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Element-specific magnetic moments of epitaxially grown Fe3Si in D03 crystal symmetry were analyzed by means of x-ray absorption spectroscopy and its associated magnetic circular dichroism. To detect the weak magnetization induced at the Si sites, measurements were performed at both the Si K edge and the Si L3,2 edges. By band structure calculations based on either the SPR-KKR method or FLAPW with GGA, the spectroscopic features could be reproduced and provide an insight to the underlying physics. In addition, comparison of the experimental data to calculated spectra made it possible for us to estimate the induced effective spin and orbital magnetic moment of Si in our sample, i.e., μseff=(−0.011±0.005) μB and μl=(−0.003±0.003) μB, respectively. The sign and the order of magnitude of the tiny orbital magnetic moment has been confirmed by application of the magneto-optical sum rule.
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PHYSICAL REVIEW B 85, 214432 (2012)
Induced magnetism on silicon in Fe3Si quasi-Heusler compound
C. Antoniak,1H. C. Herper,1Y. N. Zhang,2A. Warland,1T. Kachel,3F. Stromberg,1B. Krumme,1C. Weis,1K. Fauth,4
W. Keune,1P. Entel,1R. Q. Wu,2J. Lindner,1and H. Wende1
1Fak ul t ¨
at f¨
ur Physik and Center for Nanointegration Duisburg-Essen (CeNIDE), Universit¨
at Duisburg-Essen,
Lotharstr. 1, 47048 Duisburg, Germany
2Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
3Helmholtz-Zentrum Berlin f¨
ur Materialien und Energie – Speicherring BESSYII, Albert-Einstein-Str. 15, 12489 Berlin, Germany
4Experimentelle Physik IV, Universit¨
at W¨
urzburg, Am Hubland, 97074 W¨
urzburg, Germany
(Received 6 October 2010; published 26 June 2012)
Element-specific magnetic moments of epitaxially grown Fe3Si in D03crystal symmetry were analyzed by
means of x-ray absorption spectroscopy and its associated magnetic circular dichroism. To detect the weak
magnetization induced at the Si sites, measurements were performed at both the Si Kedge and the Si L3,2edges.
By band structure calculations based on either the SPR-KKR method or FLAPW with GGA, the spectroscopic
features could be reproduced and provide an insight to the underlying physics. In addition, comparison of
the experimental data to calculated spectra made it possible for us to estimate the induced effective spin and
orbital magnetic moment of Si in our sample, i.e., μeff
s=(0.011 ±0.005) μBand μl=(0.003 ±0.003) μB,
respectively. The sign and the order of magnitude of the tiny orbital magnetic moment has been confirmed by
application of the magneto-optical sum rule.
DOI: 10.1103/PhysRevB.85.214432 PACS number(s): 75.50.Bb, 78.70.Dm
I. INTRODUCTION
In spintronics or magnetoelectronics, the intrinsic spin of an
electron and its associated magnetic moment is used as a carrier
for information in addition to its electronic charge. Compared
to devices based on conventional charge transport, spintronic
devices offer the possibility to realize fast processing at low
power costs. The spin-polarized current needed in this case can
be generated by passing the current through a ferromagnetic
electrode. In order to combine this new field of electronics with
the established semiconductor technologies, spin injection
from the ferromagnet into a semiconductor is essential and has
already been extensively investigated.13The Fe3Si compound
on GaAs has turned out to be a promising candidate of
ferromagnet/semiconductor systems with its spin injection
efficiency of above 2% at a temperature of 150 K and 1%
at room temperature.4
Fe3Si is a quasi-Heusler compound that crystallizes in the
D03symmetry in the chemically ordered phase with a lattice
constant a=5.65 ˚
A. As depicted in Fig. 1,Featomsare
located at two inequivalent lattice sites (A and B), and Si
occupies the lattice site C. While Fe-A atoms are surrounded
by four Fe and four Si nearest neighbor atoms, Fe-B atoms
are surrounded by eight Fe nearest neighbor atoms. Random
occupancies of sites B and C, or all three sites, lead to a
B2 (CsCl)-like or A2 (bcc) symmetry, respectively. Due to
the different neighborhood in the D03structure, Fe-A and
Fe-B atoms have different magnetic moments, namely 1.2 μB
and 2.4 μBas obtained from neutron diffraction experiments.5
The structure of Fe3Si can be represented by the long-range
ordering parameters S(B2) and S(D03) which are defined by
the occupation probabilities Piof Fe at the different lattice
sites i=A, B by the following equations:6
S(B2) =1
2
PA(1 x)
x(1 x)(1)
S(D03)=1
4
2PA+PB3(1 x)
x(1 x),(2)
where xdenotes the Si content, i.e., x=0.25 in the case of
Fe3Si. A perfect D03structure is described by S(D03)=1 and
S(B2) =2/3, respectively. When grown onto a semiconductor
like GaAs, the actual crystal symmetry should be strongly dis-
turbed by interfacial diffusion7which influences the electronic
and magnetic properties as well.8To avoid diffusion of Ga
and/or As atoms into the metal, a tunnel-barrier spin-injector
was used in this work, i.e., Fe3Si was grown on 3 nm MgO
on GaAs(001). For this case, the magnetic properties can be
well controlled at the interface, which is more stable even at
elevated temperatures than direct ferromagnet/semiconductor
heterostructures. In addition, increasing the interface resis-
tance by a MgO tunnel barrier helps to reduce the large
impedance mismatch9that prevents efficient spin injection
across the interface.
