Inhomogeneous alloying in FePt nanoparticles as a reason for reduced magnetic moments

Abstract

The reduced magnetic moments of oxide-free FePt nanoparticles are discussed in terms of lattice expansion and local deviation from the averaged composition. By analyses of the extended x-ray absorption fine structure of FePt nanoparticles and bulk material measured both at the Fe K and Pt L(3) absorption edge, the composition within the single nanoparticles is found to be inhomogeneous, i.e. Pt is in a Pt-rich environment and, consequently, Fe is in an Fe-rich environment. The standard Fourier transformation-based analysis is complemented by a wavelet transformation method clearly visualizing the difference in the local composition. The dependence of the magnetic properties, i.e. the element-specific magnetic moments on the composition in chemically disordered Fe(x)Pt(1-x) alloys, is studied by fully relativistic SPR-KKR band structure calculations supported by experimental results determined from the x-ray magnetic circular dichroism of 50 nm thick films and bulk material.

Full text

IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 21 (2009) 336002 (12pp) doi:10.1088/0953-8984/21/33/336002
Inhomogeneous alloying in FePt
nanoparticles as a reason for reduced
magnetic moments
CAntoniak
1, M Spasova1, A Trunova1,KFauth
2, F Wilhelm3,
A Rogalev3,JMin
´
ar4, H Ebert4,MFarle
1and H Wende1
1Fachbereich Physik and Center for Nanointegration Duisburg-Essen (CeNIDE),
Universit¨at Duisburg-Essen, Lotharstraße 1, D-47048 Duisburg, Germany
2Experimentelle Physik IV, Universit¨at W¨urzburg, Am Hubland, D-97074 W¨urzburg,
Germany
3European Synchrotron Radiation Facility (ESRF), 6 Rue Jules Horowitz, BP 220,
F-38043 Grenoble Cedex, France
4Department Chemie und Biochemie, Ludwig-Maximilians-Universit¨at M¨unchen,
Butenandtstraße 11, D-81377 M¨unchen, Germany
E-mail: carolin.antoniak@uni-due.de
Received 6 March 2009, in final form 1 July 2009
Published 24 July 2009
Online at stacks.iop.org/JPhysCM/21/336002
Abstract
The reduced magnetic moments of oxide-free FePt nanoparticles are discussed in terms of
lattice expansion and local deviation from the averaged composition. By analyses of the
extended x-ray absorption fine structure of FePt nanoparticles and bulk material measured both
attheFeKandPtL
3absorption edge, the composition within the single nanoparticles is found
to be inhomogeneous, i.e. Pt is in a Pt-rich environment and, consequently, Fe is in an Fe-rich
environment. The standard Fourier transformation-based analysis is complemented by a
wavelet transformation method clearly visualizing the difference in the local composition. The
dependence of the magnetic properties, i.e. the element-specific magnetic moments on the
composition in chemically disordered FexPt1−xalloys, is studied by fully relativistic SPR-KKR
band structure calculations supported by experimental results determined from the x-ray
magnetic circular dichroism of 50 nm thick films and bulk material.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
FexPt1−xnanoparticles are currently the object of intense
research activity, driven both by fundamental interest and their
possible use as new ultra-high density magnetic storage media
(see, e.g., [1–7]). For the latter case, nanoparticles with
a high magnetocrystalline anisotropy (MCA) are needed to
overcome the superparamagnetic limit, i.e. data loss caused
by thermally activated magnetization fluctuations. In addition,
the magnetic moments of the nanoparticles should be low to
prevent magnetization switching caused by magnetic dipole
interactions.
One of the prime candidates for future applications is
FexPt1−xin the chemically ordered state around the equi-
atomic composition due to its high MCA density [8–11]of
about 6 ×106Jm
−3. Interestingly, the magnetic moments
in FePt nanoparticles in both the chemically disordered and
chemically ordered phase are rather small compared to the bulk
material [12,13]. The formation of the chemically ordered
L10state is driven by volume diffusion and is kinetically
suppressed. Annealing of the nanoparticles is suitable to
achieve the (partial) L10phase in nanoparticles [4,15–20].
Possibilities to boost Fe and Pt diffusion are, for example,
He-ion irradiation [21] or nitrogenization in the case of
nanoparticles prepared by gas phase condensation [19].
However, the anisotropy of non-agglomerated nanoparti-
cles with a diameter around 6 nm was found to be almost one
order of magnitude smaller than in the bulk material, which
0953-8984/09/336002+12$30.00 ©2009 IOP Publishing Ltd Printed in the UK1

