively described with the one
dimensional lattice model, the finite peak widths indicate the presence of disorder in the stripe lattice. Hellwig et al. [63] applied a model [110] to describe
moderate disorder in the domain period of the aligned structure. An important
conclusion from this work is that disorder causes a peak shift towards lower qvalues, implying that the position of the first order peak tends to overestimate
the real domain period. However, actual fitting of the diffraction curves with
this model turns out to be possible only in the most ordered case of sample A
near remanence. From this fit we obtain a Gaussian distribution in the domain
period with a standard deviation equal to 5% of the domain period and a domain wall width of 19 nm, which is considerably smaller than the 30 nm width
of the walls surrounding the uncorrelated reversed domains at high fields.
Fitting with this one-dimensional model becomes impossible for the disordered case of sample A (dots, Fig. 3.7-a). The peak width at remanence corresponds to a correlation length of only two stripes. In applied fields, the diffraction rings broaden much faster than in the aligned case, and quickly merge in
the form factor structure of uncorrelated stripes. The period, correlation length
and scattered intensity all show quasi-parabolic field dependence with only little hysteresis. The period directly after nucleation is twice as big as at remanence and always much larger than that of the aligned case due to imperfections in the lattice such as branching and end points, which prevent the system from reaching the equilibrium domain period. Also, due to disorder, the
circular dichroism becomes washed out over the whole scattering pattern and
becomes too small to be observable. Over a limited range the form factor shape
is clear enough to extract a reversed domain size, but the magnetization calculated from this is too large, probably mainly coming from an underestimation
of the period [63].
Sample B is clearly much more disordered, showing only a single broad
diffraction peak over much of the magnetization loop. The average domain distance decreases rapidly down to a minimum at 9 mT and then increases to values that fall beyond our minimum vector-transfer range. The correlation length
presents a maximum at 8 mT, but it barely deviates from unity. This behavior might indicate that the magnetization arranges in a collection of domains
that look somewhat in between a pure bubble and a stripe domain, as seen
by others [113]. Another indication of this is the wide field range at which a
clear reversed domain size can be observed. Nevertheless, the ratio of reversed
domain size to period again produces a quite acceptable estimation of the magnetization (Fig. 3.7-a). Also, in contrast with sample A, the period shows large
hysteresis, implying that the domain pattern is far from equilibrium over the
whole loop.
3.3.7.
Domain period and magnetization
The Kooy and Enz model [5] predicts the field dependence of stripes
in perpendicular fields by treating the demagnetization energy in terms of a
Fourier expansion and then minimizing the total free energy to obtain the sample magnetization and domain period at equilibrium. The parameters involved
are the saturation magnetization Ms , the uniaxial anisotropy constant Ku , the
exchange stiffness constant A and the film thickness t. They enter the expressions in the form of two dimensionless parameters: the reduced anisotropy material constant
Ku
2Ku
Q=
=
,
(3.8)
Kd
µ0 Ms2
that gives the ratio between the anisotropy energy and the demagnetization
energy, and the reduced characteristic length
λc =
γw
lc
= ,
2Kd t
t
(3.9)
√
that is a measure for the domain wall energy γw = 4 AKu . Here lc is the characteristic length. The model assumes that Q À 1, that the film thickness is
at least several times larger than the period at remanence and that the domain
wall width is negligible compared to the period. The energy lowering due to the
tilting of the magnetization close to the film surface is approximated by introducing an effective rotational permeability µ∗ = 1 + Q1 [2]. Gehanno et al. [76]
extended this model with a better approximation for the demagnetizing energy
density in order to make it applicable to films with thickness smaller than the
domain period and Q 6 1. They obtained analytical expressions for the dependence of the reversible normalized magnetization mz = Mz / Ms and the domain
period τ on the reduced field h = H /µ0 Ms :
³π
´
2
0
mz (h) = arcsin
χ h ,
π
2 r
(3.10)
60
C HAPTER 3
Figure 3.9: Comparison of the reduced reversible magnetization (top) and calculated
domain period (bottom) versus reduced field with the experimental data from sample
A (left) and B (right), with dots for the disordered and triangles for the ordered stripes.
Calculated and experimental results are shown in red/blue and black respectively.
³π
´
π 0
tχr sec
mz ( h) ,
2
2
The reduced magnetic susceptibility is:
¯
√
2 µ∗
∂mz ¯¯
0
χr =
=
exp (πλc + f (r ))
∂h ¯h=0
π
τ (h) =
where f (r ) is a slowly varying function of r = 12 (1 +
(3.11)
(3.12)
√1 ∗ ).
µ
The reduced susceptibility at remanence χr0 can be obtained from the
slope of the out-of-plane magnetization loop (see Table 3.2). By using the obtained value and µ∗ as input parameters in Eq. 3.12, we determined the char√
acteristic length lc , the domain wall energy density γw = 4 AKu = 2Kd lc , the
p
w
domain wall width δ = π A/Ku , the exchange constant A = δγ
4π and the reduced characteristic length λc = lc /t (see Table 3.2). We find that in sample A
both Q and λc are two times smaller than in sample B, reflecting the difference
in saturation magnetization.
The reversible magnetization and period calculated from Eqs. 3.10-3.11
are compared to the magnetization measured with VSM and X-ray derived periods in Fig. 3.9. In the case of sample A, the period, shown in panel (b), at
remanence is now only four times the thickness, and the correlation length is
up to eight periods in this case. Furthermore, it shows very little hysteresis.
Indeed, when magnetizing from the aligned situation, the magnetization and
domain period are predicted accurately by the model up to quite high fields.
On the one hand, this is proof of the retention of a high degree of alignment up
to the field where stripes become unstable with respect to dots. On the other
hand, this success proves the suitability of the model to describe systems with
period a few times larger than the film thickness even for very thin films.
This is in marked contrast to what was found in XRMS experiments on
aligned stripes in Co/Pt multilayered films, where the magnetization adapted
to the field by annihilating stripes, leaving surrounding stripes at the same
position [63]. We ascribe the differences between the two studies to the fact
that the Co/Pt films have a more polycrystalline structure, whereas the amorphous GdFe films studied here were flat and structurally homogeneous on the
nanometer scale. Clearly, in films with such a low level of defects, domain theory is valid.
As was mentioned before, the disorder of the stripe lattice in sample A
causes an increase of the remanent period with a factor 1.5 as compared to the
aligned case (Fig. 3.9-b). In our view this is purely caused by the branchings
and truncations of the disordered stripe system taking up more space, rather
than by domain wall pinning. Strictly speaking, the Gehanno description is applicable only to perfectly aligned one dimensional lattices while the disordered
structure is clearly two dimensional. Still, applying a brute force scaling of the
calculated period for the aligned case by a factor 1.5 produces a remarkably
good agreement with the data.
For sample B, the model gives a magnetization intermediate between the
two branches of the hysteresis loop, but clearly is inadequate in describing the
field dependence of the average domain distance. The low saturation magneti-
62
C HAPTER 3
zation implies much lower dipolar interactions between the up and down domains. This leads to a very large domain period compared to the film thickness
(τ0 /t ' 22) and a very poor correlation (see p. 309 in Ref. [2]). Furthermore, the
large hysteresis in domain period shows that the dipolar interactions are weak
compared to the residual domain pinning. We conclude that in this sample
the domain structure is not in the equilibrium state assumed in the continuum
model.
3.4.
Conclusions
In this chapter we explored the possibilities of soft X-ray resonant magnetic scattering in the study of nanometer-scale magnetic domain structures, using magnetically striped GdFe thin films as a testing ground for this promising
technique. We have worked out a description of the resonant X-ray scattering
process for circularly polarized light in the forward geometry for the case where
the linear dichroic term of the scattering cross section is important, as is the case
at the rare earth M4,5 edges. Using this description, we then went on to explain
the origin of the different scattering features in terms of the out-of-plane and the
in-plane magnetization components. Furthermore, via application of Parseval’s
theorem, a general relation between the scattered intensity and the expectation
value of the modulus of the magnetization could be derived, under the condition that the volume of domain walls and closure domains is small.
Our analysis shows that the amount of information that can ultimately
be extracted from the scattering data is limited by the degree of disorder. In the
most ordered case –the aligned stripes after in-plane saturation– the scattered
intensity shows marked circular dichroic asymmetry. At low fields this asymmetry is located at the position of the even diffraction orders, and is the result of
interference of the scattering from the out-of-plane and in-plane magnetization
components which involve the F (1) and F (2) terms of the resonant scattering
length. At high fields, the scattering becomes dominated by the form factor of
the reversed domains. The magnitude of the dichroic asymmetry provides a
direct way to determine the domain wall width. Moreover, the zero-crossings
of the asymmetry are a direct measure of the reversed domain width which, in
combination with the domain period obtained from the peak positions, yields a
second independent measure of the absolute value of the magnetization. This
value turns out to be in quite good agreement with the magnetization obtained
from VSM measurements.
Regarding the field-induced evolution of the domains in the GdFe system, we found that upon magnetizing from the aligned initial state, the domains
remain parallel to each other up to the field at which they collapse into bubbles.
In this respect, the magnetization and domain period evolve as predicted by the
domain theory of Gehanno et al. [76].
Even in the disordered case, we have been able to follow the average domain
period, the correlation length and the reversed domain size from nucleation to
saturation. The different behavior of the two samples considered can be ascribed to their difference in saturation magnetization.
64
C HAPTER 3
4
S TUDY OF MAGNETIZATION
DYNAMICS OF G D F E THIN
FILMS
The magnetization dynamics under the influence of strong magnetic field pulses of two
ferrimagnetic thin films is studied using time-resolved X-ray resonant magnetic scattering and Magneto-Optical Kerr Effect techniques. In both cases the samples are magnetically excited by a 7 kOe pulse provided by a microcoil. The two amorphous GdFe
films differ in composition and consequently in magnetization. For a composition close
to the ferrimagnetic compensation composition, the Gd subnetwork magnetization vanishes during the pulse, while the Fe magnetization initially does not reach the saturation value. Also, this sample shows a very slow relaxation stretching over hundreds of
nanoseconds. This surprising behaviour points to a loss of magnetization by non-linear
generation of spin waves which affect the Gd subnetwork more than the Fe subnetwork.
In the second sample the Fe subnetwork magnetization dominates the properties more
completely and here the response follows the magnetic pulse closely. Still, traces of spin
wave effects are visible in this sample also.
4.1.
Introduction
The study of magnetic reversal is a subject that has been attracting vast
amounts of interest. It underlies much of our computerized civilization, in
which magnetic data storage has become the default primary way of storing information. In the current devices, the switching speed is breaking through the
66
C HAPTER 4
one nanosecond barrier. This is the boundary time scale between “slow” thermally assisted switching and “fast” precessional switching. In the latter, the
macrospin of a magnetic structure switches coherently by a precessional motion driven by specially tailored field pulses [114, 115, 116, 117]. The important
questions here are what the ultimate attainable speed will be, and how one
can avoid the non-linear generation of spin waves that tend to break up the
macrospin [118, 119]. In the ultrafast dynamics limit, the formation of the magnetization is hampered by bringing the electron, lattice and spin systems out of
the thermal equilibrium [120, 121, 122].
In this work, we stay in the slow thermally assisted domain. Here magnetization switching by an external field occurs by nucleation of domains at
sites in the material where the magnetic anisotropy is lower or the magnetization higher than in the rest of the system. Once nucleated, domains grow by
motion of domain walls. This motion can be accompanied by magnetostrictive effects which tend to limit the domain walls to speeds in the range of the
speed of sound in the material, although speeds up to 10 km/s have been reported. Most practically, structural inhomogeneities can pin the domain walls,
and further thermal excitations are required to depin them. Therefore, reversal
in homogeneous films tends to be dominated by nucleation of many domains
that then coalesce to a completely reversed state, while in very homogeneous
systems a few nucleated domains can rapidly expand by domain wall motion
to reverse the whole system. Both types of behaviour can be described by the
model originally developed by Fatuzzo [123, 124]. However, realistic micromagnetic simulations [4] are necessary to discern the role of pinning centers in
the reversal process.
As magnetic storage media advance in capacity and speeds, new tools
of investigating the underlying physics on ever smaller spatial scale and ever
shorter time scales are required. For fundamental observation of domains, Kerr
microscopy, using the change of polarization of visible light upon reflection by
magnetic surfaces, is a convenient and simple method. However, the resolution is two orders of magnitude larger than the domain wall width. Lorentz
microscopy, a form of transmission electron microscopy, is able to probe the domain structure using the deflection of the electron beam by the stray field of the
magnetic domains with a few tens of nanometer resolution. The invention of the
much simpler magnetic force microscope with the same spatial resolution has
Study of magnetization dynamics of GdFe thin films
67
been a major breakthrough. Spin-polarized STM gives even atomic resolution,
but it is proportionally more difficult and, like MFM, gives only information on
the surface magnetization.
In the time domain, the fastest switching time scales can be investigated
using pump-probe experiments with ultrashort laser pulses. In these experiments, most of the energy of the laser pulse is used to excite the system magnetically thermally, while a small fraction is used to probe the magnetization
after a small time delay using the magneto-optical Kerr effect. This precessional
switching domain is out of reach for current synchrotron-based experiments,
since the time width of the electron bunches is in the 0.1 ns range. This time
structure has been used already for dynamical magnetization studies in spectroscopy [125] and photoelectron emission microscopy [114, 126]. However,
future X-ray free electron lasers will be able to access this time window, and
in some respects, the investigation presented here can be seen as a step in the
direction of the exploitation of these new incredible sources.
In this pilot study, we show that X-ray resonant magnetic scattering is
potentially a useful technique for nucleation studies on time scales between 0.1
and 100 ns and length scales between 50 and 1000 nm. We use low-defect amorphous GdFe films in which we find evidence for an unexpected decoupling of
the two ferrimagnetically coupled Gd and Fe subnetworks. We show that this
decoupling depends very sensitively on the magnetic properties of the GdFe
film.