A lot of effort has been made over the last decades to
characterize Fe3Si compounds in terms of phase stability,
structure, electronic and magnetic properties.10,11 However,
its static and dynamic magnetization behavior is strongly
dominated by Fe due to its large magnetic moment with
respect to Si and three times larger amount. Therefore, a direct
measurement of the weak magnetization of Si—necessary for
the complete understanding of the magnetic properties of the
compound—has remained a challenge for years. In this paper,
we focus on the induced magnetism on Si: By measuring
the x-ray absorption near-edge structure (XANES) and x-ray
magnetic circular dichroism (XMCD) not only at the Fe L3,2
absorption edges, but also at the Si L3,2and Si K edges, a clear
evidence of a magnetic signal from Si was found. By com-
parison with spectra obtained from band structure calculations
using the Korringa-Kohn-Rostoker (KKR) method on the one
hand and the full potential linearized augmented planewave
(FLAPW) approach on the other hand, we reached quantitative
understanding of structural and magnetic properties.
The organization of the paper is as follows: In
Sec. II,M
¨
ossbauer spectroscopy is introduced to structurally
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C. ANTONIAK et al. PHYSICAL REVIEW B 85, 214432 (2012)
FIG. 1. (Color online) Schematic B2-like and D03structure of
Fe3Si.
characterize the Fe3Si system by extracting the long-range
ordering parameters S(D03) and S(B2), respectively, before
we turn to the XANES and XMCD measurements. In Sec. III
we present the details of band structure calculations using the
two methods mentioned above. The induced magnetism of Si
in Fe3Si is discussed in Sec. IV by comparison of experimental
and calculated spectra before conclusions are given in the last
section.
II. EXPERIMENTAL
A. Performance and sample characterization
To preserve the chemical ordering, a tunnel-barrier spin-
injector was used in this work. After growing 3 nm MgO on
cleaned GaAs(001) with a (4 ×6) surface reconstruction, two
samples of 8 nm Fe3Si were prepared by coevaporation of Fe
and Si in a UHV chamber with a base pressure of 108Pa.
They were grown at a substrate temperature of 250 C with
deposition rates of 0.064 ˚
A/sof57Fe and 0.036 ˚
A/sof
Si, respectively. One sample was subsequently annealed at
500 C before capping with 3 nm MgO to prevent oxidation of
the Fe3Si film. Conversion electron M¨
ossbauer spectroscopy
(CEMS) at perpendicular incidence of the γrays onto the film
surface was employed to investigate the degree of D03order
of the two samples.
The experimental CEMS data can be fitted by the procedure
described by Arita et al.,6yielding the long-range ordering
parameters S(D03) and S(B2). The samples prepared here
obviously display a high degree of chemical and structural
order as can be seen from the M¨
ossbauer results shown in
Fig. 2. For the nonannealed sample we found S(D03)=0.86
and S(B2) =0.53, respectively. Annealing of the sample leads
to an even higher degree of chemical order as indicated by the
ordering parameters S(D03)=0.88, S(B2) =0.55.