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
may be related to a lower degree of chemical order within the
nanoparticles [12,13].
In order to understand the diffusion processes and possible
obstructions towards the L10formation, it is necessary
to structurally characterize also the chemically disordered
nanoparticles in detail as done in this work.
By the analyses of the extended x-ray absorption fine
structure (EXAFS) of oxide-free Fe0.56Pt0.44 nanoparticles,
a lattice expansion was found in our earlier work [22].
The new result of the present paper is clear evidence for
an inhomogeneous alloying within the particles. For this
purpose, the local composition is determined around Pt and
Fe probe atoms, i.e. the EXAFS is analysed at both the Pt
L3and Fe K absorption edges, respectively. Besides the
usual Fourier interpretation of the EXAFS, a complementary
wavelet transformation (WT) method, adapted from acoustic
emission analyses, is employed. It is presented as a method
to distinguish between different atomic species in an alloy and
a possibility to visualize differences in the local composition
around the absorbing atom.
The influence of an inhomogeneous composition within
FePt nanoparticles on the magnetic properties, especially on
the element-specific magnetic moments, is discussed. As
a reference, magnetic moments of chemically disordered
FexPt1−xalloys were probed as a function of Fe content
by the analysis of the x-ray magnetic circular dichroism
(XMCD) of different samples, i.e. bulk material and films of
50 nm thickness. In addition, band structure calculations were
performed for FexPt1−xbulk material using the spin-polarized
relativistic Korringa–Kohn–Rostoker (SPR-KKR) method.
The organization of this paper is as follows. In section 2,
the sample preparation and the x-ray absorption experiments
are described. In section 3, a short overview of the input
details for the SPR-KKR calculations, XMCD and EXAFS
analysis methods is given. The latter were performed using
FEFFIT [14] on the one hand and, on the other hand, wavelet
transformation was used especially for a better visualization of
the results. In section 4, the results of SPR-KKR calculations
and x-ray absorption experiments are presented which are
discussed in section 5. Finally, in section 6, conclusions are
given.
2. Experimental details
2.1. Sample preparation
Monodisperse single-crystalline FexPt1−xnanoparticles sur-
rounded by oleic acid and oleyl amine were wet-chemically
synthesized by the reduction of Pt(acac)2and thermal decom-
position of Fe(CO)5as described elsewhere [23]. The particles
were deposited onto a naturally oxidized Si wafer using the
spin coating technique. The particles tend to self-assemble in
a short-range hexagonal order [22,25] and the organic ligands
prevent the particles from agglomeration as can be seen in the
scanning electron microscopy (SEM) image in figure 1.
Here, two different samples are discussed with different
sizes and slightly different compositions. The element-
specific magnetic moments were determined for FexPt1−x
Figure 1. XANES at the carbon K and the Fe L3,2absorption edges
of FePt nanoparticles on a naturally oxidized Si substrate before
(black lines) and after (red lines) hydrogen plasma cleaning [25]. At
the carbon K edge, the spectra were normalized to the absorption
signal of a clean substrate. The inset shows an SEM image of the
sample.
nanoparticles with an Fe content of (50 ±5) at.% and a mean
diameter of 6.3 nm and for particles with an Fe content of (56±
6) at.% and a mean diameter of 4.4 nm. The Fe content was
determined by energy-dispersive x-ray spectroscopy (EDS) in
a transmission electron microscope.
In order to obtain magnetic moments of pure metallic
particles, Fe oxides and organic ligands were removed in situ
by a soft hydrogen plasma treatment [24]. The plasma
is ignited at a hydrogen pressure of about 50 Pa at the
standard radio-frequency of 13.56 MHz and a power of 50 W.
Afterwards, the pressure was reduced to 5 Pa and the sample
was transferred into the plasma chamber where it was exposed
to the plasma for 30 min. The efficiency of this treatment
was checked by measurements of the XANES at both the Fe
L3,2and carbon K absorption edges. It was found that the
Fe became completely metallic, i.e. the oxides were reduced,
and the absence of any carbon absorption line indicates that
the organic ligands were removed completely [25]. This is
shown in figure 1: in the as-prepared state, several absorption
peaks at the carbon K edge that can be assigned to electron
excitation into different molecular states could be obtained.
By comparison with spectra of alkanes and alkenes reported
in the literature [26,27], the final states are identified to be
π∗antibonding states at 285.1 eV, so-called Rydberg states
at 288.1 eV (3s, 3d not resolved energetically), σ∗(C–C)
antibonding states of carbon–carbon single bonds at 292.9 eV
and σ∗(C=C)antibonding states of carbon–carbon double
bonds around 302 eV. Additional carbon contaminations which
are unavoidable even in ultra-high vacuum conditions may
contribute to the signal at the carbon K edge. Therefore, the
2

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
spectrum was normalized to the absorption of a clean naturally
oxidized Si substrate, as was used for the deposition of the
particles.
Epitaxial FexPt1−xfilms with thicknesses around 50 nm
were grown on MgO(001) substrates at room temperature by
magnetron co-sputtering from Fe and Pt targets in a vacuum
system with a base pressure of about 10−6Pa. The deposition
rate was about 0.1 nm s−1. X-ray diffraction (XRD) indicates
a high degree of structural order and the mosaic spread is
below 1◦. The layer thickness determined by Rutherford
backscattering was found to be around (46 ±6) nm and
therefore the films are expected to exhibit bulk properties.
A polycrystalline Fe0.56Pt0.44 bulk sample was prepared
by arc melting in an Ar atmosphere. For all samples, the
composition was determined by EDS.
2.2. X-ray absorption experiments
The x-ray absorption near-edge structure (XANES) and its
associated XMCD was measured in the soft x-ray regime at
the Fe L3,2absorption edges at the bending magnet beamline
PM3 at BESSY II, Berlin (Germany). The measurements were
done at T=15 K in magnetic fields of μ0Hext =±2.8Tat
fixed photon helicity in an energy range of 0.680 keV E
0.780 keV. After each scan, the magnetic field was reversed.
Measurements at the Pt L3,2absorption edges in the hard
x-ray regime were performed at the ID12 undulator beamline
at the ESRF, Grenoble (France) at T=7Kandinmagnetic
fields up to μ0Hext =±6 T. After each scan, either the
magnetic field or the helicity of x-ray photons was reversed.
XANES and XMCD spectra were taken in the energy range
of 11.538 keV E11.645 keV and 13.244 keV E
13.374 keV. The EXAFS at the Pt L3absorption edge was
measured up to 12.581 keV, corresponding to a photoelectron
wavenumber k≈140 nm−1, and at the Fe K edge in the range
of 7.066 keV E8.319 keV.
A portable plasma chamber was attached to the
experimental endstations for an in situ cleaning of the samples.
3. Ab initio calculations and data analysis
3.1. SPR-KKR calculations
The electronic and magnetic properties of chemically
disordered FexPt1−xalloys were investigated by means of
the fully relativistic spin-polarized version of the KKR band
structure method (SPR-KKR) [28] within the framework of
spin density functional theory. For the corresponding exchange
correlation potential, the local spin density approximation
(LSDA) parametrization of Vosko et al [29] has been used.
The SPR-KKR method represents the electronic structure
in terms of the Green’s function evaluated by means of
multiple scattering theory. This feature allowed us to deal
with the chemical disorder by using the coherent potential
approximation (CPA) alloy theory.
The integration in the Brillouin zone was done over a
regular k-point grid with 225 points. The angular momentum
expansion cutoff was set to lmax =3. Larger values for the
Figure 2. Lattice constants determined by XRD of 50 nm thick
bulk-like FexPt1−xfilms as a function of Fe content. Values for
FexPt1−xbulk material taken from the literature [30]areshownfor
comparison.
cutoff yield only small changes for the magnetic moments of
less than 1%.
As structural input for the SPR-KKR calculations, lattice
constants of 50 nm thick single-crystalline FexPt1−xfilms
obtained by x-ray diffraction (XRD) were used which are in
agreement with values reported in the literature [30] (figure 2).
For the alloys with an Fe content of 27 at.%x67 at.%,
the lattice constant depends linearly on x. For an Fe content
of 72 at.% the lattice constant is smaller than expected from
linear extrapolation, a first indication of the drop of the lattice
constant to (0.3707 ±0.002) nm at 77 at.% Fe. At this
concentration, the crystal structure is already bcc as for bulk
Fe.
3.2. Sum-rule-based analysis of XMCD
To separate the transitions into the 3d states of the Fe atoms
and into the 5d final states of the Pt atoms from transitions
into higher levels (or into the continuum), a two-step-like
function was subtracted in the case of the XANES at the Fe
L3,2edges. Since the absorption at the Pt L3,2edges is not
well pronounced, this procedure would lead to a large error.
Therefore, reference spectra of Au are shifted in energy and
subtracted instead [31] after stretching the energy scale to
account for the different lattice constants in Au with respect
to FePt. As an example, XANES and XMCD spectra of
Fe and Pt measured at the L3,2absorption edges of plasma-
cleaned FePt nanoparticles with a mean diameter of 6.3 nm
are shown in figure 3(a). Note that the XMCD in the case
of Pt is enlarged by a factor of 4. In addition, the two-step-
like function and the modified Au reference spectra are shown.
Subtracting these spectra from the experimental XANES leads
to the XANES corresponding to electron excitation into 3d
(5d) final states for Fe (Pt) shown in figures 3(b) and (c).
The effective spin magnetic moment μeff
S/nhand the orbital
magnetic moment μl/nhper unoccupied final state nhcan be
determined according to the sum rules [33,34] that can be
written as [32]
μl
nh=−2
3
q
rμB(1)
μeff
s
nh=−3p+2q
rμB,(2)
3