The scope of this chapter is as follows: Section 4.2 gives a detailed description of the magnetic pulse generation and characterization. In Section 4.3,
we present the experimental techniques and the main results for the sample
closer to compensation composition, which will be discussed and a tentative
model will be presented. Section 4.4 shows the results for the second sample
and analyzes its different behaviour. In Section 4.5 we compare the results of
the two samples and draw conclusions.
4.2.
Magnetic pulse generation
The magnetic excitation was realized with microcoils and special power
supplies developed at the Laboratoire Louis Néel in Grenoble, France. This sys-
68
C HAPTER 4
Figure 4.1: Left: layout of the coil. Overall size 5×5 mm, details not to scale. Grey:
copper conductor, the darker shade indicates the contact areas. Right: SEM image of
the coil bore (courtesy of I. Snigireva, ESRF).
tem provides the strongest magnetic excitations shown so far, and allows us to
study reversal in relatively hard magnetic systems. Fig. 4.1 (left) shows an artistic view of the coil, which was lithographically patterned in a 30 µm thick Cu
layer deposited on a SiO2 -coated Si wafer of 5×5 mm2 [127]. Under the 50 µm
bore, the Si wafer has been etched away.
The darker areas at the top are the contacts to the power supply. Strong
current pulses are provided by discharging a capacitor bank using fast highpower MOSFETs. The current is confined in the bore region by the radial lines.
The rest of the coil provides mechanical strength and heat dissipation. A full
description of the pulse coil setup can be found in Ref. [128].
The right side of the figure shows a scanning electron microscopy (SEM)
image of the bore, and the white circles indicate the 50 µm coil diameter and
the 25 µm X-ray beam size, which could be centered to within ±2 µm. The visible scratches and the slight deformation of the bore were the result of breaking
away with an ultrathin tungsten pin the SiO2 membrane on which the Cu layer
was deposited.
Fig. 4.2 shows the calculated lateral (a) and axial (b) profiles of the magnetic pulse produced by the micro-coil under the conditions used in our experiments. The temporal profile (c) is shown for two different pulse lengths,
-20
-10
r (mm)
0
10
2100
69
20
a
1750
c
beam size
700
600
1400
500
B (mT)
1050
400
700
b
1050
300
200
700
100
350
0
0
0
10
20
30
h (mm)
40
50
-5 0
5 10 15 20 25 30 35 40 45 50
Time (ns)
Figure 4.2: Magnetic field provided by the microcoil system when it is operated at the
single bunch frequency of the ESRF (357 kHz). (a) Radial distribution of the magnetic
field strength at the coil surface. (b) Id. along the coil axis. The grey areas indicate the
edges of the coil. (c) Temporal evolution of the maximum current of 18 and 40 ns wide
pulses.
and was obtained by measuring the voltage difference in the coil contacts. The
shortest pulse has a width at the base of 18 ns and a FWHM of 14.5 ns. The
longer pulse is 40 ns long at the base and differs by having a more extended flat
top. Typical rise and fall times are 3-4 ns.
4.3.
Magnetic reversal in Gd0.19 Fe0.81 films
The magnetic properties and the quasistatic domain evolution of Gd0.19 Fe0.81
(previously sample B) have been discussed in Chapter 3. This sample is close
to the ferromagnetic compensation point and has a relatively low magnetization. In this section we will discuss its nucleation behaviour as revealed by
time-resolved magneto optical Kerr effect measurements and complementary
time-resolved XRMS at the Gd M5 edge.
70
C HAPTER 4
9
8
2
7
3
1
4
5
6
Oscilloscope
Pulse power
supply
Computer
Figure 4.3: Layout of the t-MOKE setup: (1) laser, (2) polarization filter at ±45◦ , (3)
mirror, (4) microscope objective, (5) sample, (6) permanent magnet, (7) polarization
analyser, (8) lens, (9) diode detector.
4.3.1.
Time-resolved MOKE
MOKE is a traditional technique to measure the magnetization of thin
films [2]. Here we describe the time-resolved version of this technique developed at the Laboratoire Louis Néel, and the results obtained with it. This t-MOKE
setup uses a fast digital storage oscilloscope to sample the Kerr signal within a
selected time window and averages it over many cycles.
Fig. 4.3 shows the schematics of the t-MOKE setup. A 5 mW continuous
HeNe (λ = 633 nm, E = 1.95 eV) laser (1) beam passes a dichroic polarizer (2),
is redirected by a mirror (3) and focussed by a microscope objective (4) onto the
sample+coil set (5). The bias field B0 (positive when parallel to the pulse) is
provided by a position-controlled permanent magnet (6). The reflected beam
travels across the analyser (7). Finally, a lens (8) focuses the beam on a 1 MHz
bandwidth Si photodiode detector (9). Both the diode intensity and the voltage
over the coil are sampled during a selected time window around the pulse by
the digital storage oscilloscope with a sampling rate of 1 Gigasamples/s. The
Kerr signal is obtained by subtracting data sets taken with the analyser at + and
-45◦ as controlled by the computer. This procedure maximizes the sensitivity
of the system [128]. The time traces averaged over several thousands of pulse
71
Figure 4.4: Normalized Kerr rotation of Gd0.19 Fe0.81 for increasing bias fields (in mT).
The dashed line indicates the end of the 25 ns pulse.
cycles are transferred via GPIB interface from the oscilloscope to the computer.
The sample substrate was clamped tightly on the coil, so that the film
was pressed against the bore. In order to check for possible heating of the film
by the coil, the whole system was heated up to ∼60◦ C, but no differences in the
magnetic response could be observed. The bias field generated by the movable
permanent magnet was calibrated against a Hall sensor placed at the position
of the sample.
Fig. 4.4 shows the Kerr response to a 700 mT, 25 ns pulse for bias fields
ranging from -210 to -50 mT, represented on a logarithmic-time axis. The signal is shown on a logarithmic axis and is normalized to the interval [-1, 1] to
represent the reduced magnetization. For the strongest bias field (-210 mT), the
pulse is just able to nucleate some domains, after a delay of more than 10 ns and
therefore in the second half of the 25 ns pulse. The decay to equilibrium in this
bias field range takes only 5 to 10 ns.
Upon reduction of the bias field, this response increases and starts earlier until
at -124 mT it shows a flat top, followed by a long tail. for -104 mT, the response
starts at 8 ns after the start of the pulse and the relaxation to negative saturation
takes more than 100 ns. These curves are similar to what Labrune et al. [124]
have observed in low anisotropy GdFe films, albeit at much slower timescales.
72
C HAPTER 4
Figure 4.5: Contour plot of the reduced magnetization m, where white is corresponds
to mz =-1 and black is mz =1. Again a vertical white line indicates the end of the pulse. In
order to plot the delay on a logarithmic time scale, 20 ns have been added to the delay
time. The thick white line indicates the middle of the mz =1 ridge (see text).
However, the curves taken at even lower bias show that the magnetization in
this plateau reaches only 90% of the saturation value.
In fact, for these lower bias fields, the signal continues to increase long after the
pulse has finished, reaching saturation only at 80 ns delay time.
Finally, in the absence of bias, the remanent state contains domains and the
response starts promptly at the beginning of the pulse. Complete saturation is
reached now already after 10 ns, and decay to the original state sets in only after
250 ns. The response in this region is very irreproducible, apparently because
of the presence of very slow magnetic background fluctuations.
Fig. 4.5 shows the contour plot of all t-MOKE curves for bias fields ranging from -50 to -210 mT, where the time base has been shifted by 20 ns in order
to allow the use of a logarithmic scale. The 0.9 magnetization plateau and the
saturation ridge at later times are clearly seen. The thick white line indicates the
middle of the ridge.
B
73
18 ns magnetic pulse
100 ps X-ray pulse
Magnetic response
0
t
B0
Dt
2.8 ms
Figure 4.6: Schematic layout of the stroboscopic XRMS experiment. As in the MOKE
experiment the sample, saturated in the negative direction by the bias field B0 , is excited
by a magnetic pulse. ∆t is the delay time between the start of the pulse and the 100 ps
X-ray pulse.
4.3.2.
Time-resolved XRMS
The puzzling result of the previous section is that when starting out from
a saturated state, the MOKE intensity initially only reaches 90% of the saturation value, and reaches the latter only with long delay. In order to resolve this
issue, we performed time-resolved dichroism and X-ray scattering data taken at
the Gd M5 edge. Fig. 4.6 shows the timing schematics. The power supply was
triggered by a delay generator that was synchronized to the synchrotron bunch
marker signal. The pulse duration was 18 ns. We used the single bunch mode
of operation, in which the X-ray pulse length is about 80 to 100 ps, and the time
between pulses 2.8 µs, allowing the sample to relax back to equilibrium.
The Gd magnetic response was probed by the X-ray pulse at a delay time
∆t. Unfortunately lack of time prevented us from measuring also the Fe L3 response. Most of the data were collected by integrating the scattered intensity
with an X-ray diode. Data-acquisition times were typically several seconds per
delay time, corresponding to ∼ 106 cycles. In addition, q-resolved data were obtained with the 2D detector described in Sect. 3.2.2. Compared to those experiments, here the count rate is strongly reduced: firstly, the single-bunch intensity
is typically 20 times lower than under normal conditions; secondly, the use of a
25-µm beam costs a factor ∼ 150. Finally, during nucleation, there is not much
to scatter from, and we had to use image acquisition times of 15 minutes.
74
C HAPTER 4
Figure 4.7: (a) Raw data of the scattered intensity with +1 and -1 helicity. (b) Relative
magnetization mz (pink) and normalized scattering S (cyan). Full line: shape of the 18
ns pulse.
Data treatment
±
Fig. 4.7-a shows an example of the time trace of the intensity Idio
, collected at the diode after blocking the transmitted beam with the beam stop.
It unavoidably contains a spurious background intensity Sb generated by pinholes and optics before the sample, which can be large compared to the true
scattering signal S, especially when observing domain nucleation. As discussed
before, both signals are attenuated by the dichroic sample transmission factor.
Thus, we can write
±
Idio
I0±
±
= T ± ( S + Sb ) = e − µ t ( S + Sb ) ,
where I0± is the incident intensity, T ± is the helicity dependent transmission, µ±
is the dichroic absorption coefficient and t the film thickness.
Since the absorption dichroism µc = µ+ − µ− is linearly dependent on the zcomponent of the Gd magnetization, we find for the helicity scattered intensity
and the reduced magnetization mzGd
+
−
S + Sb ∝ 1/2( Idio
+ Idio
),
+
−
I − Idio
mzGd ∝ dio
+
− .
Idio
+ Idio
(4.1)
(4.2)
75
Figure 4.8: Contour plots of (a) mzGd (t, B) and (b) S (t, B) from sample Gd0.19 Fe0.81 in the
high bias-short delay time region. The colour bars indicate the corresponding intensity
scales. The vertical full lines indicate the duration of the magnetic pulse.
After subtracting the background Sb and normalizing the result from zero to
unity, we obtain the relative scattered intensity S (t) = S(t)/S(t = 0, B = 0),
which is a measure of the number of scattering magnetic domains [63, 110, 129].
Fig. 4.7-b shows an example of these signals in comparison with the time trace
of the magnetic pulse.
Results
Data like those in Fig. 4.7 were collected for many different bias field
values. The results were condensed in mzGd (t) and S(t) vs t contour plots as in
Figs. 4.8-4.9. These figures correspond to two different data sets: the first one
shows the early stages of the pulse (from -1 to 24 ns) and the high bias field
range from -225 to 10 mT, while the second dataset gives the low bias range
between -51 to 10 mT over a much longer time window of 600 ns.
The high bias contour plot of the Gd subnetwork magnetization Figs. 4.8a shows an overall agreement with the MOKE data, although the detailed comparison is slightly hampered by the different pulse widths. Note that the contrast is reversed as the Gd magnetization is opposite to that of the Fe. As in the
MOKE data, the change in the magnetization sets in about 5 ns after the start of
76
C HAPTER 4
the pulse at low bias and 8 ns at high bias. Most of this delay can probably be
ascribed to the rise time of the pulse.
At bias fields beyond -150 mT, the induced Gd magnetization lasts only a few
nanoseconds. The MOKE signal seems to peak later than the Gd signal. In
this region there is some scattering, apparently from the induced domains, with
more intensity at the end of the pulse.
At lower bias fields, between -150 and -50 mT the magnetic response increases
in amplitude and basically follows the pulse. The scattering however splits up
in two ridges centered on the regions where the time rate of change of the magnetization is highest. In this region the MOKE signal basically shows similar
behaviour.
For bias fields between -50 and -20 mT, the sample is still saturated between
pulses, but the field pulse first produces a huge scattering ridge, after which
the magnetic signal completely vanishes, as does the scattering signal. This
extremely surprising state (seen in more detail in Fig. 4.9), moreover lasts up
to 90 ns, well beyond the end of the pulse. Note however that this anomalous
behaviour coincides with the reduced magnetization plateau of the MOKE data.
Finally, for the lowest biases the sample is no longer saturated before
the pulse. As in the MOKE data, the magnetization now reacts promptly to the
pulse, and the recovery to equilibrium lasts up to 600 ns. The scattered intensity
reacts synchronously with the magnetization and is decreased for all bias fields.
In order to get an impression of the correlation lengths involved, we measured the q-resolved scattering at the fields indicated by the dashed horizontal
lines in Fig. 4.8. The high-field data, taken at B0 = -48 mT, are shown in Fig. 4.10a. The extremely weak signal indicates long correlation length as indicated on
the top scale, and perhaps an average distance between nucleation centers of
about 200 nm during the first scattering ridge at the moment where the magnetization is changing fastest. At the second ridge at the end of the pulse, the
correlation lengths are even longer.