X-ray absorption measurements were performed at the PM-
3 bending magnet beamline at the HZB-BESSY II synchrotron
radiation facility in Berlin/Germany at T=14 K in magnetic
fields of μ0Hext 1 T in total electron yield (TEY) mode
by measuring the sample drain current. The SX700-type
plane grating monochromator (PGM) offers the possibility
to measure at variable degree of circular polarization σin the
energy range between 20 eV and about 2000 eV with an energy
resolution in the order of 103–104. Here, the photon energy
was varied between 90 eV E130 eV around the Si L3,2
absorption edges, 680 eV E790 eV around the Fe L3,2
edges, and 1820 eV E1960 eV around the Si K edge.
For all cases, the fixed focus constant was set to the standard
value cff =2.25. With the specific settings actually used in
our experiment, the absolute values of energy resolution were
FIG. 2. (Color online) Conversion electron M¨
ossbauer data of
nonannealed (upper panel) and annealed (lower panel) Fe3Si at room
temperature and fitted spectra with the extracted long-range ordering
parameters S(D03) and S(B2). Note that a perfect D03symmetry is
represented by S(D03)=1andS(B2)=2/3.
estimated to be 15 meV at 100 eV and 1.24 eV at 1850 eV,
respectively.
In order to optimize the experimental figure of merit—
containing σ2times the photon flux—different out-of-plane
(vertical) angles of the emitted x-rays with respect to the
storage ring plane had to be used for the various photon
energies. The different resulting values of σwere calculated
for the energy of Si L3,2,SiK,andFeL
3absorption edges using
the well-known equations for the emission characteristics of
the radiation.12 At the Fe L3edge the calculated values were
checked by measuring the asymmetry of an Fe bulk sample
for different monochromator settings, i.e., for x-rays emitted
under different vertical angles. For the actual settings used we
found σ=92.5% for measurements at the Fe L3,2absorption
edges, σ=76.5% at the Si K edge, and σ=88.0% at the Si
L3,2absorption edges.
After each scan, either the magnetic field or the photon
helicity was reversed. Field-dependent magnetization curves
were measured at the photon energy of 710 eV at the Fe L3
edge normalized to the pre-edge signal at 700 eV and at the
Si K edge at a photon energy of 1851 eV normalized to the
pre-edge signal at 1841 eV.
For XANES and XMCD data analysis, a linear background
was subtracted from the experimental data. In the case of Fe,
electron excitations into the final 3dstates were separated from
the ones into higher states or the continuum by a two steplike
function necessary for the determination of spin and orbital
magnetic moments by a standard sum rule-based analysis.1315
Since this procedure fails in the case of Si due to its broad p
band, spin and orbital magnetic moments of Si were estimated
by comparison to calculated spectra. Only the sign and the
order of magnitude could reliably be estimated by application
of the sum rule for XMCD at the K edge.16,17 The intra-atomic
dipole term μtthat is included in the experimentally obtained
effective spin magnetic moment μeff
s=μs+7μtis assumed
to be negligible in the cubic Fe3Si system investigated in this
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INDUCED MAGNETISM ON SILICON IN Fe3Si ... PHYSICAL REVIEW B 85, 214432 (2012)
FIG. 3. (Color online) X-ray absorption near-edge structure and circular dichroism at Si L3,2,FeL
3,2, and Si K absorption edges of annealed
Fe3Si measured at T=14 K under normal x-ray incidence. The external magnetic field was applied parallel to the x-ray beam.
work. However, since μtis probably not vanishing completely,
the spin magnetic moments derived from experimental data are
denoted effective spin magnetic moment.
B. Results
Experimental x-ray absorption spectra of Fe and Si in
Fe3Si are shown in Fig. 3. In the case of Fe, the spectra are
already corrected for self-absorption and saturation effects18
assuming an electron escape depth of λe=2nm.Similartothe
CEMS data, no significant difference between the annealed and
nonannealed sample is observed. Thus, we focus here on the
annealed sample which exhibits a slightly improved chemical
ordering. At the Fe L3,2absorption edges, the spectral shape
of XANES and its associated XMCD indicate an Fe-d/Si-sp
hybridization of Fe on lattice sites A (cf. Fig. 6) as discussed
in the literature on the basis of calculated spin and angular
momentum resolved density of states.8
In the case of Si, the L3and L2edges are not energetically
well separated. There are six spectral features visible in the
XANES shown in Fig. 3. Four of them, aL,bL,cL, and dL,arise
from Si in Fe3Si as will be revealed later by comparison with
calculated spectra. (The index Lis related to the absorption
edge.) The small pre-edge peak at 95 eV can be assigned
to Mg of the MgO cap layer. An additional shoulder in the
experimental XANES above bL(around 107 eV) may be an
indication for a Si-rich interface to the MgO cap layer since Si
tends to segregate at the surface of Fe-Si alloys. The XMCD
signal at the Si L3,2absorption edges shows a maximum
asymmetry of only about 0.8% and is enlarged by a factor of
10 in Fig. 3for clarity. In order to ensure the reliability of the
XMCD signal, not only pairs of spectra with reversed sample
magnetization but also with different polarization of x-rays
were analyzed. Interestingly, a meaningful XMCD can only
be found around 104 eV, the position of the peak bL. Compared
to the Fe signal at the L3absorption edge, the reversed sign
of the XMCD at the Si sites already suggests an antiparallel
alignment of Fe and Si spins.