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
Figure 3. (a) XANES (black lines) and its associated XMCD (red lines) at both Fe and Pt L3,2absorption edges of 6.3 nm FePt nanoparticles.
Note the different scaling of the ordinate for Fe and Pt absorption spectra. In addition, the XMCD signal at the Pt edges is enlarged by a factor
of 4. Light grey lines refer to a two-step-like function in the case of Fe and modified Au reference spectra in the case of Pt. (b), (c) XANES,
XMCD and their integrals (dashed lines) after background (light grey lines in (a)) subtraction. The integral of XMCD is enlarged by a factor
of 2 for both Fe and Pt.
where pis the integral of XMCD over the energy range of L3
absorption edge, qis the integral of XMCD over the energy
range of L3and L2absorption edges, and ris the integral of
XANES(3d) in the case of Fe and XANES(5d) in the case
of Pt over the energy range of L3and L2absorption edges.
The quality of the integrals of experimental data presented
in figure 3is sufficient to extract the values for p,qand r
validating the procedure of background subtraction using Au
reference spectra in the case of Pt.
For the numbers of unoccupied final states nh(Fe)≈3.41
at the Fe sites and nh(Pt)≈1.74 at the Pt sites were used
as obtained from band structure calculations. Due to the
procedure of background subtraction, the spectra in figure 3(c)
correspond to a number of unoccupied final 5d states ˜nh(Pt)=
nh(Pt)−nh(Au)with nh(Au)=0.75.
Note that the effective spin magnetic moment μeff
S=
μS+7μtconsists of the spin magnetic moment and a magnetic
dipole moment accounting for a possible asphericity of the spin
density distribution.
Measurements performed in the total electron yield (TEY)
mode were corrected for saturation effects [35,36]usingan
electron escape depth of 2 nm. Variation of the escape depth
between 1.7 and 2.5 nm did not have any visible effect on
the saturation. For a reliable correction of saturation effects
it is further necessary to obtain the absorption coefficient in
absolute values from the measured TEY in arbitrary units.
Therefore the spectra were fitted in the pre- and post-edge
regions to the calculated absorption coefficient of non-resonant
absorption [37]. Measurements of the TEY signal at different
angles between the incident x-rays and the sample normal
improved the accuracy.
3.3. EXAFS analysis and simulations
The EXAFS oscillations χ(k)were extracted from experimen-
tal absorption data by fitting and subtracting the atomic back-
ground using the AUTOBK algorithm [38] with a threshold
frequency Rbkg =0.11 nm. For Fourier transformation of the
experimental data as a function of photoelectron wavenumber
k,thekweighted data were used in the range between
kmin ≈20 nm−1and kmax ≈125 nm−1in a Kaiser–Bessel
window with dk=1nm
−1. For Fourier transformation
of the experimental data obtained at the Fe K edge of the
nanoparticles, a smaller krange between kmin ≈20.0nm
−1
and kmax ≈80 nm−1hadtobeusedsincethedataaremore
noisy (figure 6).
For the calculation of the scattering paths j,andthe
simulation of the EXAFS respectively, the structure of the
material has to be put in, i.e. the position and the type of
element of the absorber and backscatterer. The calculation of
the scattering paths was done using the software Artemis [39]
based on the algorithms of the FEFFIT [14] and FEFF [40,41]
programs.
In these programs, the full χ(k)spectrum is represented
as the sum of the imaginary part of contributions from different
paths:
χ(k)=
j
Im (˜χj(k)) (3)
4

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
Figure 4. (a) Backscattering amplitude of Fe and Pt as a function of
photoelectron wavenumber. (b) Effective backscattering amplitude of
Fe and Pt and EXAFS phase shift as a function of the photoelectron
wavenumber. The grey line in the coordinates plane at the bottom
refer to the dependence of the phase shift on the wavenumber. In all
cases Pt is the absorber atom.
where ˜χj(k)is the contribution calculated from a particular
scattering path jthat may either be a single or a multiple
scattering path and can be written as
˜χj(k)=S2
0N∗
jFj(k)
kR2
j
exp[2ikRj+iδj(k)]
×exp[−2Rj/λ(k)−2k2σ2
j].(4)
In this equation, S2
0denotes an amplitude reduction factor
due to many-body effects, N∗
jis the effective coordination
number, Fj(k)is the effective scattering amplitude, Rjis half
the total length of the scattering path, λ(k)is the mean free
path length of the photoelectron with wavenumber k,δjis
an effective total phase shift (including contributions from the
central atom and all scattering atoms) and exp[−2σ2
jk2]is the
EXAFS Debye–Waller factor. In figure 4, the EXAFS phase
shifts and effective backscattering amplitudes for Fe and Pt are
shown as a function of wavenumber. The correspondence of
the variables in equation (4) to the entries of an FEFF output
file is [43]
mag[feff]×red factor −→ Fj(k)
real[2∗phc]+phase[feff]−→δj(k)
where ‘mag[feff]’ denotes the backscattering curved wave
amplitude and ‘red factor’ is a reduction factor that
approximates the losses due to multiple electron excitations at
the absorbing atom caused by the creation of a core hole in
x-ray absorption experiments. ‘real[2*phc]’ is twice the real
part of the central atom phase shift and ‘phase[feff]’ is the
backscattering curved wave phase. More detailed information
about the notation in FEFF codes, input and output files can be
found elsewhere [42,43].
The backscattering amplitude is also shown as a 2D
graphic in figure 4(a) for an easier reading of the kvalues of
interesting points of the backscattering amplitude, e.g. maxima
and minima. Fe has the maximum backscattering amplitude
at k≈60 nm−1.Atthiskvalue the backscattering
amplitude of Pt atoms exhibits a local minimum. The strong
reduction in the Pt amplitude over a small range at this point is
connected with a more rapidly changing phase. This effect is
known in the literature as the generalized Ramsauer–Townsend
effect [44,45]. In a simple picture, the wavelength of the
outgoing photoelectron (about 0.1 nm for k≈60 nm−1)is
well matched to the size of the scatterer. In this case, the
photoelectron may tunnel through the scattering potential and
the scattering cross section vanishes, leading to a dip in the
backscattering amplitude at a fairly distinct wavenumber.
In order to fit the calculated EXAFS signal to the
experimentally obtained one, FEFFIT uses the cumulant
expansion [46,47] with the first four cumulants (R,σ2,
C3,C4) of the pair distribution function of atoms around the
absorber atom. Accounting for thermal or configurational
disorder, the complex wavenumber pis introduced and should
be used instead of k. The imaginary part of prepresents losses
of photoelectron coherence including the mean free path and
core-hole lifetime. The resulting modified EXAFS equation
can be written as [42]
˜χj=S2
0N∗
jFj(k)
k(Rj+Rj)2exp[2ikRj+iδj(k)]
×exp[2i(pRj−2pσ2
j/Rj−2p3C3,j/3)]
×exp[−2Rj/λ(k)−2p2σ2
j−2p4C4,j/3].(5)
It turned out that, for the data examined here, it is
not necessary to include the fourth-order cumulant in the
fitting procedure. Even the third cumulant accounting for an
anharmonicity of the interatomic potential does not have to
be included for a proper simulation of the experimental data
presented here.
To model the chemically disordered FexPt1−xalloys,
fitting of the experimental data was performed using the
sum of EXAFS calculated for the absorber in a pure fcc Fe
environment and in a pure fcc Pt environment, respectively,
with the same distance of nearest neighbours. The overall
amplitudes for these two cases is a measure of the Fe and Pt
content.
Especially in alloys, it is interesting to distinguish between
the contributions of the different atomic species located
at the same distance to the EXAFS signal. A powerful
tool to visualize these contributions is the use of wavelet
transformation (WT) [48]. Like the Fourier transformation,
the WT is a mathematical complete transformation, i.e. the
backward WT recovers the original data again [49]. The main
idea behind WT is to replace the infinitely expanded periodic
oscillations in a Fourier transformation by located wavelets as
a kernel for the integral transformation.
5