The time evolution of the q-resolved intensity distribution for the strongly
scattering remanent case is shown in Fig. 4.10-b. Surprisingly, during the pulse,
the diffraction curve does not seem to change noticeably, except for the 50%
reduction of the intensity already visible along the upper dashed line in the
contour plot (Fig. 4.8). This is in marked contrast with the increase of the period
77
Figure 4.9: Contour plots of (a) mzGd (t, B) and (b) S (t, B) from sample Gd0.19 Fe0.81 in the
low bias-long delay time region. The colour bars indicate the corresponding intensity
scales. The vertical full lines indicate the duration of the magnetic pulse. 20 ns have
been added to the delay time to use logarithmic time scale.
observed in the quasi-static case and we have to conclude that apparently the
correlated domain system is quite rigid under the fast pulse. The average domain size τ = 864±8 nm with a correlation length ξ = q/∆q = 0.92 is very similar
to the values of the remanent system (934 nm and 1.2 respectively) obtained in
the previous chapter. It is however still quite possible that the pulse increases
the width of the up domains at the expense of that of the down domains. In
principle such a breathing of the domains without a change in the periodicity
would reduce the first order intensity. In principle the second and higher even
order intensities should increase, however, already in the quasi-static situation
these are not visible in these disordered samples.
In the previous chapter we have used Parseval’s theorem to show that
the scattered intensity is proportional to 1 − hmz i2 . In all quasi-static datasets
that we encountered so far, this relation was observed. Inspection of the magnetization and scattering contour plots suffices to see that in these dynamic measurements this is not the case. Instead, we see that the strongest scattering occurs on the edges of the magnetization contour, where the rate of change of the
magnetization is highest.
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Figure 4.10: Semi-log plot of diffraction patterns from Gd0.19 Fe0.81 taken during the
pulse for (a) saturated sample and (b) relaxed domain state (dashed white lines in
Fig. 4.9). On the right of each curve the delay time is given in ns.
Violation of Parseval’s theorem means that either the Gd magnetization
has turned in-plane or the length of the magnetization vector has decreased. We
can not discriminate directly between the two cases. However, the absence of
scattering in the plateau region means that the Gd subnetwork is in a homogeneous magnetization state. The ultimate reduction of the length of the magnetization occurs when the sample is driven above the Curie temperature. That
this is not the case is obvious from the MOKE data which show a clear magnetic
signal. We surmise that the Gd magnetization is reduced by the generation of
spin waves, as will be discussed in more detail below.
4.3.3.
79
Discussion
In order to interpret these time-resolved MOKE and XMRS results we
have to consider the origin of the MOKE signal and the magnetic structure of
amorphous GdFe alloys.
Crystalline Fe has a negative Kerr rotation between 0.5 and 5 eV and reaches
0.28’ at 1.1 eV, while pure Gd has a positive Kerr rotation in the entire spectral
range with a strong peak at 4.2 eV due to p-d interband transitions. According to Hansen [98], in the infrared and red spectral range, the MOKE signal of
GdFe alloys is dominated by Fe 3d and Gd 5d intraband transitions, while at
higher energies p-d and d- f interband transitions dominate. Since the Gd and
Fe subnetworks are antiparallel, the total Kerr angle is negative above the compensation point. For our samples and at the HeNe laser frequency, the Fe Kerr
contribution is 20 times larger (θKFe ≈-30’ [130]) than the Gd (θKGd ≈ 1.4’ [131]),
so that the MOKE signal is primarily sensitive to the behaviour of the Fe subnetwork [98, 130, 131, 132, 133, 134].
The magnetic order in RT systems involves an Fe-Fe exchange interaction that is dominating the Gd-Fe indirect exchange, while the Gd-Gd interaction does not play any role [134]. In the amorphous system, the details of the
magnetic structure are not clear. There may be dispersion in the Fe directions,
and Mansuripur [4] claims the importance of both parallel and antiparallel couplings in the Fe subnetwork. While in L6=0 rare-earth elements, the R moments
are strongly dispersed around the surface normal, in GdFe the Gd spin-only
moment should be well aligned. In the rest of the chapter we will ignore possible moment dispersion as it does not seem to play an important role.
In our samples the Fe moment is larger than the Gd moment, so that before the beginning of the pulse, the Fe magnetization is along the bias field direction. The pulsed field completely overwhelms the bias field and, as a result,
the Fe magnetization reverses. Clearly, at the start of the pulse, the Gd magnetization is initially parallel to the pulse-field direction. As the Fe subnetwork
reverses, the Fe-Gd exchange prevails over the pulse field and tries to rotate the
Gd moment against the pulse field. Indeed, in the Gd signal we do see a few ns
of scatter indicating nucleation of domains. For high bias fields, these domains
are annihilated at the end of the pulse. However, for bias fields between -50 and
-20 mT the Gd magnetization disappears, only to resurface much after the end
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of the pulse. At the same time the Fe signal from t-MOKE does reach only 90%
of the saturation value.
Ferrimagnetic RT films are known to be susceptible to field-driven spin
reorientation transitions when they are close to the compensation point. In
that case, a ferrimagnet is quite similar to an antiferromagnet which, in high
applied fields, can make a spin-flop transition. In this spin-flopped state, the
antiferromagnetic anisotropy direction is normal to the field but the moments
of the two subnetworks rotate away from this direction into the field direction [135, 136, 137, 138]. Indeed, in an XMCD study of the amorphous ErFe
compound, a sister compound of the GdFe system, it was found that at the compensation temperature, the Er and Fe moments are parallel in applied fields.
A simple interpretation of this behaviour could invoke the dynamic analogy of such a reorientation transition. However, if this were the only explanation, the Gd moment should not vanish but become positive. We therefore have
to look to a further mechanism that can reduce the magnetization in the way
observed here. Such a mechanism can be the generation of spin waves.
Coherent spin reorientation is well described by the Landau-LifshitzGilbert equation [139]:
∂m
= −γ m × Be f f + αγ m × (m × Be f f ).
∂t
(4.3)
In this equation, γ is the gyromagnetic frequency and α a phenomenological
damping parameter. The first term describes the precessional motion of a spin
that has been deflected from its equilibrium position in the field Be f f . The
Gilbert damping term causes the precessing spin to spiral back to the equilibrium magnetization axis. In this equation, the magnetization is assumed to be
conserved. However, in hard driven systems the non-linear precessional motion of the spin generates spin waves. When enough spin waves are generated,
different parts of the system start to lose phase coherence, causing the net spin
moment of the system to decrease. This phenomenon was first observed as a
saturation effect in ferromagnetic resonance experiments [140], and was theoretically described by Callen [118]. In recent laser-driven pump-probe experiments by Silva et al. [141], these effects were also found to be observable in the
time domain in the form of a reduction of the length of the magnetization vector. These results were subsequently explained by Safonov [142] in an approach
81
Figure 4.11: Contour plots of (a) mzGd (t, B) and (b) S (t, B) from sample GdFe5 . The
vertical full lines indicate the duration of the magnetic pulse. The white dashed lines
indicate the bias fields at which the q-resolved data were collected.
based on the Callen model, in which the precessing spins generate magnons
which eventually break up the coherent precessional motion.
It should be stressed that in the work of Silva and most other studies, the
response of soft permalloy films is studied using somewhat faster but relatively
weak field pulses. In the present case, the field pulse is large compared to the
anisotropy and bias fields. Under these conditions, the generation of spin waves
is a likely origin of the vanishing Gd moment and the reduced Fe moment.
Apparently, the Gd network is affected more than the Fe network. A possible
explanation is that the Gd is aligned primarily by the Fe-Gd indirect exchange.
The pulse field is opposite to this interaction. The Fe network on the other hand
is subject to the strong Fe-Fe direct exchange.
4.4.
Magnetic reversal in GdFe5
4.4.1.
Time-resolved XRMS
Time-resolved XRMS data from GdFe 5 (sample A in the previous chapter) are condensed in the form of contour plots in Fig. 4.11, showing the Gd
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Figure 4.12: Diffraction patterns from GdFe5 as explained in Fig. 4.10.
magnetization mzGd and the scattered intensity. We see that the pulse induces an
increase in mzGd that disappears when the pulse is finished. The amount of deflection of the contour lines decreases as the modulus of the bias field decreases.
The MOKE results showed very similar time scales.
In saturating bias fields, the scattered intensity increases during the pulse
due to the nucleation of domains. For weaker fields, the start of the domain
scattering is similar as in Gd0.19 Fe0.81 . However, the return to the equilibrium
position is very prompt. Also, there is no direct sign of a vanishing Gd moment.
However, also in this case Parseval’s theorem is not fulfilled, pointing to a decrease of the Gd moment.
Again we measured q-resolved data in the saturated and domain states,
at bias fields B0 = -113 and 32 mT, indicated by dashed white lines in Fig. 4.11. In
the saturated state (Fig. 4.12-a), the top of the field pulse is just able to produce
83
some nucleated domains, which scatter to a very weak ring. As in the previously discussed sample, there is a weak scattered signal at very low q which,
after 6.3 ns, develops a broad maximum corresponding to a correlation length
of 225 nm. Due to the low signal intensity, it is very difficult to extract information from these curves, and the presence is mainly justified as an experiment
that is worth improving.
The diffraction curves from the system in the domain state (Fig. 4.12-b)
display a clear first diffraction order peak. The average period τ=198 nm agrees
again reasonably well with the static period τ=232 nm. As in the other sample,
the peak position does not appreciably change during the pulse while the intensity is reduced, in contrast to the change in period observed in the quasistatic
case. This stiffness of the domain lattice suggests the presence of domain-wall
resonance modes [143], the archetypical response to perpendicular excitations.
We argue that the reduction of the scattered intensity is due to a partial reduction of mzGd magnetization during the pulse. In the down-domains that have
their Fe magnetization in the direction of the pulse, the Gd moments are oriented against the pulse field by the Gd-Fe exchange. When the Fe magnetization is saturated in the pulse field direction, it drags the Gd spins along, leading
to a considerable spin canting of the Gd moments. This would reduce the scattering contrast without affecting the average period.
From the t-XRMS results we conclude that the response of GdFe5 to the
pulse is mainly driven by nucleation and domain wall motion. However, the
scattering S disagrees with 1 − hmz i2 around remanence. This suggests that
the spin-flop transition proposed for the other sample is also present. However,
this effect is weaker here, since mzGd is reduced but not cancelled, and the system
relaxes immediately after the pulse finishes.
4.5.
Conclusions and outlook
We have shown that time-resolved XRMS is a useful technique for studies on nanoscale magnetic phenomena. With the current synchrotron sources, it
provides the magnetization and scattering from domains, as well as the domain
sizes with a current spatial and time resolution of 30 nm and 100 ps.
The combined use of XRMS and MOKE allowed us to study the breaking
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of the antiparallel coupling in amorphous GdFe ferrimagnetic films subjected
to very strong magnetic pulses. In a sample that is close to the ferrimagnetic
compensation composition, we observe a reduction of the Fe magnetization in
the reversed state and the complete disappearance of the Gd magnetization.
Also, relaxation to the equilibrium state of the total magnetization lasts much
longer than the pulse. If domains are present prior to the pulse, the reduced
Gd contrast seems to affect only the domains initially oriented against the pulse
direction. In this case relaxation times are even longer.
The loss of magnetization is interpreted as a dynamical spin-flop transition in combination with spin wave excitation. Spin-flop transitions have been
predicted and observed in amorphous ferrimagnets, but always under quasistatic conditions of applied field and temperature. Apparently, in the dynamical situation described here, the Fe magnetization follows initially the pulse,
but the weak Fe-Gd exchange coupling is not strong enough to keep the Gd
antiparallel to the Fe subnetwork. This could be due to the generation of vast
amounts of non-linear spin waves that lead to the decoupling and the reduction
of the Fe magnetization and the complete disappearance of the Gd magnetization. Very likely, these spin waves transfer energy to the phonon bath, leading
to a temperature rise of the sample in the early stage of the pulse. After the
pulse has ended, the sample cools down again, and in equilibrium with it the
spin waves damp down, resulting in a restoration of the coupling. Only then
the reunited magnetic structure starts to decay back to the equilibrium situation
via thermally assisted nucleation as described by Labrune [124].
In contrast, in a sample with composition further away from compensation, that is, with higher Fe content, the magnetization closely follows the
temporal evolution of the pulse. Here also, the loss of scattered intensity is a
sign of a decrease of the Gd sublattice magnetization. The largest difference in
the magnetic properties of the samples are the saturation magnetization Ms and
the quasistatic nucleation field B⊥
nuc , which both decrease on nearing the compensation composition. Thus, the ratio between the maximum pulse field and
the quasistatic nucleation field is 10 for GdFe5 and 150 for Gd0.19 Fe0.81 . This
means that for the pulse amplitude used here, the former sample is excited less
strongly than the latter, and spin wave excitation is not as important. The difference in relaxation times back to equilibrium then is only due to a difference
in magnetization, as is normal in thermally assisted nucleation processes.
85
This pilot study opens a new experimental approach in the study of magnetization dynamics. Since scattering is an incoherent technique, it is not limited
to systems with well-defined nucleation centers, as in the case of time-resolved
imaging techniques, but can be used for the study of nucleation studies as presented here. Unfortunately, our q-resolved results suffered from a lack of signal,
not enough to record higher harmonics which would have allowed an assessment of the relative width of up and down domains. We estimate that an intensity gain of three orders of magnitude would be readily achievable by using
a better focused beam line and a back-thinned CCD camera optimized for soft
X rays. Obviously, future work will require more extensive characterization
of the pulse height dependence and should include the Fe response measured
at the Fe L3 edge. More extensive XMCD studies might reveal changes in the
orbital and spin moments which could shed more light on possible spin reorientation transitions. On the theory side, micromagnetic or analytical simulations
with time-dependent exchange constants would help to understand better the
present energy transfer mechanisms.