The XMCD at the K edge is sensitive only to the orbital
magnetic contribution which is known to be very small.
Nevertheless, in our experiment a clear magnetic signal was
measured with a maximum XMCD asymmetry of about 0.3%.
Although this value of asymmetry is extremely small, we were
able to directly measure the field-dependent magnetization by
detecting the absorption signal at the energy position of the
maximum XMCD signal, i.e., 1851 eV, while sweeping the
external magnetic field.19 The signal was normalized to the pre-
edge signal at 1841 eV. Equivalent measurements were per-
formed at the Fe L3edge at photon energies of 710 and 700 eV,
respectively. The results are shown in Fig. 4. Although it is
almost at the detection limit, it can clearly be seen that the
field dependence of the Si XMCD follows the one measured
at the Fe sites. A magnetic hysteresis could not be measured
since the superconducting magnet used in this experiment is
not well suited to resolve small coercive fields.
III. AB INITIO CALCULATIONS
A. Computational details
In order to provide insight for the explanation of experi-
mental data, the XANES and XMCD spectra of bulk Fe3Si
were calculated using density functional approaches. The
optical absorption tensor was calculated by means of the linear
response formula proposed by Wang and Callaway.20 While
the calculated XANES and XMCD spectra at the Fe L3,2
absorption edges match well the measured data,8the reliability
of calculations at the Si edges is unclear due to the delocalized
nature of its 3pstates. In particular, the influence of muffin
tin (MT) approximation on the quality of spectra is not known
at the present. Here we use two different methods, namely
the spin polarized relativistic KKR (SPR-KKR) technique21
FIG. 4. (Color online) Element-specific field dependent magne-
tization measured by means of XMCD at the Fe L3edge (710 eV)
and Si K edge (1851 eV), respectively.
214432-3
C. ANTONIAK et al. PHYSICAL REVIEW B 85, 214432 (2012)
and the full-potential linear augmented plane wave (FLAPW)
method, for the determination of magnetic properties of
Fe3Si. Using these two methods also gives the possibility
to ensure that the results do not significantly depend on the
approximations made in the electronic structure calculations,
namely the atomic sphere approximation (ASA) or non-fully-
relativistic treatment.
Within the SPR-KKR method the electronic structure is
represented in terms of Green’s functions evaluated by means
of the multiple scattering theory. The ASA is adopted and the
interstitial region is eliminated by using overlapping spheres.
In contrast, the FLAPW is viewed as the most precise approach
with no shape approximation in the entire space for wave
function, charge density, and potential.22,23 The core electrons
were described fully-relativistic, while the valence electrons
are treated in a scalar-relativistic manner, and the spin-orbit
coupling term for the valence states was invoked second
variationally.24 In both SPR-KKR and FLAPW calculations
we used the generalized gradient approximation (GGA) in
the parametrization of Perdew, Burke, and Ernzerhof25,26
to describe the exchange correlation interaction. The lattice
constant of the D03unit cell was chosen based on experi-
mental data, a=5.65 ˚
A. Integrations over the Brillouin zone
(BZ) were evaluated over a 20 ×20 ×20 k-point grid. The
convergence against energy cutoffs and the maximum angular
momentum lmax were carefully monitored. In the SPR-KKR
calculations lmax =3 was used for the calculation of the spec-
tra, whereas lmax =8 was used in the FLAPW calculations.