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
Figure 5. Contour plot of the wavelet-transformed EXAFS of
FexPt1−xnanoparticles in the as-prepared state.
One may realize the WT as an improved short-term
Fourier transformation (STFT) which determines the Fourier
coefficients of the original data multiplied by a window
function, i.e. the k-dependent EXAFS data are transformed in
several intervals of k. In STFT, a high resolution in kyields a
low resolution in rand vice versa. By contrast, the advantage
of WT is the use of a scalable mother wavelet or analysing
wavelet ψ(k)as a window function for the transformation.
The basis of the transformed signal is generated not only
by translation, but also by scaling of the analysing wavelet
yielding high resolution both in kand rspace. In this work,
the AGU-Vallen wavelet software was used [50], which was
developed for acoustic emission analyses, but can easily be
adapted for EXAFS analyses. As analysing wavelet, a Gabor
wavelet based on the Gaussian function is used. It has the form
ψ(k)∝rc
γ1/2
exp−1
2rck
γ2
+irck(6)
with a centre length rcand a constant γwhich determines
resolutions both of the dimensioning in kand of the bandwidth
in r. This parameter is chosen to be γ=π√2ln 2 to satisfy
the admissibility condition, i.e. the integral over a wavelet
is zero and the wavelet functions satisfy the orthonormality
condition [50].
In EXAFS analysis, the kdependence of the absorption
signal can be resolved by WT. Figure 5shows the WT of
FexPt1−xnanoparticles in the as-prepared state containing also
Fe oxides and organic ligands at the surface. It was chosen
as one example of a sample that consists not only of a binary
alloy but also of light elements like carbon and oxygen. The
kposition of maxima in the WT is connected to the different
elements via the individual kpositions of their maximum
backscattering amplitude. Thus, the WT maxima at low k
values correspond to the EXAFS signal of light elements like
carbon and oxygen. It can even be distinguished between
the contribution of the Fe and Pt atoms in the FexPt1−xalloy
with the same nearest-neighbour distance, since the kvalue of
the maximum of the WT differs significantly for the lighter
(ZFe =26) and the heavier (ZPt =78) backscattering atoms.
Note that there is a shift between the radial distance rin the
plot and the geometrical distance between nearest-neighbour
atoms due to the EXAFS phase shift.
4. Results
4.1. Crystal structure and alloying in FePt nanoparticles
XRD, electron diffraction (ED) and high-resolution transmis-
sion electron microscopy (HR TEM) [51] analyses indicate a
lattice expansion in FexPt1−xnanoparticles in comparison to
the corresponding bulk material. By the analysis of the EXAFS
oscillations of hydrogen-plasma-cleaned nanoparticles, it has
already been shown that this lattice expansion is an intrinsic
property of the nanoparticles and is neither caused by the
organic ligands surrounding the nanoparticles nor by Fe
oxides that are present in as-prepared nanoparticles exposed
to air [22].
Here, we focus on the local composition determined by
EXAFS. The k-weighted experimental data and the result of
the simulations that fit best are shown in figure 6. The window
used for Fourier transformation of the data is also outlined.
Note that the maximum value of the window function equals 1.
The Fourier transform of the experimental EXAFS data of both
Fe0.56Pt0.44 bulk material and plasma-cleaned nanoparticles
and the simulations that fit best are shown as a function of
radial distance. Fitting of the calculated Fourier transform was
performed in the range between r≈0.11 and 0.34 nm; only
nearest-neighbour contributions are included.
Before turning to the case of the nanoparticle system,
EXAFS results of the bulk reference sample will be compared
to the lattice constant and composition determined by other
methods. The best fit to the experimental EXAFS data was
obtained for simulations assuming (59±4) at.% Fe around the
Pt probe atoms and (55 ±6) at.% around the Fe probe atoms.
These values are the same within experimental errors and are
in good agreement with the Fe content determined by EDS
((56 ±3) at.%). Additionally, the lattice constant used in the
simulations, i.e. 0.383 nm, equals the lattice constant obtained
from XRD (0.384 ±0.002) nm. The error of lattice constants
determined by EXAFS analysis was estimated by varying the
lattice constant in the simulations.
In the case of nanoparticles, the reduction of the envelope
of EXAFS oscillations due to the Ramsauer–Townsend effect
in Pt corresponds to a reduction of the amplitudeof the Fourier
transform in a small region of raround r≈0.21 nm. This
reduction is strongly pronounced in the case of the EXAFS
data measured at the Pt L3absorption edge of the nanoparticles,
indicating a Pt enrichment around the Pt probe atoms. In
fact, in the nanoparticles (40 ±8) at.% Fe has to be assumed
for a proper simulation of the experimental data measured
at the Pt L3edge which does not match the value found by
EDS ((56 ±5) at.% Fe). This difference is not a conflict
between EXAFS and EDS results, but simply reflects that an
averaging technique like EDS does not allow for the detection
of an inhomogeneous composition of the investigated sample
whereas the EXAFS technique does. The reason is that
EXAFS stems from scattering of the photoelectron at the local
surrounding of the probe atoms. Thus, it can be concluded
that the Pt absorbing atoms are in a Pt-rich environment and
the Fe atoms are in an Fe-rich environment. From the Fe
content around the Pt atoms and the averaged value, the Fe
content in the near environment of the Fe atoms is expected to
6