Future X-ray Free Elector Lasers (XFELs) will provide coherent 100 fs
pulses with intensities comparable to the integrated intensity in one second at a
third generation synchrotron. These sources offer huge potential for magnetooptical studies well into the coherent spin rotation regime, and may enable the
study of spin-lattice interactions. Time resolved resonant magnetic scattering
will certainly feature prominently among the techniques used at these sources.
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5
A N XRMS STUDY OF
ION - BEAM - PATTERNED
a-G D T B F E THIN FILMS
In an attempt to produce well-defined domain nucleation centers, square arrays of artificial defects were produced by focused-ion-beam irradiation of amorphous Gd11.3 Tb3.7 Fe85
thin films. Using X-ray resonant magnetic scattering we followed the domain structure
over the magnetization loop. Rather than affecting the domain nucleation mechanism,
the irradiated dots are found to hinder domain wall motion and thus strongly affect the
alignment and size of the domain pattern.
5.1.
Introduction
In the previous two chapters we studied the static and dynamic evolution of magnetic domains in nearly defect-free thin films with perpendicular
anisotropy using X-ray resonant magnetic scattering. As is clearly illustrated
in these chapters, the Fourier transform involved in scattering dictates that the
amount of information that can be obtained from a scattering experiment increases with the degree of order of the scattering object.
In the present chapter, we impose order on the pinning landscape of similar films using a focused ion beam (FIB) to reduce the out-of-plane anisotropy
in a square grid of nanodots with a diameter comparable to the domain wall
thickness. The underlying assumption was that these dots would act as pref-
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erential nucleation sites, allowing us to film the growing domains using the
time-resolved technique described in the previous chapter. By reducing the ion
fluence, one would in this way be able to extrapolate to the intrinsic nucleation
behavior. As will become clear in the chapter, even the lowest ion fluence used
here causes the anisotropy to lie in the film plane. As a result, the nucleation
field is not affected by the dots. However, the domain patterns are strongly affected. We find that at remanence the dots form strong domain pinning centers,
while in applied fields they are the preferred sites for the down domains.
Ion irradiation has been extensively used to modify the magnetic properties of crystalline [144, 145, 146, 147, 148] and multilayered [149, 150] magnetic
materials. In these systems, ion irradiation decreases the crystalline order or
leads to interface mixing. In films with an out-of-plane easy axis, this results in
a reduction of the perpendicular magnetic anisotropy [151, 152].
In amorphous metallic films, the energy of the incident ion causes a partial annealing of the film, leading to the formation of nanocrystallites [153]. As
far as we can tell, no studies on the effect of ion irradiation on the magnetism of
amorphous films have been performed so far. Since the perpendicular magnetic
anisotropy in rare earth-transition metal films is due to anisotropic pair correlations frozen in during the deposition process, the expectation is that the partial
annealing reduces the anisotropy.
In the course of this project, rare earth-transition metal films of different
composition were irradiated with square lattice patterns, with a range of interdot spacings a and ion fluences φ. The film described here differs from the GdFe
samples studied in the previous two chapters in that it contains a small fraction
of Tb. Owing to its single-ion anisotropy, small fractions of Tb content are sufficient to cause a marked increase in Ku . This, together with the concomitant slow
domain-wall propagation [124], results in a very disordered domain pattern for
the demagnetized pristine sample.
Here we use XRMS to monitor the evolution of the domain pattern over
the magnetization curve, obtaining the averaged microscopic properties of the
system such as domain orientation and domain size. We show that the FIB irradiation indeed locally reduces the perpendicular anisotropy in RT films on
the nanometer scale without significantly changing the film topography. This
An XRMS study of ion-beam-patterned a-GdTbFe thin films
89
Figure 5.1: Hysteresis loops of pristine Gd11.3 Tb3.7 Fe85 . Out-of-plane loop (black) measured with polar MOKE and in-plane loop (red) measured with longitudinal SQUID.
causes the irregular native domains to have a preferential orientation in the direction of the dot array.
In Sect. 5.2 we will describe the properties of the as-grown GdTbFe samples and the effect of FIB irradiation on their magnetic properties. The results
from the XRMS data will be presented in Sect. 5.3 and discussed in Sect. 5.4.
Finally, the main conclusions will be outlined in Sect. 5.5.
5.2.
Experimental
5.2.1.
Samples
The amorphous 50 nm thin Gd11.3 Tb3.7 Fe85 films was deposited by molecular electron beam evaporation as described in Sect. 3.2.1. Superconducting
quantum interference device (SQUID) magnetometry and magneto-optical Kerr
effect (MOKE) were used to characterize the sample. Fig. 5.1 shows the perpendicular and in-plane hysteresis loops of the pristine sample.
The uniaxial anisotropy constant Ku can be estimated from the in-plane
nucleation field Bcr and the saturation magnetization Ms as 1/2 Ms (Bcr − µ0 Ms ).
An interpolation of literature values [154] for Gb15 Fe85 and Tb15 Fe85 was used
to estimate the exchange stiffness constant A. The resulting value yields in turn
a domain wall width δ which is ∼50 times smaller than the average domain
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Table 5.1: Properties of a pristine Gd11.3 Tb3.7 Fe85 film.
t
(nm)
50
Ms
(kA/m)
320
Bcr
(mT )
1256
Bc
(mT )
22.6
Ku
(105 J /m3 )
1.4
size at remanence τ0 ∼ 400 nm. The obtained magnetic parameters are listed in
Table 5.1.
5.2.2.
Focused-ion-beam irradiation
Initial investigations used the wide-beam ion implanter at AMOLF to irradiate GdFe films with low-fluence doses of 125 keV Ar+ ions. Fig. 5.2 shows
the polar MOKE hysteresis loops of the pristine and irradiated films with increasing fluence (for sake of clarity, only the downwards branch of the hysteresis loop is shown). In the inset, the increasing perpendicular saturation field
and the decreasing slope at remanence prove that the perpendicular magnetic
anisotropy gradually decreases with increasing fluence, in accordance with the
literature [145, 151]. These results demonstrate that even these low doses strongly
decrease the out-of-plane anisotropy without changing the surface morphology:
even the smallest dose is sufficient to destroy the typical stripe signature of the
hysteresis loop and to cause the magnetization to rotate in-plane.
Figure 5.2: Polar MOKE hysteresis loops of a-GdFe5 film homogeneously irradiated
with 125 keV Ar+ ions. Inset: saturation field (black) and slope at remanence (red).
91
Table 5.1: Continued
Kd
5
(10 J /m3 )
Q
0.62
2.25
A
(10−12 J /m)
1.02
δ
(nm)
8.5
γm
−
(10 4 J /m2 )
15.1
As a next step, the focused-ion-beam facility at MESA+ (University of
Twente) was employed to pattern the specimens. Using a 30 keV Ga+ ion beam
that was focused to nominally 30 nm, nine square lattices of resolution-limited
dots were written on both samples. Both the nominal interdot spacing a (200,
300 and 400 nm) and ion fluence φ (1, 5, 10·1014 ions/cm2 ) were varied (see layout in Fig. 5.3-a). Unfortunately, irradiation of large areas was not feasible with
the employed FIB system, so that the exact dependence of the magnetization
and anisotropy on the ion fluence is not known.
Simulations of the ion-atom collisions were carried out with the software
package Stopping and Range of Ions in Matter (SRIM) [155]. For the employed ion,
energy and target, they showed a Ga+ depth range of 14 nm and indicated collisions as deep as ca. 70% of the layer thickness. In the following, x̂ will designate
the writing direction and ŷ the normal direction. Due to the scattering of the
collision process, the dot radius is increased by ∼15 nm.
Fig. 5.3-b shows the topography of the patterned GdTbFe film as imaged
with atomic force microscopy (AFM). The white dots in the AFM images are
probably Al2 O3 grains, coming from the the oxidation of the Al capping layer,
that dominate the sample roughness. Although the change in height due to the
ion-beam irradiation is small, we can observe the dots as small irregular indentations due to the local sputtering of atoms. The indentations have a diameter
of ∼60 nm and a depth of 2 nm for high fluence (50·1014 ions/cm2 ). This agrees
well with the predicted sputtering yield of 5.3 atoms/ion and the dot broadening as obtained from SRIM simulations. The indentation depth at high fluence
is comparable to the 3 nm roughness of the sample, as can be seen from the section in Fig. 5.3-b. We found that the dot shape is sometimes ellipsoidal with the
major axis along the writing direction. This means that anisotropy patterning
with FIB at these low fluences is almost non-destructive leaving the continuous
film intact.
92
a
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300
400
I
IV
VII
5
II
V
VIII
10
III
VI
IX
1
yy
a
2
0
xx
200 mm
c
b
-2
Height (nm)
200
f
y
x
Figure 5.3: a) Layout of the FIB-modified sample with nine irradiated areas for nominal
interdot spacing a = 200, 300, 400 nm and ion fluence φ = 1, 5, 10·1014 ions/cm2 . b) Top:
AFM image of field IX; bottom: height profile of the region in between dotted lines (2
µm scan). c) MFM image measured under in-situ field (15 µm scan, field IX, B = 60 mT).
5.3.
Results
The experimental setup used for the X-ray scattering measurements is
described in Sect. 3.2 and Ref. [18]. In these measurements we used a 100 µm
diameter beam tuned to the Gd M5 absorption edge. The sample was positioned so that the writing direction was horizontal and a vertical knife edge
was used as beam stop. For each field, the hysteresis loop was measured using
the XMCD signal. Contrary to our expectations, the results were identical to
that of the pristine sample for all irradiated areas.
Fig. 5.4 groups the most representative examples of the X-ray scattering
patterns in the vast dataset. Firstly, for the pristine sample (first five images in
the top row), the scattering patterns are typical for very disordered magnetic
domain lattices. At the onset of nucleation (image #1), a circularly-symmetric
intensity disc appears, without any sign of higher orders. As the applied field
increases, the disc evolves to a broad ring with increasing maximum-intensity
wavevector transfer for higher fields. The largest radius corresponds to a domain size τ ∼ 400 nm. As the sample magnetization approaches saturation, the
ring intensity fades out and ultimately its radius decreases.
Secondly, the last image of the top row shows an example of the diffraction pattern of an irradiated area (field IX) under conditions where the pristine sample is saturated and does not diffract. The FIB-induced changes in the
93
Figure 5.4: Field-dependent evolution of the X-ray resonant magnetic scattering patterns. The top row first gives five images of the pristine sample under increasing magnetic fields followed by the diffraction pattern of field IX in the saturated state. The rest
of the figure shows four representative examples of the domain scattering patterns for
each of the nine irradiated regions of the sample in the order as shown in Fig. 5.3. In
each panel, B increases in the indicated order. In all cases, the transmitted beam (white
spot, size not to scale) indicates the q=(0 0) point. Long tick marks are separated by 10
µm−1 .
94
C HAPTER 5
structure produce a square diffraction pattern. The diffraction peaks that can be
labelled with Miller indices (i j), where i and j range enumerate the spots perpendicular and parallel to the beam stop. In this example, the (0 5) spot is still
visible. Such patterns could be observed in all nine areas, and the integrated
intensity was found to scale with the ion fluence. The patterns disappear when
the photon energy is moved away from the Gd M5 resonance, which proves
that they result from a structure in the perpendicular magnetization and not
from charge structure due to the implanted Ga+ ions. Since the pristine parts
are saturated perpendicularly to the film, it implies that the moments in the irradiated areas must have obtained an in-plane anisotropy component. The total
integrated intensity of this pattern was found to reach a maximum at -30 mT,
indicating that the spins in the dots rotate in the sum of the applied and demagnetizing fields.
The dot spacing derived from these dot diffraction patterns were determined to be a = 225, 350, 420 nm with an error of 2 nm. These values are all
substantially higher than the nominal values 200, 300 and 400 nm.
The remainder of Fig. 5.4 shows four typical domain scattering patterns
for each of the nine areas shown in Fig. 5.3. Each of the four images was taken
at fields where the magnetization is approximately -30, 0, 30 and 60% of the
saturation value, increasing with the pattern’s ordinal number. The position
of the direct beam is indicated by a white spot on the left side of each pattern.
Background subtraction was carried out in all the images, either with a constant
value or by using an image measured at saturation.
• a = 225 nm (left column, array I, II, III): At nucleation (images #1), two features different from the pristine case appear: firstly, the (0 1) diffraction peak of
the irradiated lattice appears as a bright, slightly elongated spot. Secondly, the
domain scattering has a wedge-like shape for low fluences and a rod-like shape
as the fluence increases. When the magnetic field is increased (images #2), the
domain scattering shifts to higher q values, evolving towards the circular shape
of the pristine case. There is a clear intensity concentration on the q x axis, nearly
at the point corresponding to Miller indices (0 1/2), which is more pronounced
for the high fluences. For fields where the magnetization reaches 30% of the
saturation value (images #3), both the ring and the (0 1/2) peak intensities decrease, although the latter remains the most intense feature. Close to saturation
95
(images #4), the ring intensity fades out and only the (0 1) peak remains.
• a = 340 nm (middle column, array IV, V, VI): Although the overall behaviour
of the scattering patterns is the same as for the areas I, II and III, the rod-like
shape at nucleation is more pronounced in this series and its intensity again increases with fluence. The (0 1) diffraction peak lies now appreciably closer to
the domain scattering circle and is nearly incorporated in it. Again the intensity
maxima in the domain scattering is highest on the q x axis. For higher magnetic
fields, the evolution towards a ring-like pattern with an accumulation of intensity at (0 1) direction is repeated, more pronounced now than for a = 225 nm.