B. Results
The magnetic moments obtained from the ab initio calcula-
tions are summarized in Table I. Obviously the spin moments
μsat the Fe sites are overestimated by both methods. It
has been noted in many theoretical studies2729 that for the
transition metals, in particular the 3dmetals, the GGA always
produce larger lattice parameters and smaller bulk moduli
compared with the local spin density approximation (LSDA)
results. It was also pointed out by Singh and Ashkenazi30 that
in GGA there is an increased tendency towards magnetism in
general, and particularly towards larger magnetic energies for
magnetic materials, which in other cases may just result in a
small quantitative error. Furthermore, discrepancies between
the magnetic moments obtained from FLAPW and SPR-KKR
are mainly dedicated to the choice of the Wigner Seitz sphere
used for the projection to the lattice.
XANES and XMCD spectra at the Si L3,2and K edges as
well as the Fe L3,2edges calculated by means of SPR-KKR and
FLAPW method, respectively, are shown in Fig. 5. The nicely
reproduced main features of the experimental XANES and
XMCD indicate the validity of our computational approaches
TABLE I. Site-specific spin and orbital magnetic moments of Fe
and Si in Fe3Si calculated by SPR-KKR and FLAPW.
Fe A sites Fe B sites Si C sites
method KKR FLAPW KKR FLAPW KKR FLAPW
μs[μB] 1.39 1.33 2.67 2.55 0.121 0.062
μl[μB] 0.030 0.020 0.054 0.051 0.0019 0.0004
and parametrizations. The D03structure assumed in our cal-
culations should be rather dominant in the measured samples.
As evidence for the insignificance of ASA, the spectroscopic
profiles obtained from the SPR-KKR and FLAPW methods
closely follow each other in the entire energy range. This can
be understood since the x-ray spectra depend on the overlap
between valence and atomic-like core states. The two peaks at
95 and 107 eV arise from the MgO buffer layer and possible
deviations from the Fe3Si composition at the film surface and
hence are missing in the theoretical data. As in the experiment,
the Si L3,2XANES spectrum exhibit an onset peak at the
photon energy of about 97 eV followed by three pronounced
peaks at 104, 110, and 121 eV denoted as aL,bL,cL, and dLas
in Fig. 3. The XMCD spectrum only shows an intense positive
peak at bLin good accordance with the experimental data. The
amplitudes of the XMCD at the Si absorption edges appears
to be very weak at both the L3,2and K edges (less than 1% of
the XANES). This indicates that the induced spin and orbital
magnetic moments on Si are small (cf. Table I).
Since both XANES and XMCD signals are related to the
dipole transitions from the inner-shell states to the unoccupied
valence states,31,32 it is useful to analyze the density of states
(DOS) above the Fermi level EF. Here, the partial DOS curves
of Fe3Si obtained from the FLAPW are presented in Fig. 6.
As discussed in the literature,8,33 the two types of Fe atoms
have different electronic properties, and the Fe-A atoms have
a strong effect on the DOS profiles of Si atoms. Interestingly,
there are two pronounced peaks in the Si s-DOS curves at about
5 eV above EF, slightly split in two spin channels. They reflect
the hybridization between the t2gorbitals of Fe-A atoms and
the Si sstates. Via intra-atomic hybridization, this feature can
also be found in the dDOS and result in the peaks in the Si L3,2
XMCD curves at 104 eV. (For an easier assignment, this region
is denoted as bin the DOS since it is related to the spectral
features of XANES and XMCD denoted bL,bKin Fig. 5.)
The K edge involves electronic excitations from the 1score
states towards the pconduction states. These states mediate
the magnetization in Fe3Si and are the main ingredients in the
valence and conduction bands of this alloy. Figure 6shows that
the contribution to the positive onset at the Si K edge XMCD is
ascribed to the pstate above EFin the majority spin channel.
The pronounced resonant peaks for Si, Fe-A, and Fe-B atoms
in 1–2 eV (denoted a) are responsible for the large negative
peak of the XMCD spectra at the Si K edge (denoted aK).
IV. DISCUSSION
The results of XANES and XMCD spectra plotted in
Fig. 7display that the density functional calculations using
the perfect D03structure reproduce very well the experimental
data, in particular the XMCD. It is well known3335 that XMCD
spectra of dia- or paramagnetic elements with induced ferro-
magnetism in an alloy can be utilized to characterize atomic
arrangements since their spectroscopic features are highly
sensitive to the change in interactions with ferromagnetic
species. It is reasonable to conclude that the Fe3Si films used in
the experiment consist mainly of D03symmetry. In addition,
the good agreement between theory and experiment in the
XMCD features indicates the possibility of determining tiny
magnetic moments in complex compounds.