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
Figure 6. Upper graphics: EXAFS data measured at room temperature at the Fe K absorption edge (left panel) and Pt L3absorption edge
(right panel) and simulations (filled circles) of bulk Fe0.56Pt0.44 (blue solid lines) and Fe0.56Pt0.44 nanoparticles (red solid lines). The dashed
line corresponds to the window used for Fourier transformation. Lower graphics: Fourier transform of experimental EXAFS data (lines)
shown in the upper graphics and simulations (filled circles). A smaller window for the Fourier transformation had to be used for the data
measured at the Fe K edge of nanoparticles causing a slightly different shape and position of centroid.
Table 1. Lattice constant at room temperature of Fe0.56Pt0.44
nanoparticles and the corresponding bulk alloy determined by
different methods (cf [22]).
Lattice constant, a(nm)
Method Bulk material Nanoparticles
Fe EXAFS 0.383 ±0.004 0.387 ±0.008
Pt EXAFS 0.383 ±0.003 0.387 ±0.004
XRD 0.384 ±0.002 0.388 ±0.002
HR TEM, ED — 0.389 ±0.006
be around 72 at.%. The analysis of the experimental EXAFS
data measured at the Fe K edge support this conclusion, i.e. the
Fe probe atoms are in an Fe-rich environment containing
(70 ±12) at.% Fe. Note that the larger error bar is due to the
smaller krange of Fourier transformation accounting for the
smaller signal-to-noise ratio in the EXAFS spectrum (figure 6).
In tables 1and 2, the lattice constants and Fe contents are
summarized.
Within experimental errors, no different lattice constants
for the Fe-rich and Pt-rich regions were found in the
nanoparticles. One may argue that the differences in the
EXAFS of the nanoparticles compared to the bulk EXAFS
is an effect of a flat and asymmetric pair potential at the
surface caused by a reduced coordination number. But, in fact,
introducing a non-vanishing third cumulant which describes
such an effect yields a stretching of the EXAFS at higher k
values (contraction of the nearest-neighbour distance) which
was not observed here. Even with a small but reasonable value
of c3=10−7nm3it is not possible to simulate the experimental
data properly.
Table 2. Composition of Fe0.56 Pt0.44 nanoparticles and the
corresponding bulk alloy determined by different methods. The
composition obtained by EXAFS is given by the local composition
(first shell) around the Fe probe atoms and the Pt probe atoms,
respectively.
Fe content, x(at.%)
Method Bulk material Nanoparticles
Fe EXAFS 55 ±670±12
Pt EXAFS 59 ±440±8
EDS 56 ±356±6
To visualize the different Fe and Pt contents around the
probe atoms in the bulk material and in the nanoparticles,
the WT method was employed. Since the effects are rather
small, in figure 7the difference of the bulk and nanoparticle
EXAFS is shown, i.e. the wavelet transformed bulk data were
subtracted from the wavelet-transformed nanoparticle data.
The analysed data measured at the Pt L3edge show a clear
minimum at k≈60 nm−1,r≈0.21 nm (figure 7(right)),
indicating less Fe nearest-neighbour atoms of the Pt probe
atoms than in the bulk alloy. Accordingly, at approximately
the same radial distance the WT is increasing at high k
values, indicating a higher probability to find Pt atoms as
nearest neighbours of the Pt absorbing atoms. The slightly
different rvalues of Fe and Pt maxima may be due to different
backscattering phases [48]. Although the experimental data
obtained at the Fe K edge are noisy for higher values of k,the
results using WT are reasonable. A maximum at low kvalues
and a (less pronounced) minimum at high kvalues shown
in figure 4(left) indicate more Fe and less Pt atoms around
7

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
Figure 7. 3D surface plot of the difference between wavelet-transformed EXAFS of Fe and Pt absorber atoms in nanoparticles and bulk
material. The difference measured at the Fe K edge (left) reveals the change around the Fe sites whereas the difference measured at the Pt L3
absorption edge (right) reveals the change in the surrounding of Pt sites. The positions of the Fe and Pt nearest-neighbour (nn) atom
backscattering maxima are marked.
the Fe probe atoms in nanoparticles with respect to the bulk
material.
4.2. Element-specific magnetic moments in FexPt1−xalloys:
bulk materials and nanoparticles
The deviation of the local composition from the averaged value
presented in the previous section may strongly influence the
magnetic properties of the FexPt1−xnanoparticles, e.g. the
element-specific magnetic moments at the Fe and Pt sites as
reported in the literature [12,13,25]. In order to rate these
values experimentally found in nanoparticles (table 3), the
corresponding magnetic moments of the bulk materials are
needed. In this work, we present not only experimentally
obtained magnetic moments of bulk-like FexPt1−xfilms, but
also results of SPR-KKR band structure calculations.
The calculated spin and orbital magnetic moments at
both the Fe and Pt sites are given in table 4. We found
that the magnetic moment at the Fe sites is increasing with
increasing Pt content, whereas the Pt magnetic moments
remain largely unchanged. The increase in the case of Fe
can be essentially explained by the increase of the lattice
constant which usually yields larger magnetic moments in
ferromagnetic and antiferromagnetic materials, e.g. in Fe [55].
Due to a reduction in the hybridization of Fe d states, the
increase of the magnetic moment at the Fe sites is connected
to a sharpening of the density of states (DOS). The calculated
DOSisshowninfigure8for three different compositions,
i.e. Fe0.32Pt0.68,Fe
0.58Pt0.42 and Fe0.68 Pt0.32. Besides the spin-
resolved total DOS, the angular momentum (s, p, d)-resolved
partial densities of states are also shown. The shape of the
DOS is in agreement with the calculated DOS for randomly
disordered Fe0.50Pt0.50 alloys reported in the literature [52]. In
general, the chemical disorder yields rather smooth changes
in the DOS, i.e. possible fine structures that may be present
for perfectly ordered systems are washed out. At the Fe sites,
Table 3. Experimentally obtained effective spin and orbital
magnetic moments at the Fe and Pt sites of Fe0.56Pt0.44 bulk material,
Fe0.50Pt0.50 nanoparticles with a mean diameter of 6.3 nm, and the
moments at the Fe sites of Fe0.56 Pt0.44 nanoparticles with a mean
diameter of 4.4 nm. The values taken from [12] were recalculated
using nh=3.41.
Fe0.56Pt0.44 bulk material
μeff
S(Fe)/μB2.59 ±0.26
μl(Fe)/μB0.076 ±0.014
μeff
S(Pt)/μB0.47 ±0.02
μl(Pt)/μB0.045 ±0.006
Fe0.50Pt0.50 nanoparticles [12], d=6.3nm
μeff
S(Fe)/μB2.28 ±0.25
μl(Fe)/μB0.048 ±0.010
μeff
S(Pt)/μB0.41 ±0.02
μl(Pt)/μB0.054 ±0.006
Fe0.56Pt0.44 nanoparticles, d=4.4nm
μeff
S(Fe)/μB2.13 ±0.21
μl(Fe)/μB0.062 ±0.014
the relatively narrow d bands are strongly exchange-split. A
clear broadening of the DOS at the Fe sites for the Fe-rich
alloy is visible and the difference between the majority and
the minority band becomes smaller. At the Pt sites, the d
bands are broader by a factor of about two and only a slight
composition dependence is visible corresponding to an almost
constant magnetic moment.
The averaged total magnetic moment per atom is in
perfect agreement with experimental data reported in the
literature [54]. In order to compare not only the averaged
magnetic moments, but the element-specific spin and orbital
magnetic moments, XMCD measurements on a bulk-like
system were performed and analysed. The experimental results
on 50 nm thick FexPt1−xfilms are in qualitative agreement
8