• a = 420 nm (right column, array VII, VIII, IX): The initial rod-like intensity
at nucleation and the (0 1) peak are more pronounced than ever. In this case
also the (0 2) and (1 1) diffraction peaks are visible. For higher magnetic fields,
the scattering ring expands (images #2) and engulfs (images #3) the (0 1) peak,
clearly because the average domain size coincides with the interdot spacing.
Although the (1 0) reflections are hidden by the beamstop, it seems that
the diffraction patterns do not have a true rectangular structure, as indicated
by the rod like structures such as in the pattern IX-1. This asymmetry can be
ascribed to the FIB writing process.
Images like the ones discussed here were taken with over the whole magnetization loop with a small field increment. In order to compare the different
areas more precisely, the scattering patterns were angularly integrated, even
though such an integration is strictly applicable only to the isotropic pristine
area but not to the patterned areas, due to their rectangular symmetry. The
resulting curves I (qr ) were collected in contour plots, shown in Fig. 5.5. The
pristine area shows the quasi-parabolic dispersion of the scattering maxima as
observed in samples with disordered domain patterns. The patterned areas
have an additional ridge of intensity at fixed qr that is caused by the (0 1) reflection. For each I (qr ) curve, the domain scattering feature was fitted with a
Lorentzian function to obtain the evolution of the intensity maximum q M (B)
with the magnetic field, indicated in the contour plots by white dots.
The contour plots clearly show that for the smallest dot spacing the domain scattering does not interact with the dot scattering in q space. Although
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I
IV
VII
II
V
VIII
III
VI
IX
Figure 5.5: Contour plots of the scattered intensity as a function of field B and momentum transfer qr . The panels correspond to the pristine sample (top left) and the nine irradiated areas with interdot spacing and ion fluence as specified in the previous figure.
The scattered intensities are normalized to the maximum domain scattering intensity.
The positions of the maxima of the domain-scattered intensity q M (B) are indicated with
white circles.
97
the spacing is much smaller than the average domain size, the evolution of the
latter with field is not affected, which seems to indicate that the domains can
adapt to the dots. The fact that the (0 1) reflections are so clear indicates that
adjacent dots are relatively often in domains with opposite magnetization, an
interpretation that is corroborated by the MFM image taken in a perpendicular
magnetic field (Fig. 5.3-c).
The intermediate dot spacing is clearly closer to the average domain
spacing, and the dot scattering is much stronger in this case, a sign that the
localization of the domains on the dots is stronger. This is even more so the case
for the 420 nm spacing, which matches the intrinsic domain size at high fields.
For the highest doses, there is a clear change in the position of the maximum
intensity curve.
To bring this out more clearly, Fig. 5.6 compares the field dependence of
the domain size obtained from the intensity maxima of the pristine area with
that of the patterned areas for each of the three lattice spacings. For the 225 nm
and 340 nm spacing (panel a and b), the data match up well with the pristine
behaviour. For the largest spacing of 420 nm (c) we clearly see that for the
lowest dose the field-dependence of the domain size is still identical to that
of the pristine sample, while the two higher fluences show a clear lock-in of
the domain size with the interdot spacing at the field where the two become
comparable.
5.4.
Discussion
The fact that all irradiated areas show the same hysteresis curve as was
measured with XMCD, nucleating at the same magnetic field, means that the
dots do not act as low-field nucleation centers. This is clearly different from
what is seen in another study where ion irradiation is used to mix Pt/Co multilayers [151]. However, the dots do have an effect on the position and orientation
of the domain wall.
The FIB irradiation has an effect on the position, orientation and the size
of the domains. The positional lock-in can be inferred from the large intensity of the (0 1) Bragg peak which strongly varies with the applied field, while
higher-index peaks have no or very little intensity. This effect can be interpreted
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Figure 5.6: Average magnetic correlation length for the pristine sample (full line) and
for the nine irradiated areas (symbols). The interdot spacing is 225 (a), 340 (b), 420 (c)
nm, indicated in (c) by a dotted line.
with the help of the MFM image taken under applied field (Fig. 5.3-c): after nucleation, the reversed domains find it energetically more favorable to include
the irradiated areas, independent of their size or orientation. This causes adjacent spots to have opposite magnetization which brings out the (0 1) and (1 0)
diffraction spots. Because of the slight anisotropy in the FIB writing process, the
(0 1) correlations seem to be more strongly present stronger than the (1 0) ones.
The orientation of the domains is affected by the asymmetry in the FIB writing
process, and should be removable in future. Finally, he size lock-in is observed
when the interdot spacing matches the domain size and if the fluence is high
enough. This only happens for the largest spacing and the two highest doses.
5.5.
Conclusions
This study illustrates the strength of focused ion beam patterning in tailoring the arrangement of magnetic domains by locally changing the magnetic
anisotropy. The domain structure of FIB-patterned Gd11.3 Tb3.7 Fe85 thin films
has been followed with XRMS and MFM. The MFM data show that in applied
fields the dots are hosts to the down domains. The high sensitivity of X-ray resonant magnetic scattering allowed us to study the effect of these lattices on the
magnetic domain structure over the complete field range. We find that fluences
as small as 1 ion/nm2 of 30 keV Ga+ ions are enough to destroy the perpendicular magnetic anisotropy of the material without changing the film topography.
99
We conclude that the magnetic anisotropy patterning has a strong effect
on the position of the domains, which favour to include at least one irradiated
dot. The strength of the effect scales with the ion fluence. When the typical
domain size approaches a multiple of the interdot spacing, the domain lattice
accommodates to the dot array and is locked to that size over a large field interval.
If the original aim of creating controlled domain nucleation centers is to
be reached, even lower doses will have to be used. However, the present system
forms a very interesting artificial defect system that could serve as a test bed for
the study domain wall propagation in inhomogeneous samples. Indeed, this
work will be followed up with transmission X-ray microscopy experiments.
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6
A N X- RAY MAGNETO - OPTICAL
STUDY OF MAGNETIC REVERSAL
IN PERPENDICULAR
EXCHANGE - COUPLED
[P T /C O ] n /F E M N MULTILAYERS
We used X-ray magnetic circular dichroism and X-ray resonant magnetic scattering
to investigate the room-temperature exchange bias found in perpendicular anisotropy
[Pt/Co]n multilayers coupled to antiferromagnetic FeMn films. About half a monolayer
of Fe spins at the interface is found to be uncompensated. A fraction of these uncompensated spins are pinned in the exchange bias direction. The amount of pinned spins
increases for smaller numbers of [Pt/Co] bilayers and seems to be responsible for the exchange bias. This scenario, already observed at low temperatures for in-plane exchange
bias systems, clearly applies also to the perpendicular counterparts at room temperature.
Remarkable differences are found in the magnetic correlation length for two samples and
between the forward and backward branches of the hysteresis loop.
6.1.
Introduction
The exchange-coupling effect observed in ferromagnetic/antiferromagnetic
bilayers has led in the last decade to important technological applications such
as spin valves and magnetic random access media. The effect was discovered
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C HAPTER 6
already in 1956 by Meiklejohn and Bean [156, 157], who observed an offset
along the field axis of the hysteresis loop of the ferromagnetic layer and an enhancement of the coercivity which appeared only when the bilayer system was
cooled down through the Néel temperature under a saturating magnetic field.
Although already at that time it was clear that this effect was somehow connected to the F/AF interface, little progress in its understanding was achieved
for decades.
Several models of the exchange-coupling phenomena have been proposed: Meiklejohn assumed [158] a direct exchange coupling between the F and
AF spins at an ideal perfectly flat interface. The spins of the last AF monolayer
at the interface, frozen into a certain direction by the neighbouring AF spins,
would couple to the adjacent F spins, breaking the symmetry of the F magnetic
reversal. This model results in an ad hoc unidirectional interface anisotropy that
explained the hysteretic shift, but it implied much larger shifts than the obtained
ones.
Later it was realized that the realistic roughness at the F/AF interface
would reduce the number of F/AF spin pairs with direct interaction [159], thus
supporting the experimental data. However, perpendicular antiferromagnetic
domain walls near the interface [160, 161] or spin-flopping in the AF layers [162]
would lead to the same result.
Another key concept is the existence of uncompensated AF spins at the
interface, which will prefer to align with the F neighbours. Depending on
whether these uncompensated AF spins flip with the F layer or not, they are
said to be unpinned or pinned. Recently, element-specific X-ray spectromicroscopy allowed the direct observation of uncompensated antiferromagnetic
spins at the interface [163, 164]. Other studies [165, 166, 167, 168] have been devoted to the 3D structure of these spins. Furthermore, by using X-ray circular
magnetic dichroism (XMCD), Ohldag et al. [169] showed that the interfacial AF
unpinned spins increase the coercive field whereas the pinned spins produce
the exchange-bias field.
Although almost all studies on exchange-coupled systems have focused
on systems with in-plane magnetization, very recently perpendicular exchange
coupling has also been found. Systems based on Pt/Co [109, 166, 167, 170, 171,
An X-ray magneto-optical study of magnetic reversal in perpendicular
103
172, 173] and Pt/FeCo [174] multilayers with perpendicular magnetic anisotropy
can be exchange-coupled with several AF materials, such as Fe2 F [170], CoO [109,
166, 167, 173], FeMn [171, 174, 175] or NiO [172]. In the last two cases the exchange coupling persists well above room temperature. In general, the perpendicular exchange bias is weaker, possibly as a result of the in-plane preferential
ordering of the AF compounds.
In this chapter, we present a magnetization reversal study of room temperature perpendicular exchange coupled F/AF films by means of XMCD and
polarization-dependent soft X-ray resonant magnetic scattering (XRMS). The
motivation for this study is to understand the mechanisms that govern the
magnetization reversal as well as to study the role of the interfacial coupling
strength on it.
The layout of the chapter is as follows: Sect. 6.2 gives an overview of the
samples and the current status of their understanding, Sect. 6.3 discusses the
spectroscopic, magnetization and scattering results and Sect. 6.4 summarizes
the conclusions.
6.2.
The [Pt/Co]n /FeMn perpendicular exchange bias
system
The out-of-plane preferential axis of the Pt/Co multilayers originates
from the Pt/Co interface anisotropies [176]. The perpendicular exchange-bias
effect induced by a FeMn overlayer was first discovered at the Commissariat à
l’Energie Atomique (CEA) facility, Grenoble (France) [174, 177], which is also the
source of our samples. An extensive review of the growth, structural and magnetic characterization of the system can be found in Ref. [175], which we will
summarize here.
The original samples were grown on Si substrates by magnetron sputtering without purposely applying a magnetic field. However, a significant stray
field from the magnetron perpendicular to plane exists on the substrate during
deposition. The AF layers are therefore grown on Pt/Co multilayers that were
nearly magnetically saturated. The samples were cooled under a perpendicular
magnetic field from above 150 ◦ C, which in turn gave the final exchange field
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C HAPTER 6
Pt
FeMn
Co
Pt
tAF = 10 nm
0.4 nm
2.3 nm
n
Si3N4
Figure 6.1: Cross section of the samples. Starting with a Pt layer, Pt/Co multilayer were
deposited 100 nm-thick Si3 N4 membranes. The thickness of the FeMn layers was t AF =
10 nm. A Pt capping layer was added to prevent sample degradation. The number of
bilayers was 15 for sample A and 10 for sample B.
B E . Atomic force microscope measurements reveal a very low roughness (RMS
< 1.5 Å) and X-ray diffraction data showed a clear fcc (111) texture in both the
[Pt/Co] multilayer and the FeMn layer.
The two-dimensional parameter space, spanned by the thickness of the
ferromagnetic layer (represented by the number of bilayers n) and the AF layer
thickness t AF , reveals a very rich phenomenology [175]. In the absence of the
AF layer, the Pt/Co multilayer always presents perpendicular anisotropy, due
to the interface anisotropy of the Co atoms, with a coercive field BC that increases with the number of bilayers n [176]. Such free multilayers have a square
hysteresis loop as shown in the inset of Fig. 6.2, which also defines the coercive
and exchange bias fields.
When such multilayers are capped with a 7 nm thick FeMn layer, the
large easy-plane anisotropy at the F/AF interface causes an in-plane anisotropy
for n = 2. For n = 3, the competition between the in-plane and out-of-plane
anisotropies results in the formation of stripe domains at remanence, with a different exchange bias for the up- and down domains. For n ≥ 4, the samples exhibit out-of-plane anisotropy [178] and the hysteresis loops develop some tails
related to the inter-domain magnetostatic correlation [77].
For n ≥ 4, both the coercive and exchange-bias field increase with the
105
Table 6.1: Magnetic properties of the [Pt/Co]n /FeMn multilayers.
Sample
n
A
B
15
10
BC
(mT )
18.8
14.6
BE
(mT )
0
−4.0
thickness t AF of the FeMn layer, the faster so for larger n. However, while the
coercive field soon saturates and decreases, the exchange bias field increases
until it saturates. Finally, for the thickest AF layers, both fields are equal and
almost independent of t AF .
For our experiments, we used a range of [Pt(2.3 nm)/Co(0.4 nm)]n multilayers, where n is the number of bilayers, coated with a FeMn(10 nm) layer and
a protective 2 nm thick Pt layer. In order to allow transmission experiments,
these samples were grown on 100 nm-thick Si3 N4 membranes, which did not
change the properties. From this series, the results for two samples with n = 15
(sample A) and 10 (sample B) bilayers are presented here. As can be seen from
Table 6.1, only the latter sample shows exchange bias, but has a lower coercive
field.
6.3.
Results and discussion
6.3.1.
XMCD spectroscopy
Fig. 6.2 shows the Co L2,3 normalized absorption and circular dichroic
spectra for both samples. The absorption spectra were measured in transmission in the flipping mode, in which the field is flipped at every energy point. In
order to eliminate asymmetries caused by non-magnetic absorptive processes,
these spectra were acquired for ±1 light helicities and the resulting spectra were
averaged. The difference between the two absorption spectra, the XMCD signal, is plotted in the bottom panels of Fig. 6.2. For both samples, the asymmetry
µ+ −µ−
ratio between the dichroic and the absorption R = µ+ +µ− amounts to 26%, in
good agreement with XMCD measurements on Co/Pd mutilayers [179].