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FIG. 5. (Color online) Calculated XANES and XMCD spectra at the Si L3,2,Fe
3,2and Si K edges by means of SPR-KKR (upper panel)
and FLAPW (lower panel), respectively.
Taking a closer look at the XANES and XMCD signals, the
agreement of the Si XANES is less satisfactory compared to
the XMCD. Since we only considered the initial state effect
in the optical transition, we do not attempt to go much beyond
the comparison on peak positions. Furthermore, the FLAPW
method produced more fine structures in the higher energy
range compared to the SPR-KKR results. This discrepancy
can be assigned to the fact that the SPR-KKR method uses
Wigner-Seitz partition for the whole space, thus eliminating
the interstitial region from the formalism.27,36
The effective spin and orbital magnetic moments at the Fe
sites were determined by a sum-rule based analysis of the
FIG. 6. (Color online) The spin and orbital resolved density of
states of Fe3Si. Positive and negative sides are for the spin-up and
spin-down parts, respectively. The amplitude for Si s-, p-, and d-states
are rescaled by a factor of 10.
XMCD and are listed in Table II. Note that it is impossible
to distinguish between the moments of Fe on lattice sites A
and B through analyzing the absorption spectra at the L3,2
edges since the differences in energy position and spectral
shape are marginal. The averaged Fe moment is significantly
smaller than in bulk α-Fe and in good agreement to values
reported earlier.8For a better comparison with our calculations,
the magnetic moments obtained from theory were also site
averaged and listed in Table II.
The intrinsic and instrumental broadening of the experi-
mental spectra yield a strong overlap of the L3and L2edges
of Si. Also the FLAPW calculation shows that the energy
separation between 2p1/2and 2p3/2states is only 0.6 eV. Thus,
a straight-forward determination of spin and orbital magnetic
moments by integral methods is impossible.37 Nevertheless,
the good agreement between theory and experiment allows
us to access this information from theory with confidence. To
better appreciate the quality of our results, the experimental
Si XMCD signal at both L3,2and K edges are rescaled and
compared in Fig. 7. The magnetic moments in our sample can
be estimated by comparing the scaling factors of XANES and
XMCD. This procedure is commonly used for experimental
data for which the standard sum-rule based analysis fails.
At the Si K edge, the experimental XANES was scaled
by a constant factor to fit the intensity of the corresponding
spectrum calculated by the SPR-KKR method in the pre-
and post-edge region. Note that the spectra shown in Fig. 7
correspond to the absorption cross-section in units of Mb
(1 b =1028 m2) and no longer in arbitrary units. However,
scaling the XMCD with the same factor is not sufficient
to achieve good agreement between experimentally and
theoretically obtained dichroism. At the Si L3,2edges, the
experimental XMCD spectrum had to be enlarged by a factor
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C. ANTONIAK et al. PHYSICAL REVIEW B 85, 214432 (2012)
FIG. 7. (Color online) Experimentally obtained and calculated XANES and XMCD at the Si L3,2absorption edges and the Si K edge,
respectively. The experimental data were normalized to fit the calculated XANES intensity in the pre- and post-edge region. To fit the intensity
of the calculated dichroism, experimental XMCD data have been scaled by an additional factor that is used for an estimation of the magnetic
moments of Si in the Fe3Si sample.
of about 6 in order to coincide with the calculated one. Since
the major contribution to the XMCD asymmetry arises from
the spin magnetic moment in this case, it can be concluded
that the spin magnetic moment at the Si atoms in our sample
is roughly eight times smaller than the theoretically expected
value, i.e., μeff
s=(0.011 ±0.005) μB. At the Si K edge,
the experimental XMCD signal is sensitive only to the orbital
magnetic moment and has to be scaled down by a factor of
0.4 to be in good agreement with the calculated spectrum.
Consequently, the orbital magnetic moment in our sample is
about twice as large as the theoretically expected value, i.e.,
μl=(0.003 ±0.003) μB. The large error bar arises not only
from the low signal-to-noise ratio of the experimental data, but
also from the difference in calculated magnetic moments by
TABLE II. Site-averaged (effective) spin and orbital magnetic
moments of Fe and Si in Fe3Si determined by XMCD and band
structure calculations by two different approaches. Note that the
effective spin magnetic moment μeff
sextracted from experimental
data is denoted μsfor an easier reading of the table.