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
Figure 8. Spin-and angular momentum-resolved density of states at
the Fe sites (upper panel) and Pt sites (lower panel) calculated for
FexPt1−xchemically disordered bulk alloys using x=32 at.%,
x=48 at.% and x=68 at.%, respectively.
Table 4. Spin and orbital magnetic moments at the Fe and Pt sites in
chemically disordered FexPt1−xalloys obtained from SPR-KKR
band structure calculations.
x/at.% 324048606872
μS(Fe)/μB3.045 2.979 2.912 2.818 2.757 2.700
μl(Fe)/μB0.065 0.069 0.073 0.077 0.079 0.077
μS(Pt)/μB0.221 0.231 0.232 0.227 0.224 0.228
μl(Pt)/μB0.042 0.045 0.047 0.048 0.049 0.047
with the theoretically calculated results, i.e. the spin magnetic
moments at the Fe sites are reduced in Fe-rich FexPt1−xalloys
(figure 9in section 5). For Fe contents up to about 50 at.% the
calculated values also match quantitatively the experimental
data. At the highest Fe content studied in this work (≈70 at.%),
the calculated value is larger by about 0.5μBwith respect to
the experimentally obtained one. At the Pt sites, the calculated
values are smaller by a factor of about two, but in agreement
with other calculated values reported in the literature [52]. The
reason for this disagreement between theory and experiment is
yet unclear.
In the nanoparticles, the effective spin magnetic moment
at the Fe sites is reduced by 20–30% with respect to the
corresponding bulk material [12,13] and shows a slight size
dependence [25]. The experimentally obtained values are listed
in table 3. Note that the values taken from [12] are recalculated
for a different number of unoccupied final states that was
obtained from SPR-KKR calculations for bulk material as
presented in this work, i.e. nh=3.41 instead of nh=3.705
which was taken from earlier work [53].
5. Discussion
The magnetic moments at the Fe sites of chemically disordered
FexPt1−xnanoparticles were found to be reduced by 20–30%
Figure 9. Experimentally obtained effective spin magnetic moments
at the Fe sites of chemically disordered FexPt1−xfilms and bulk
material, respectively, as a function of Fe content. The moments in
nanoparticles are assigned to the averaged compositions determined
by EDS. The local composition determined by EXAFS for the
4.4 nm nanoparticles is also marked by an arrow on the top axis. For
the 6.3 nm nanoparticles the local composition is estimated assuming
the same relative deviation from the averaged value. The light grey
arrow in the graph illustrates the difference in averaged and local
composition. See tables 2and 3for missing error bars.
with respect to the corresponding bulk material [12,13]. As
a consequence, the induced magnetic moments at the Pt sites
are also smaller in the nanoparticles. Since the latter are rather
small, we focus on the discussion of the magnetic moments at
the Fe sites showing significant changes.
There are two possible reasons for the reduced magnetic
moments found by EXAFS analysis: the lattice expansion and
the inhomogeneous composition. The lattice expansion cannot
be the reason for the reduced magnetic moments since a larger
lattice constant yields larger magnetic moments at the Fe sites.
We validated this by SPR-KKR calculations, which yield a
slight increase by 0.6% for the spin magnetic moment at the
Fe sites for a lattice constant that is 1% larger than in the
bulk (not shown here). Similar trends are reported for other
ferromagnetic or antiferromagnetic materials, e.g. for bcc and
fccFe[55].
However, the deviation of the local composition from the
averaged value is an apposite explanation. As presented in
this work, the Pt atoms are in a Pt-rich environment compared
to the averaged composition, whereas Fe atoms are in an
Fe-rich environment in the nanoparticles. In figure 9,the
effective spin magnetic moments at the Fe sites of FexPt1−x
chemically disordered bulk-like alloys are shown as a function
of Fe content. It is clearly visible that μeff
Sis decreasing
monotonically with increasing Fe content. The values of μeff
S
for FexPt1−xparticles are also shown in this graphic. (For more
clarity, the errors were omitted in the graph.) The moments
are assigned to the averaged compositions of the Fe0.50Pt0.50
particles with a mean diameter of 6.3 nm and the Fe0.56Pt0.44
particles with a mean diameter of 4.4 nm, respectively. Also
the local composition determined from EXAFS analysis is
9