In order to explore the magnetic state of the F/AF interface, we performed Fe L2,3 XMCD measurements. Fig. 6.3 shows the absorption and dichroic
spectra for both samples. Despite the very poor signal-to-noise ratio, the exis-
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C HAPTER 6
A (n =15)
B (n =10)
Difference
Normalized XAS
12
10
12
BE
10
8
8
6
6
4
2
4
BC
2
0
2
0
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
770 775 780 785 790 795 800 805 810770 775 780 785 790 795 800 805 810
Photon Energy (eV)
Photon Energy (eV)
Figure 6.2: Top panels: Co L2,3 absorption spectra of sample A (left) and B (right) obtained with parallel (dots) and antiparallel (line) alignment of photon spin and magnetization vector. The spectra were scaled so that the intensity jump over the whole
spectrum is one. Bottom panels: circular dichroic spectra as the difference of the absorption spectra. Inset: schematic of the relative absorption hysteresis loop, showing
the coercive and exchange fields BC,E .
tence of a very small circular-dichroic signal at the L3 edge indicates that some
of the Fe spins are ferromagnetic and present a non-negligible projection in the
out-to-plane direction. This is substantiated by the FeMn spin structure in the
(111) planes [180], that presents one spin oriented fully perpendicular to that
plane. At the F/AF interface, this uncompensated spin may flip along with the
F layer, giving rise to a circular dichroic signal.
The dichroic asymmetry ratio R, defined as the ratio of the maximum
amplitudes of the L3 XMCD and helicity averaged absorption, is 1.7 ± 0.6%
for sample A (n = 15), and 1.3 ± 0.5% for sample B (n = 10). Using the bulk
FeMn lattice parameter of 3.63 Å [168, 181] and a typical maximum dichroic
asymmetry ratio for fcc-Fe of R ∼ 25% [182, 183], we find that these values
correspond to amounts of 1.8 ± 0.7 monolayers (ML) of FeMn for sample A
B (n =10)
Normalized XAS
A (n =15)
Difference
107
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
0.2
0.2
0.1
0.1
0.0
0.0
-0.1
-0.1
-0.2
-0.2
700 705 710 715 720 725 730 735 740700 705 710 715 720 725 730 735 740
Photon Energy (eV)
Photon Energy (eV)
Figure 6.3: Fe L2,3 X-ray absorption and circular dichroic spectra of sample A (left) and
B (right). As a guide to the eye, a B-spline function of the data of the bottom panels is
shown with a full line.
and 1.4 ± 0.6 ML for sample B. These values are somewhat larger than the ones
obtained for in-plane systems by Ohldag et al. [169].
6.3.2.
Element-specific hysteresis loops
In order to verify the ferromagnetic behaviour of both layers, we measured the element specific hysteresis loops by measuring the field dependence
of the dichroic absorption signal at the photon energy giving maximum contrast. The data shown in Fig. 6.4 are the result of averaging typically 10 loops,
taken at field sweep rates always lower than 10 mT/s. The data have been normalized to the helicity-averaged absorption µ0 = 1/2(µ+ + µ− ).
In the n = 15 sample A (left panel), the Co hysteresis loop presents a
significant coercive field of 18.8 mT and no exchange bias field, while the n =
10 sample B (right panel) shows a somewhat lower coercivity of 14.6 mT and a
clear exchange bias of -4 mT. Both loops reproduce the results measured with
MOKE. Since the coercive field of the free [Pt/Co] multilayer is 5 mT [175], it is
clear that the exchange coupling at the F/AF interface leads to an enhancement
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C HAPTER 6
Figure 6.4: Element-specific perpendicular hysteresis loops taken at photon energies
corresponding to the maximum Co- and Fe-L3 XMCD. Full dots: Co data, left axis, open
circles: Fe data, right axis. Black/blue and red/cyan indicate respectively increasing
and decreasing fields.
of the coercive field in both cases.
With respect to the Fe-L3 hysteresis loops (open symbols in Fig. 6.4), it
is clear that the uncompensated Fe spins follow the reversal of the F layer and
that they are ferromagnetically coupled to the adjacent Co spins in both cases,
which indicates that they are located at the F/AF interface.
The relative absorption loop of sample A shows the normal behaviour
of a ferromagnetic system: it is symmetric with respect to the unpolarized absorption µ0 , with a saturation amplitude of 1.6%. This symmetry indicates that
all the uncompensated Fe spins are unpinned, i.e., all flip when the F layer is
reversed.
The Fe hysteresis loop of sample B displays a reduction of the vertical
amplitude together with a vertical shift of the loop. Both effects can be understood in the frame of Ohldag’s model [169], in which the presence of pinned
spins results in a gives a field independent XMCD amplitude and thus a vertical shift of the XMCD hysteresis loop. Despite the poor quality of the data,
especially at the increasing field branch, we can estimate from this vertical shift
that the number of unpinned uncompensated spins is about 1.3 ML, implying
that the spins of 0.5 ML are pinned in a fixed direction.
6.3.3.
109
Scattering
We made use of the spatial resolution of XRMS to follow the magnetic
domain structure during reversal. In all cases, circularly symmetric scattering
patterns where obtained. These were radially integrated to obtain the q dependent scattered intensity I (qr ). These curves present a single broad peak, comparable the data for GdFe discussed in Sect. 3.3.2.
Fig. 6.5 compares the Co-L3 absorption hysteresis loops for both samples, shown in panels (a), with the data extracted from these curves. Panel (b)
shows the average magnetic correlation length τ, defined here as the distance
over which the magnetization is in the up or down direction obtained from the
position of maximum intensity of the I (qr ) curve. Panel (c) shows the width at
half maximum ξ of the diffraction peak, normalized to τ, which is a measure of
the extent to which this correlation length is defined. Finally, panel (d) gives the
total scattered intensity.
The data for sample A (left) are symmetric in field. Since the intensity
data for the positive field branch had less scatter, they have been used for the
negative branch also. The evolution of the magnetic correlation length in this
sample shows a quasi-parabolic shape: close to nucleation and saturation it diverges to values above 1 micron, corresponding to the small q limit set by the
beam stop. A minimum correlation length of about τ = 440 nm is found in the
field range where the magnetization changes roughly linearly with the applied
field. As measured by the relative width of the scattering curve ξ /τ this correlation length is also best defined in this range, although even at the maximum
value the domains are completely uncorrelated in their relative positions.
The magnetic correlation length of the n = 10 sample B shows a markedly
different behaviour, as shown in Fig. 6.5-c. The two branches of the hysteresis loop for the opposite field directions display a strong asymmetry: while the
branch in the exchange-bias field direction (black data points) again has a quasiparabolic shape, the branch in the opposite direction (red data points) shows
larger correlation lengths at nucleation, which fall off continuously to the saturation field. This distinct behaviour is very likely due to the difference in the
effective field acting on the ferromagnetic layer, which crudely speaking is the
sum of applied and exchange-bias fields.
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Figure 6.5: Absorption and XRMS data measured at the Co-L3 edge. Left: sample A (15
ML Pt/Co), right: sample B (10 ML Pt/Co). Black/red: increasing/decreasing field.
From top to bottom: a) hysteresis loops (full line); b) magnetic correlation length τ
derived from the maximum of the scattered intensity curve I (qr ), c) ratio of the FWHM
of I (qr ) to τ, d) total integrated scattered intensity (•), compared with the 1 − hmz i2
curve (line).
However, that this interpretation is too simple is clear from the fact that
the minimum domain size is attained at the same absolute field values in both
branches. This seems to imply that the domain size is dictated mainly by the
applied field only, where the exchange field has the only role of shifting the nucleation and saturation fields.
111
The magnetic correlation length in both branches is even less defined
than in sample A. Since in thin films with perpendicular anisotropy the domain
size is determined by the balance between the gain in magnetostatic energy realized by the formation of domains versus the cost of creating domain walls,
this difference is likely to be due to the stronger magnetization and therefore
dipolar interactions in sample A. However, the pinned uncompensated spins in
sample B may play a role by acting as an extra set of defects that hamper domain wall propagation.
Magnetic reversal in systems with a high density of structural defects
and grain boundaries is usually explained by an activation energy of the Barkhausen volume VB , which is the typical volume that is reversed in nucleation
and domain-wall propagation [184, 185, 186]. From time-resolved MOKE experiments [175] on samples with n = 4 and t AF = 7 nm, it has been inferred that
Barkhausen volumes VB are smaller when the applied field is opposite to the
exchange bias. Although we can not identify the magnetic correlation length
directly with the diameter of the Barkhausen volumes, the observed asymmetry in the former seems to support this picture.
The total scattered intensity shown in Fig. 6.5-d closely follows the 1 −
hmz curve in both samples. This is another confirmation of the applicability
of Parseval’s theorem as discussed in Sect. 3.3.4, but also implies that the magnetization is almost completely oriented perpendicular to the sample plane.
i2
6.4.
Conclusions
In this chapter we investigated the origin of the perpendicular exchange
bias that is found in ferromagnetic Pt/Co multilayers capped with an antiferromagnetic FeMn layer. Specifically, two samples differing in the multilayer
thickness were studied, where only the thinner system showed exchange bias.
In both samples, transmission XMCD measurements revealed the presence of uncompensated Fe spins. Element-specific hysteresis loops showed that
these uncompensated spins were directly coupled to the ferromagnetic multilayer, suggesting that they are located at the Co/FeMn interface. From these
measurements the amount of uncompensated spins was estimated as 1.8 mono-
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C HAPTER 6
layers of FeMn, which is about two times larger than found previously [169].
For the n = 15 sample that does not show exchange bias, the uncompensated
spins rotate with the F layer, i.e., they are unpinned. In contrast, in the n =
10 sample, about 15% of the uncompensated spins are pinned by the ferromagnetic layer and do not reverse direction when the field is applied against
the exchange bias direction, apparently because the exchange interaction with
the ferromagnetic layer is weaker in this case. The existence of pinned uncompensated spins, which was already demonstrated in low-temperature in-plane
exchange bias systems, is therefore confirmed in this room-temperature perpendicular exchange-bias systems.
XRMS was used to measure the field dependence of the magnetic correlation length. Both samples show highly uncorrelated domain structures, typical
for a system with strong domain wall pinning by interfacial defects and grain
boundaries. Another consequence of this pinning is that the minimum correlation length is not found at the coercive field as expected from micromagnetic
theory (see Sect. 3.3.7).
The most notable result is the marked asymmetry in magnetic correlation length for the two different field directions found in the n = 10 system
that shows exchange bias. The fact that in both branches the minimum value
is attained at the same absolute value of the applied field suggests that the domain evolution is determined by the applied field and that the exchange bias
field primarily shifts the nucleation and saturation fields. Clearly, the magnetic correlation lengths measured here are much too large to be interpreted
directly as Barkhausen volumes. However, it is reasonable to suggest that the
two are related, in which case our data would confirm the asymmetry in the
Barkhausen volume that was recently arrived at indirectly from time-resolved
MOKE measurements [187]. To make this point clearer, further transmission
X-ray microscopy experiments are required, as they would give more insight in
the detailed magnetic domain structure in these highly disordered samples.
7
C ONCLUSION AND O UTLOOK
Magneto-optical techniques have been extremely important in magnetic
research, especially in magnetic domain studies and ultrafast dynamical studies. This is mainly due to their versatility: they can easily be combined with
high magnetic fields and a wide range of temperatures. The discovery of the
strong magneto-optical effects in the X-ray range greatly extended the possibilities, at first through the discovery of magneto-optical sum rules and more
recently through the exploitation of the short wavelengths which offer in principle much higher spatial resolution.
This thesis explores the novel technique of X-ray Resonant Magnetic
Scattering in transmission mode in studies of the static domain structures in
thin films as well as their dynamical evolution. Before concluding this thesis
with a summary of the results, we think it is worthwhile to briefly assess the
experimental technique, in particular in comparison with the most important
other optical techniques: transmission X-ray microscopy as regards spatial resolution, and the magneto-optical Kerr effect as regards magnetization measurements.
One of the most important technical aspects of XRMS in transmission
geometry is that it is, in principle, a very straightforward technique. In the pioneering phase in which the experiments described here were performed, this
simplicity was often offset by the burden of the detailed alignment of the setup
on the beamline at the start of each experiment. The beamline on which these
experiments were performed is a fantastic spectroscopy beamline with high flux
and perfect control over the polarization, but it was not designed with scattering
114
in mind. With a stable soft X-ray small angle scattering station on a purposebuild beamline, with well characterized collimators, beam stops, detectors, etc.,
it is possible to investigate large volumes of samples relatively easily [63, 68].
We will briefly venture to access the merits of such a system in comparison with
a transmission X-ray microscopy beamline.
The transmission geometry renders both techniques sensitive to the magnetization profiles integrated over the film thickness. Transmission limits the
thickness of the films to about hundred nanometer and requires the use of ultrathin Si3 N4 membranes as substrate, which clearly limits the number of systems that can be studied, a shortcoming that is shared with Lorentz transmission electron microscopy and transmission X-ray microscopy. Although XRMS
is also used in reflectivity geometry, the detailed interpretation of the results is
correspondingly more complicated in that case.