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
marked by an arrow at the top axis. Assigning the value of
μeff
Sto this local composition, the nanoparticle data fits within
experimental error bars to the moments at the Fe sites in 50 nm
thick films.
For the larger particles, no EXAFS data were measured.
Therefore, the local composition was estimated assuming the
same relative deviation from the averaged value, i.e. an Fe
enrichment of about 27% around the Fe atoms. Starting from
the averaged composition of Fe0.50Pt0.50,thisleadstoanFe
content of about 63 at.%. Again, assigning the value of μeff
S
to this local composition, the nanoparticle data fits to the
reference curve of the moments of the 50 nm thick films.
This indicates that the inhomogeneous compositionwithin
the nanoparticles is very likely the reason for the strongly
reduced magnetic moments in the nanoparticles compared
to the corresponding bulk material of the same averaged
composition.
Note that, from the analyses presented here, it is not
possible to specify the inhomogeneity of the alloy, i.e. to
distinguish a possible core/shell-like structure from random
clustering of the chemical elements within the nanoparticles.
In the literature, several other reasons for reduced
magnetic moments in nanoparticles are discussed, e.g. spin
canting effects [24] or the influence of an intra-atomic dipole
term in the XMCD, the latter being a quite frequent problem
of sum-rule-based analysis of XMCD [33,34] yielding an
effective spin magnetic moment μeff
Sper unoccupied final state
nh(cf section 3.2). Although these effects are expected to be
too small to cause the distinct drop by 20–30% of the magnetic
moment when reducing the system dimension from the bulk to
nanoparticles, they will be briefly discussed below for the sake
of completeness.
For single-crystalline materials with weak spin–orbit
coupling, the magnetic dipole moment μtthat contributes to
μeff
Scan be eliminated by angular-dependent measurements of
the XMCD [56]. In ensembles of FexPt1−xnanoparticles with
a strong spin–orbit coupling, μtcannot be eliminated, and even
for randomly oriented crystallographic axes μtwill not cancel
out [57]. A negative contribution of μtespecially from surface
atoms reduces μeff
Sderived from XMCD analysis and will
lead to a further decrease for analysed data from nanoparticle
systems due to their larger fraction of surface atoms compared
to 50 nm thick films or bulk material. One may note that, in the
case of Fe nanoclusters, a decrease of μeff
Swith decreasing size
was associated with a negative contribution of μt[58]. This
may also be the reason for the slight size dependence found in
FePt nanoparticles reported earlier [25].
In addition, changes in the number of unoccupied final
states nhinfluence the experimentally determined μeff
Ssince
this number has to be known for its quantification. For both
nanoparticles and films, the same number of nhwas used.
However, these effects mentioned above are too small
to cause a reduction of the magnetic moment by 20–
30% compared to bulk material. A spin canting effect in
nanoparticles can also reduce the measured magnetic moments.
It occurs in systems with a high MCA compared to the
exchange coupling which favours a collinear alignment of the
spins. A magnetic moment that is reduced by 20–30%, as is
the case here, corresponds to one or two ‘magnetically dead’
surface layers, i.e. extremely strong spin canting yielding a
vanishing net magnetization that was not obtained in metallic
nanoparticles. Such a strong spin canting would also be
expected to influence the field-dependent magnetization in a
way that at high external magnetic fields a slope should be
visible arising from the canted spins that can hardly be forced
into the direction of the external field. In magnetic hysteresis
on FePt nanoparticle systems measured element-specifically at
the Fe L3edge as presented, for example, in [12,25]sucha
slope in the high-field region was not observed, indicating the
absence of strongly canted surface spins. From a theoretical
point of view, there is the possibility that for nanoparticles a
small spin canting may exist [59,60] if one assumes MCA
densities in the volume and at the surface that are even larger
than in the chemically ordered FePt L10phase [59]. In the low-
anisotropic chemically disordered state of FePt investigated in
this work, such canting effects are also assumed to be quite
unlikely.
In summary, the inhomogeneous composition within the
nanoparticles seems to be the most probable explanation for
the reduced magnetic moments. Since this reduction is also
reported for FexPt1−xnanoparticles around the equi-atomic
composition prepared by gas phase condensation, one may
conclude that the inhomogeneity can be found in FexPt1−x
particles independently of the preparation method. The
preferential formation of Fe-rich and Pt-rich regions within
the nanoparticles could also influence the formation of the L10
state and lower the degree of chemical order.
Besides the FexPt1−xsystem, a local deviation of the
composition with respect to the averaged value may also occur
in nanoparticles of various binary alloys.
6. Conclusion
By the analyses of the EXAFS of hydrogen-plasma-cleaned
Fe0.56Pt0.44 nanoparticles and bulk material, not only a
lattice expansion [22], but also a local deviation of the
averaged composition was found, i.e. Fe is in an Fe-rich
environment and Pt is in a Pt-rich environment. The usual
Fourier transformation-based analysis of the EXAFS was
complemented by a wavelet transformation method.
The composition inhomogeneities are likely the reason for
the reduced magnetic moments of the nanoparticles by 20–30%
with respect to the bulk material [12,13] since the magnetic
moments at the Fe sites are decreasing with increasing Fe
content in the near environment. The latter dependence was
found by SPR-KKR band structure calculations and XMCD
experiments on bulk-like systems.
Acknowledgments
We would like to thank S Sun (Brown U) for providing
nanoparticles, J-U Thiele (Hitachi) for thin film preparation,
and M Acet and T Krenke (U Duisburg-Essen) for
the preparation of the bulk reference sample. We
thank M Vennemann and M Acet (U Duisburg-Essen)
for XRD measurements and for help in the XMCD
10

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
measurements, U Wiedwald (U Ulm), H-G Boyen (U Hasselt),
N Friedenberger and S Stienen (U Duisburg-Essen) are
acknowledged as well as P Voisin and S Feite (ESRF)
for technical assistance, and the BESSY II staff, especially
T Kachel and H Pfau, for their kind support. We thank
MKoˇsuth (LMU M¨unchen), R Meyer and H Herper
(U Duisburg-Essen) for helpful discussions.
This work was financially supported by the DFG
(SFB445), the BMBF (05 ES3XBA/5), the ESRF and the EU
(MRTN-CT-2004-0055667, ‘SyntOrbMag’).
References
[1] Chantrell R W, Weller D, Klemmer T J, Sun S and
Fullerton E E 2002 J. Appl. Phys. 91 6866
[2] Antoniak C, Lindner J and Farle M 2005 Europhys. Lett.
70 250
[3] Bian B, Laughlin D E, Sato K and Hirotsu Y 2000 J. Appl.
Phys. 87 6962
[4] Chen M-P, Nishio H, Kitamoto Y and Yamamoto H 2005 J.
Appl. Phys. 97 10J321
[5] Kim C K, Kan D, Veres T, Normadin F, Liao J K, Kim H H,
Lee S-H, Zahn M and Muhammed M 2005 J. Appl. Phys.
97 10Q918
[6] Ulmeanu M, Antoniak C, Wiedwald U, Farle M, Frait Z and
Sun S 2004 Phys. Rev. B69 054417
[7] Dorman J L, Fiorani D and Tronc E 1997 Adv. Chem. Phys.
98 283
[8] Ivanov O A, Solina L V, Demshina V A and Magat L M 1973
Phys. Met. Metall. 35 81
[9] Visokay M R and Sinclair R 1995 Appl. Phys. Lett. 66 1692
[10] Thiele J-U, Folks L, Toney M F and Weller D 1998 J. Appl.
Phys. 84 5686
[11] Shima T, Takanashi K, Takahashi Y K and Hono K 2004 Appl.
Phys. Lett. 85 2571
[12] Antoniak C et al 2006 Phys. Rev. Lett. 97 117201
[13] Dmitrieva O et al 2007 Phys. Rev. B76 064414
[14] Newville M 2001 J. Synchrotron Radiat. 8322
[15] Mizuno M, Sasaki Y, Yu A C C and Inoue M 2004 Langmuir
20 11305
[16] Yu A C C, Mizuno M, Sasaki Y, Inoue M, Kondo H, Ohta I,
Djayaprawira D and Takahashi M 2003 Appl. Phys. Lett.
82 4352
[17] Sun S, Anders S, Hamann H F, Thiele J-U, Baglin J E E,
Thomson T, Fullerton E E, Murray C B and Terris B D 2002
J. Am. Chem. Soc. 124 2884
[18] Stappert S, Rellinghaus B, Acet M and Wassermann E F 2003
J. Cryst. Growth 440 252
[19] Dmitrieva O, Acet M, Dumpich G, K¨astner J, Antoniak C,
Farle M and Fauth K 2006 J. Phys. D: Appl. Phys. 39 4741
[20] Li D, Poudyal N, Nandwana V, Jin Z, Elkins K and Liu J P
2006 J. Appl. Phys. 99 08E911
[21] Wiedwald U, Klimmer A, Kern B, Han L, Boyen H-G,
Ziemann P and Fauth K 2007 Appl. Phys. Lett. 90 062508
[22] Antoniak C, Trunova A, Spasova M, Farle M, Wende H,
Wilhelm F and Rogalev A 2008 Phys. Rev. B78 0401406R
[23] Sun S, Murray C B, Weller D, Folks L and Moser A 2000
Science 287 1989
[24] Boyen H-G et al 2005 Adv. Mater. 17 574
[25] Antoniak C and Farle M 2007 Mod. Phys. Lett. B21 1111
[26] St¨ohr J, Sette F and Johnson A L 1984 Phys. Rev. Lett. 53 1684
[27] Hitchcock A P, Beaulieu S, Stell T, St¨ohr J and Sette F 1984
J. Chem. Phys. 80 3927
[28] Ebert H et al The Munich SPR-KKR Package, Version 3.6
http://olymp.cup.uni-muenchen.de/ak/ebert/SPRKKR
Ebert H 2000 Fully relativistic band structure calculations for
magnetic solids—formalism and application Electronic
Structure and Physical Properties of Solids (Springer
Lecture Notes in Physics vol 535) ed H Dreyss´e (Berlin:
Springer) p 191
[29] Vosko S H, Wilk L and Nusair M 1980 Can. J. Phys. 58 1200
[30] Pearson W B 1958 A Handbook of Lattice Spacings and
Structures of Metals and Alloys (Oxford: Pergamon) p 634
[31] Grange W et al 1998 Phys. Rev. B58 6298
[32] Chen C T, Idzerda Y U, Lin H-J, Smith N V, Meigs G,
Chaban E, Ho G H, Pellegrin E and Sette F 1995 Phys. Rev.
Lett. 75 152
[33] Thole B T, Carra P, Sette F and van der Laan G 1992 Phys. Rev.
Lett. 68 1943
[34] Carra P, Thole B T, Altarelli M and Wang X 1993 Phys. Rev.
Lett. 70 694
[35] Nakajima R, St¨ohr J and Idzerda Y U 1999 Phys. Rev. B
59 6421
[36] Fauth K 2004 Appl. Phys. Lett. 85 3271
[37] Henke B L, Gullikson E M and Davis J C 1993 X-ray
interactions: photoabsorption, scattering, transmission, and
reflection at E=50–30000 eV, Z=1–92 At. Data Nucl.
Data Tables 54 181–342 http://henke.lbl.gov/
optical constants/
[38] Newville M, Livin¸ˇs P, Yacoby Y, Rehr J J and Stern E A 1993
Phys. Rev. B47 14126
[39] Ravel B and Newville M 2005 J. Synchrotron Radiat. 12 537
[40] Ankudinov A L, Ravel B, Rehr J J and Conradson S D 1998
Phys. Rev. B58 7565
[41] Zabinsky S I, Rehr J J, Ankudinov A, Albers R C and
Eller M J 1995 Phys. Rev. B52 2995
[42] Newville M 2001 J. Synchrotron Radiat. 896
[43] The FEFF project homepage http://leonardo.phys.washington.
edu/feff/
[44] McKale A G, Veal B W, Paulikas A P, Chan S-K and
Knapp G S 1998 Phys. Rev. B38 10919
[45] Fax´en H and Holtsmark J 1927 Z. Phys. 45 307
[46] Bunker G 1983 Nucl. Instrum. Methods 207 437
[47] Kendall M G 1958 The Advanced Theory of Statistics vol 1
(London: Hodder Arnorld)
[48] Funke H, Scheinost A C and Chukalina M 2005 Phys. Rev. B
71 094110
[49] Grossmann A and Morlet J 1984 SIAM J. Math. Anal. 15 723
[50] Suzuki H, Kinjo T, Hayashi Y, Takemoto M and Ono K 1996
J. Acoust. Emiss. 14 69
AGU-Vallen wavelet package http://www.vallen.de/wavelet/
[51] Wang R M, Dmitrieva O, Farle M, Dumpich G, Ye H Q,
Poppa H, Kilaas R and Kisielowski C 2008 Phys.Rev.Lett.
100 017205
[52] Perlov Ya, Ebert H, Yaresko A N, Antonov V N and
Weller D 1998 Solid State Commun. 105 273
[53] Galanakis I, Alouani M and Dreyss´e H 2002 J. Magn. Magn.
Mater. 242 27
[54] Landolt H and B¨ornstein R 1986 Numerical data and
Functional Relationships in Science and Technology (New
Series vol III/19a) (Berlin: Springer) and references therein
[55] Herper H C, Hoffmann E and Entel P 1999 Phys. Rev. B
60 3839
[56] St ¨ohr J and K¨onig H 1995 Phys. Rev. Lett. 75 3748
11

J. Phys.: Condens. Matter 21 (2009) 336002 C Antoniak et al
[57] Ederer C, Komelj M and F¨ahnle M 2003 Phys. Rev. B
68 052402
[58] Edmonds K W, Binns C, Baker S H, Thornton S C, Norris C,
Goedkoop J B, Finazzi M and Brookes N B 1999 Phys. Rev.
B60 472
[59] Labaye Y, Crisan O, Berger L, Greneche J M and Coey J M D
2002 J. Appl. Phys. 91 8715
[60] Garanin D A and Kachkachi H 2003 Phys.Rev.Lett.
90 065504
12