The strongest resonances (transition-metal L2,3 and rare-earth M4,5 edges)
occur in the soft X-ray range at wavelengths between 1.5 and 0.8 nm. In theory,
XRMS therefore has an excellent spatial resolution, given by the diffraction limit
of the wavelength of the resonant X rays. Indeed, this resolution has been attained in XRMS studies of electronic superstructures in correlated systems such
as multilayers [111] and layered manganites [188]. However, as in any scattering experiment, in order to exploit that resolution, the scattered intensity has
to be measured up to large scattering angles. More importantly, in scattering
experiments the extractable information strongly depends on the order of the
sample. In magnetic domain studies, the best resolution is obtained in highly
ordered parallel stripe domain lattices [13, 18, 67, 72, 92]. In this case it is possible to obtain information on the structure of domain walls with a resolution
of 10 to 25 nm which can be compared with micromagnetic calculations. In the
case of the disordered domain structures that are discussed in this thesis, the
resolution is determined by the disorder, and the average structure can be resolved with some 50 nm resolution at best, which is more than two times worse
than the resolution of a transmission X-ray microscope.
TXM currently has a resolution of some 25 nm, still very far from the
diffraction limit, and this was the main stimulus for our use of XRMS. However,
the development of the Fresnel zone plate lenses used in them is still continuing. More importantly, these lenses produce a direct image and one does not
Conclusion and Outlook
115
have to take recourse to modelling the measured intensities as is necessary in
XRMS.
Another much quoted advantage of X-ray magneto-optical techniques
is their chemical sensitivity, which allows one to measure sublattice magnetizations with great accuracy [189, 125]. This should be qualified to some extent since, for instance, most alloyed and multilayer systems have fairly well
defined magneto-optical spectral features in the infrared to ultraviolet range,
which can also be used to separate the magnetic contributions of different sublattices in multicomponent systems to some extent. For static spatially-resolved
X-ray techniques like resonant scattering or microscopy, the chemical sensitivity
is not very important, as the different sublattices are linked by exchange interactions and the information obtained at different resonances is the same.
We conclude that the unique strength of XRMS in comparison to MOKE
and TXM is in dynamic nucleation studies in homogeneous systems, where the
nucleation can appear randomly, which means that imaging techniques would
not observe any structure under stroboscopic illumination. The reverse side
of this maximum disorder situation is that the amount of information that can
be extracted is low. In more ordered samples, such as patterned thin films or
nanostructures, the dynamics is more reproducible, and transmission X-ray microscopy may be more useful.
7.1.
Outlook
The main goal of this thesis project was to study domain nucleation dynamics in homogeneous systems using time-resolved XRMS. Overall this goal
has been achieved. We have shown that even with the used tiny beams and
single-bunch operation of the synchrotron, the magnetization and the total scattered intensity can be followed with a resolution of 100 ps. Preliminary data on
the magnetic correlation lengths relate mainly to the interdomain distances. An
important objective was to follow the form factor of the nucleating domains.
This aim could not yet be achieved due to lack of flux and poor detector sensitivity. However, vast improvements in data quality are still possible by using a
more optimized setup.
An unexpected outcome of the experiment was that we obtained evi-
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dence for spin reorientation transitions of the subnetworks in the ferrimagnetic
GdFe film, superimposed on the reversal dynamics. This is an interesting research area in itself and, to our knowledge, no prior results on spin reorientation transitions on these timescales are available. Ironically, insufficient time
meant we could not provide the direct proof of this feature in this thesis and we
had to use magneto-optical Kerr effect data to obtain the information on the Fe
sublattice. Nonetheless, we think we do have proven that the potential for spin
reorientation transitions studies using the very intense pulses of microcoils is
huge.
With the aim of increasing the amount of order in the nucleation landscape, we patterned the thin films with very low doses of Ga+ ions using a
focused-ion-beam system. Although dynamic experiments could not yet be
performed, the influence of these nucleation centers on the diffraction pattern
in static fields is reported. Such anisotropy-engineered systems present many
interesting phenomena in their own right, which are the subject of a follow-up
study using field-dependent MFM and transmission X-ray microscopy, the latter ultimately also in a pump-probe mode.
Finally, an experiment on perpendicular exchange-bias systems shows
that even very thin samples can be studied and that, even in transmission geometry, the sensitivity is sufficient to measure uncompensated interfacial spins
which play a decisive role in the exchange bias process. Here the transmission
geometry has the advantage that the magnetic contributions to the magnetic
moment of the uncompensated spins can in principle be measured in an absolute way.
Time-resolved dynamical studies using visible light have a tradition of
some 30 years, and clearly pulsed lasers outperform the third-generation synchrotrons in terms of flux per pulse and pulse duration. This means that timeresolved XRMS is not able to access the forefront of magnetization dynamics
at present, which addresses coherent precessional switching. The development
of X-ray Free Electron Lasers (XFEL) over the coming decade will completely
change this situation. It can be expected that there it will be possible to combine 100 fs time resolution with nanometer spatial resolution. For those days
to come, it may become possible to access spin-magnon interactions during domain nucleation.
A
S ENSITIVITY OF THE G D 3+
OPTICAL CONSTANTS TO THE
CALCULATION PARAMETERS
A.1.
Atomic multiplet calculation
In Sect. 2.2, we introduced the atomic multiplet calculations that were
used to compare the Gd3+ M4,5 calculated and measured absorption and dichroic
spectra. From the comparison, best fitting values for the reduction of the Slater
parameters κ1,2,3 , the Γ 5/ , Γ 3/ core-hole lifetimes, Fano asymmetry factor q 3/
2
2
2
and the line broadening σg due to the finite experimental resolution were obtained, as listed in Table A.1.
In order to test the strength of the solution, σ0,c,l ; F (0,1,2) and their squared
moduli were calculated for slightly different values of the fitting parameters
Table A.1: Fitting parameters for the Gd3+ calculated absorption spectra. First row:
best fitting; second and third rows: test values.
κ1
κ2
κ3
Γ 5/
Γ 5/
( Ffk f )
( Fdk f )
( Gdk f )
(eV )
(eV )
0.83
0.80
0.90
0.95
0.90
1
0.85
0.80
0.90
0.3
0.2
0.4
0.4
0.3
0.5
2
117
2
q 3/
2
σg
(eV )
12
−
−
0.3
0.2
0.4
118
C HAPTER A
Figure A.1: Left: comparison of the experimental (open symbols) and calculated absorption cross sections (lines) with best-fitting parameters to calculated spectra with
variations of the downscaling factors of the Slater parameters. Right: comparison of the
calculated atomic scattering lengths. The labels correspond to the factors, e.g., 123456
stands for κ1 = 0.12, κ2 = 0.34, κ3 = 0.56.
varied one at a time, and listed also in Table A.1.
Fig. A.1 shows spectra for the best-fitting values of κn and for the varying ones. Minor changes are observed in the shape of the three spectra and the
main effect appears as small energy shifts of the absorption lines. The largest
shift, amounting about 0.5 eV, happens for κ1 = 0.90. This, together with the
fact that all the lines shifts are in the same direction, make the scattering cross
sections and total scattered intensities quite insensitive to the reductions.
The result of varying the line broadenings by ±0.1 eV is shown in Fig. A.2.
As expected, smaller lifetimes and better experimental resolution lead to narrower and higher features in the absorption spectra. These changes in the spectra lead to increases of up to 15% with respect to the best fitted curves, and
APPENDIX A
119
Figure A.2: Left: comparison of the experimental (open symbols) and calculated absorption cross sections (lines) with best-fitting parameters to calculated spectra with
variations of the lifetime broadenings. Right: comparison of the calculated atomic scattering lengths. A 123 label corresponds to Γ 5 = 0.1 eV, Γ 3 = 0.2 eV and σg = 0.3
/2
/2
eV.
this is accordingly reflected in Im[ F (0,1,2) ]. The real parts obtained by the KK
transforms Re[ F (0,1,2) ] are affected somewhat close to the edges but the wings
are completely insensitive (unlike the derivative with respect to the energy). Finally, only a ∼15% change is observed at the maxima and minima of the total
scattered intensities, naturally coming from the imaginary part of the scattering
cross sections.
Since we only have the Gd3+ experimental data, no test for different Fano
asymmetry parameter has been undertaken. Nonetheless, very similar values
along the Lanthanide series have been found [27].
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S UMMARY
This thesis provides a broad-scope survey exploring the various possibilities that soft X-ray resonant magnetic scattering offers for studying out-ofplane magnetic domains found in thin magnetic films.
This technique takes advantage of the strong magneto-optical contrast
of the atomic resonances in the soft X-ray range. In the case of the rare-earth
elements, the M4,5 (3d → 4 f transitions) isotropic, circular and linear dichroic
absorption spectra are obtained by atomic multiplet calculations. Application
of the Kramers-Kronig transforms to these spectra allows us to obtain the complete set of magneto-optical constants: the resonant scattering factors as well
as the specific Faraday and Voigt rotation angles. Precise knowledge of these
spectra is imperative for the planning and the analysis of resonant experiments,
while at the same time it offers useful insights into the development of novel
compact Cherenkov radiation-based X-ray sources.
A complete description is presented of the information that can be extracted from scattering patterns of disordered domains found in amorphous
GdFe thin films under quasi-static magnetic fields. The intentionally grown
perpendicular magnetic anisotropy of these systems produces a collection of
out-of-plane magnetic domains that are dressed by Bloch walls and closure domains. Magnetic reversal is achieved through nucleation and domain wall motion. The average domain period, correlation length and reversed domain size
were measured from the remanent state all the way up to magnetic saturation.
In the case of aligned stripes, the period can be predicted by analytical stripe
domain models, which prove to be non-applicable for the case of disordered
domains. Furthermore, a general relation between the ensemble-averaged outof-plane magnetization and the total scattered intensity is derived, which is fulfilled in all the cases studied here.
A pioneering experiment combining the X-ray resonant scattering technique and magneto-optical Kerr effect with very strong magnetic pulses allowed us to follow the magnetization and scattering of the same GdFe films
138
S UMMARY
with spatial and temporal resolutions of 50 nm and 100 ps respectively. Rather
unexpectedly, for one composition the antiparallel coupling between the two
subnetworks was found to break during and after the magnetic pulse, causing
the Gd out-of-plane magnetization to vanish and relaxation of the system taking as long as 100 ns. For the other case, the system response followed the pulse
temporal evolution, although a decrease in the Gd-subnetwork magnetization
was again seen. This striking novel phenomenon is tentatively explained as the
dynamical analogue of the static magnetically-driven spin-flop transition observed in other rare-earth/transition-metal alloys. The distinct response of the
two samples is likely to originate from the different saturation magnetization.
In order to control the domain nucleation process, focused-ion-beam irradiation was used to locally modify the magnetic properties of amorphous
GdTbFe thin films. These have a high intrinsic perpendicular magnetic anisotropy and display a very uncorrelated domain pattern at remanence. Rather than
modifying the nucleation field, this process affected the size, position and direction of the reversed domains upon magnetic saturation to levels depending
on the ion fluence and interdot spacing.
Finally, we have used X-ray magnetic circular dichroism and resonant
magnetic scattering to study the reversal behaviour of two room-temperature
perpendicular exchange-bias [Pt/Co]n /FeMn multilayer systems. In both cases,
uncompensated Fe spins at the ferromagnetic/antiferromagnetic interface were
found and their thickness estimated. However, when the systems exhibited exchange bias, a small fraction of these spins was pinned, causing a vertical shift in
the Fe-related absorption hysteresis loop. This constitutes the first experimental proof of this behaviour, previously observed in low-temperature in-plane
exchange-bias systems, being reproduced by its perpendicular counterpart.
S AMENVATTING
Dit proefschrift bevat een breedschalig overzicht van de mogelijkheden
die magnetisch resonante zachte Röntgenverstrooiing bieden om de loodrecht
op het basisvlak georiënteerde magnetische domeinen in dunne magnetische
lagen te bestuderen.
Deze techniek maakt gebruik van het sterke magneto-optische contrast
tussen de verschillende atomaire resonanties in het zachte Röntgengebied. In
het geval van de zeldzame-aarden, M4,5 (3d → 4 f ) overgangen, kunnen de
isotrope, circulaire en lineaire dichroide absorptiespectra verkregen worden door
middel van atomaire multiplet berekeningen. Toepassing van de Kramers-Kronig
relaties op deze spectra geven ons de volledige magneto-optische constanten:
de resonantie verstrooiingsfactoren, alsmede de soortelijke Faraday en Voigt
rotatiehoeken. Nauwkeurige kennis van deze spectra is een vereiste voor het
opstellen en analyseren van dergelijke resonantieexperimenten. Tevens wordt
op die manier nuttig inzicht verkregen in de ontwikkeling van de nieuwe compacte Röntgenbronnen welke gebaseerd zijn op Cherenkovstraling.
Een volledige beschrijving van de informatie die kan worden verkregen
uit de verstrooiingspatronen van wanordelijke domeinen in amorfe GdFe lagen
in quasi-statische magnetische velden wordt in dit proefschrift gegeven. The
gegroeide rechthoekige assymetrie van deze systemen levert een verzameling
loodrecht op het vlak liggende magnetische domeinen die omhuld worden door
Blochwanden en fluxsluitingsdomeinen. Magnetische omkering wordt bereikt
door middel van nucleatie en de beweging van de domeinwanden. De evolutie van de gemiddelde domeinperiode, correlatielengte en van de omgekeerde
domeingrootte werd gevolgd vanaf de remanentietoestand tot aan de magnetische verzadiging. In het geval van de langs elkaar liggende stripes kan de periode worden voorspeld met behulp van analytische stripe-domein modellen
die echter niet toepasbaar zijn op wanordelijke domeinen. Voorts werd een
algemene relatie afgeleid tussen de ensemble-gemiddelde loodrechte magnetizatie en de totale verstrooiingsintensiteit. Deze relatie is geldig voor alle in dit
proefschrift behandelde gevallen.
Een baanbrekend experiment waarbij de Röntgen-resonante verstrooi-
140
S AMENVATTING
ingstechnieken en het magneto-optisch Kerr effect werden samengevoegd in
combinatie met zeer sterke magnetische pulsen, maakte het mogelijk om de
magnetizatie en verstrooiing van dezelfde GdFe films te volgen met ruimtelijke
en tijds-resoluties van respectievelijk 50 nm en 100 ps.
Nogal onverwachts bleek voor een bepaalde samenstelling de antiparallele wisselwerking tussen de twee subnetwerken te breken tijdens en na de
magnetische puls, waardoor de loodrechte magnetizatie van het Gd verdween
en het systeem pas relaxeerde na 100 ns. Voor het andere geval volgde het
systeem de tijdsevolutie van de puls, hoewel een afname van de magnetizatie
van het Gd-subnetwerk wederom werd waargenomen. Dit opvallend nieuwe
fenomeen kan vooralsnog worden geinterpreteerd als de dynamische analoog
van de statische magnetisch-gedreven spin-flop overgangen die worden waargenomen in andere legeringen van zeldzame-aarde en overgangsmetalen. Het
kenmerkende respons van beide monsters vindt waarschijnlijk zijn oorsprong
in de verschillende verzadigingsmagnetizaties.
Om het nucleatieproces van de domeinen onder controle te krijgen werd
gebruik gemaakt van gefocusseerde ionen bundelstraling om zodoende de magnetische eigenschappen van de amorfe GdTbFe dunne lagen lokaal te modificeren. Deze lagen hebben een hogere intrinsieke loodrechte magnetische anisotropie en vertonen een zeer ongecorreleerd domeinpatroon bij remanentie. In
plaats van een verandering van het nucleatieveld werd de grootte, positie en de
richting van de omgekeerde domeinen bij magnetische verzadiging aangetast
tot een nivo dat afhankelijk was van de ionenvloei en de onderlinge puntsafstand.
Ten slotte hebben we Röntgen magnetische circulair dichroisme en magnetisch resonante verstrooiing toegepast om het omkeringsgedrag te bestuderen van twee loodrechte exchange-bias [Pt/Co]n /FeMn multilaag systemen
op kamertemperatuur. In beide gevallen is de aanwezigheid van ongecompenseerde Fe spins op het ferromagnetische/anti-ferromagnetische grensvlak
aangetoond en is hun dikte bepaald. Echter, wanneer de systemen exchangebias vertoonden werd een klein gedeelte van deze spins gepinned, wat leidde
tot een vertikale verschuiving van de Fe-afhankelijke absorptiehystereselus. Dit
is het eerste experimentele bewijs dat dit gedrag, reeds eerder geobserveerd
in lage-temperatuur in-plane exchange-bias systemen, wordt gereproduceerd
door zijn loodrechte tegenhanger.
R ESUMEN
En la era actual de la tecnologı́a de la información, muchos dispositivos están basados en láminas magnéticas delgadas. Como ejemplos más conocidos, podemos citar los discos duros de nuestro ordenador y sus cabezas de
lectura/escritura, que resultan indispensables en el quehacer diario. Estos dispositivos alojan o interaccionan con el protagonista de esta tesis: el dominio
magnético. Estos dominios son áreas pequeñı́simas de la lámina delgada que
están uniformemente magnetizados en una dirección determinada. En pocas
palabras, la imanación en cada uno de estos dominios viene determinada por
el tamaño de los espines atómicos y su grado de alineamiento. En la barrera
entre dos de estos dominios, los espines atómicos cambian de dirección gradualmente. Cuando la cabeza lectora vuela rasante sobre el disco duro, detecta
estos cambios en la dirección de la imanación, que son interpretados como unos
y ceros, los bits.
Actualmente vivimos una carrera desenfrenada en la capacidad requerida de almacenaje de información. Esto se traduce en una disminución acelerada
del tamaño de los bits, cuya anchura actualmente es de unos 25 nanómetros,
unas mil veces menor que el diámetro de un cabello humano y unos cientos de
veces el tamaño del átomo. De seguir al ritmo actual, la carrera desembocará en
el átomo, pero se impone una pregunta: ¿cuál es el tamaño mı́nimo de un dominio magnético estable?.
La sola mención de la estabilidad, que sólo tiene sentido en un determinado lapso de tiempo, nos conduce a la segunda cuestión: ¿cuál es la máxima
velocidad a la que un dominio puede revertir su dirección?. En los discos duros
más recientes, este proceso lleva solamente unos pocos nanosegundos.
Está clara por tanto la importancia, tanto académica como tecnológica,
de los dominios magnéticos, y la necesidad de técnicas capaces de dar información local de los mismos y su comportamiento dinámico. A este respecto,
las técnicas de microscopı́a como las de Lorentz, Kerr o la microscopı́a de fuerza magnética parecen las más adecuadas, pero presentan inconvenientes como
una resolución espacial limitada, dificultad para aplicar campos magnéticos altos o tiempos de medición muy prolongados. Como alternativa, proponemos el
142
R ESUMEN
uso de rayos X en el estudio de la dinámica de la magnetización en dominios
magnéticos. Los rayos X poseen la ventaja de una resolución espacial máxima
de varios angstroms en casi cualquier condición de campo magnético y temperatura. Lamentablemente, la inexistencia de lentes para rayos X blandos de
calidad suficiente en el momento de la realización de esta tesis implicó el uso
de scattering en vez de microscopı́a de rayos X.
En concreto, esta tesis explora las capacidades que la técnica de scattering
resonante magnético de rayos X (XRMS en sus siglas en inglés), ofrece al estudio de dominios magnéticos. Esta técnica usa el alto contraste magneto-óptico
de las resonancias atómicas en el rango de los rayos X blandos. En el caso de
los elementos quı́micos de tierras raras, los espectros de absorción isótropa y
de dicroı́smo circular y lineal de los umbrales M4,5 se pueden obtener a partir de cálculos de multipletes atómicos. La aplicación de las transformadas de
Kramers-Kronig permite obtener las constantes magneto-ópticas: los factores de
scattering magnético y los ángulos de rotación especı́fica de Faraday y Voigt. Un
conocimiento preciso de estos espectros es esencial a la hora de analizar los datos obtenidos y de planificar futuros experimentos. Además, pueden ser útiles
en el desarrollo de un tipo nuevo de fuentes compactas de rayos X blandos basadas en la radiación de Cherenkov.
A continuación se presenta una descripción completa de la información
que se puede extraer de los patrones de scattering de dominios desordenados
presentes en láminas delgadas de GdFe sometidas a campos magnéticos estáticos. Los patrones de scattering a lo largo del ciclo de histéresis permiten extraer
el periodo, el tamaño de los dominios invertidos y la longitud de correlación
medios. Sin embargo, sólo cuando la red de dominios está inicialmente ordenada, la cantidad de información extraı́ble es máxima y modelos analı́ticos permiten calcular el periodo, que coincide con gran precisión con los valores experimentales.
Posteriormente, la respuesta de estos sistemas a pulsos magnéticos muy
intensos se ha estudiado mediante las técnicas de scattering resonante magnético y efecto magneto-óptico Kerr, obteniendo la evolución temporal de la imanación y la intensidad de scattering de láminas delgadas de GdFe con resolución
espacial y temporal de 50 nm y 100 ps respectivamente. Sorprendentemente,
el comportamiento esperado de nucleación de dominios y desplazamientos de
muro no es universal, y el acoplo antiparalelo que existe bajo condiciones cua-
R ESUMEN
143
siestáticas queda temporalmente cancelado durante y después del pulso, provocando la anulación de la tercera componente de la imanación de la subred
de Gd. Ésta es la primera vez que se observa este comportamiento, que se explica como el análogo dinámico de las transiciones de reorientación de espı́n
controladas por el campo magnético observadas en aleaciones de metales de
transición con tierras raras.
Con la intención de controlar el proceso de nucleación de dominios, usamos un haz de iones focalizado para escribir una red de puntos, modificando
localmente las propiedades magnéticas de láminas delgadas amorfas de GdTbFe. En vez de afectar el campo de nucleación, la irradiación provocó cambios en
el tamaño, posición y dirección de los dominios revertidos después de saturar
magnéticamente la muestra. Estos cambios dependerán de la dosis de iones y
de la distancia entre puntos.
Además, se usó la técnica de dicroı́smo circular magnético de rayos X para estudiar el mecanismo de reversión de dos sistemas de multicapas [Pt/Co]n /FeMn
con exchange bias perpendicular al plano de la muestra y a temperatura ambiente. En ambos casos se observó cuantitativamente la presencia de espines de
Fe descompensados en la frontera entre las capas ferro- y antimagnética. Cuando estos sistemas exhiben exchange bias, un pequeña porción de dichos espines
se encuentran fijos, causando un desplazamiento vertical del ciclo de histéresis
del hierro. Ésta es la primera vez que este fenómeno, conocido de sistemas con
exchange bias en el plano de la muestra y a baja temperatura, se observa en
sistemas con imanación fuera del plano.
Finalmente, las bondades e inconvenientes de XRMS se resumen en el
capı́tulo de conclusiones. Allı́ se explica claramente que el orden de la red de
dominios magnéticos para maximizar la cantidad de información extraı́ble bajo
condiciones cuasi-estáticas. Sin embargo, la técnica de XRMS es especialmente
útil para estudios en dinámica donde los procesos de nucleación y desplazamiento de muro no están limitados por defectos estructurales en la muestra.
Con la aparición de las futuras fuentes de radiación de sincrotrón de cuarta
generación o láseres de rayos X, se espera poder combinar resoluciones temporales de 100 femtosegundos con espaciales del orden de un nanómetro. Bajo estas condiciones, se podrá observar la aparición de interacciones espı́n-magnón
durante la nucleación de dominios magnéticos.
A CKNOWLEDGEMENTS
Firstly, I want to thank Jeroen Goedkoop for taking me onboard his group and
giving me the opportunity to complete my Ph.D. Despite the asbestos crisis, the
long and dreadful beamtimes, the sometimes hazardous and always arduous
work, we managed to deliver it ashore.
I also thank Mark Golden for taking over Friso van der Veen as my official promotor. Mark, your detailed reading of the thesis manuscript was very useful;
Friso, I had a great pleasure in sharing a beamtime and discussions with you.
Carrying out any synchrotron experiment on your own is simply impossible,
and I am greatly in debt to my group mates: Joost, Olivier, Mark and lately
Stan. Huib, thanks for those beautiful samples you grow.
For the calculations presented in Chapter 2, I used the version of Cowan’s code
provided by Frank de Groot: thanks for your patience explaining me some of
the secrets of the atomic multiplet calculations and their implementation.
The dynamical studies shown in Chapter 4 were the result of our collaboration
with the beamline ID08 at ESRF and the XMCD group at Louis Néel Laboratoire. I am indebted to Nick Brookes for adopting me as one of his Ph.D.
students in Grenoble when the asbestos was pouring in Amsterdam, and for
his dedication to our experiments as a local contact; to Kenneth Larsson† , the
best technician I have ever met and a very sensible person. Stefania Pizzini, Jan
Vogel, Yann Pennec, Marlio Bonfim and Julio Camarero, thanks a lot for your
support with the dynamical measurements and your help when our group was
too thin for a beamtime.
To ion bombard Huib’s precious samples, we counted with the help of several
people: Albert Polman, Max Tien, Teun van Dillen (AMOLF ), Vishwas Gadgil
(MESA+ ), Jeroen Luigjes and Hugo Schlatter (WZI ), thanks to you all.
The samples studied in Chapter 6 came from Bernard Dieny’s group at CEA
in Grenoble. Many thanks to him and the people involved: Flavio Garcia and
Jordi Sort.
I want to acknowledge the scientific, technical and secretarial staff of the van
der Waals - Zeeman Institute for their professional support every time I needed
it, and ESRF for the hospitality during my stay there.
T O MY FRIENDS
Even in Physics, a Ph.D. gives you the chance to meet lots of people,
especially if you had a long one like mine. But let’s start from the beginning,
around five years, five directors and an asbestos crisis ago, when the Cheapies
were various and manyfold: Joost, Mark, Olivier and Jeroen as Commander
in Chief. There was no experiment too difficult for you, guys! Well, almost.
Together with Michel and Jeroen, you instructed me in the Kriterion tradition
where we shared many beers and dinners afterwards.
Other old members of the WZI scientific community to be remembered:
Pedro, Mohammed, Takashi, Femius, Lydia, Emmanuelle, Juan, Boris, Zhang
Lian, Yingkai, Tom, Maçiek, Mark, Vinh, Ronald, Yu Tao. And present ones:
Dennis, Leonid, Henk, Iuliana, Stan, Jeroen and Jesse, Gianni, Huy, Sharareh,
Iman, Anton, Sarah, Tracy, Yves, Salima and Ashmae.
Que la vida en Ámsterdam sin la mafia española plus la légion etrangère
no serı́a lo mismo es obvio. Jaime, Manu, Marc, Juan, Jorge, Marinella, Rafa,
Alex, Andrea, Rùben, Daniele, Silke, Nacho, Diego, Miriam, Marı́a, Salvo, Manu,
Mischa, Jordi, Annemarieke, José, Javier, Viney, Timi, Dorothée, Marina y a
aquellos que me dejé y que mañana recordaré: muchas gracias por vuestro
apoyo en los dı́as grises y en el resto también!.
During my stay in Grenoble I met very nice people. Manu, Sofı́a, Gloria, Silvia, Javier & Javier, David, Sarnjeet, Christian, Tobias, Mónica, Eva, Julio,
Alberto, Céline, Federica, Peter, Jorge and Barry: thanks a lot for the good moments.
Dedico esta tesis a mi madre y mis hermanos, por su apoyo incondicional antes y durante esta tesis y a Marı́a, mi compañera de viaje durante estos
años. Muchı́simas gracias por tu ayuda en el parto, porque ¿quién dijo que los
hombres no paren?.

Static and dynamic X-ray resonant magnetic scattering studies on

Transcription

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