Fe μs[μB]μl[μB]
experiment 1.76 ±0.10 0.073 ±0.01
KKR 1.82 0.038
FLAPW 1.73 0.030
Si μs[μB]μl[μB]
experiment 0.011 ±0.005 0.003 ±0.003
KKR 0.121 0.0019
FLAPW 0.062 0.0004
the two different methods, although the amplitude of XMCD
is roughly the same.
For the sake of completeness, the magneto-optical sum rule
has been applied to the data obtained at the Si K edges as
presented below. However, since the energy cutoff for the
integral and hence the number of pholes are not well defined
for the itinerant pstates, one should keep in mind that the
validity of this analysis is questionable in our case. Following
the magneto-optical sum rule for the K edge as derived by
Igarashi and Hirai,16,17 the orbital magnetic moment can be
calculated according to
μp
l=2
3np
h
Kμc(E)dE
Kμ0(E)dE,(3)
where μc=μ+μis the XMCD signal and μ0=μ++
μis the so-called white line intensity of the XANES.
The latter is shown in Fig. 8after subtraction of a steplike
background together with the integrals of the white line and
XMCD respectively are shown in Fig. 8for the experimental
data and the spectra calculated by the SPR-KKR method.
Using a rough estimation for the number of unoccupied p
states, np
h=3, we obtain for the calculated spectra an orbital
magnetic moment of about μl≈−0.0015 μBin agreement
with the value obtained directly by this calculation. However,
it can be seen in Fig. 8that the value depends on the cutoff
energy for the integrals. For the case of the experimental
data, the value of μldepends even stronger on the cutoff
energy. The strong oscillations of the XMCD signal and,
consequently, in the integral of the XMCD may be related to
the magnetic counterpart of the extended x-ray absorption fine
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INDUCED MAGNETISM ON SILICON IN Fe3Si ... PHYSICAL REVIEW B 85, 214432 (2012)
FIG. 8. (Color online) XANES after subtraction of steplike back-
ground for experimental data (gray line) and SPR-KKR calculation
(red line), respectively, and their integrals (top). Integral of XMCD
signal of experimental data and SPR-KKR calculation (bottom).
structure (MEXAFS). While the extended x-ray absorption
fine structure (EXAFS) is an interference effect between the
outgoing photoelectron as a matter wave and backscattered
waves from neighboring atoms, MEXAFS includes a spin
dependence of the scattering events.37 In our case, the Si
atoms are surrounded by Fe atoms with a quite large magnetic
moment. Thus, the MEXAFS is expected to give a quite large
contribution to our magnetic signal with respect to the small
XMCD of Si with its tiny magnetic moment, and the integral
value of the Si XMCD can only be estimated. Here, we
choose the value by averaging the signal above 1862 eV as
depicted by a horizontal line in Fig. 8. With this method the
orbital magnetic moment amounts to μl≈−0.003μBwhich
is in agreement with the value presented above obtained by
scaling the experimental data to fit the calculated spectra.
Although the absolute value from the sum-rule-based analysis
is ambiguous, the negative sign of μlcan be confirmed. In
addition, it is obvious that the integral of the XMCD (Fig. 8),
and consequently the orbital magnetic moment, is larger in the
experiment than in the SPR-KKR calculation.
In the following, we turn to the discussion of some reasons
for the different spin and orbital magnetic moments in theory
and experiment. The spin magnetic moments at the Si sites
may be reduced by a nonperfect surface of the Fe3Si film: As
already mentioned above, the shoulder in the XANES above
the Si L3,2absorption edge may indicate a segregation of Si
at the Fe3Si surface which likely occurs in Fe-Si alloys and
alters the composition ratio and atomic structure. This is
reported in the literature,38 where the cubic FeSi (c-FeSi)
was found to influence the spectral shape of photoemission
spectra39 of Fe3Si a few eV above the main absorption
edge similar to our experimental findings. In addition, the
measurements presented in this work are surface sensitive.
Especially at low photon energies, the x-ray attenuation length
in the MgO cap layer and the Fe3Si is reduced to about 10 nm.40
Therefore, even a thin Si-enriched layer at the surface of Fe3Si
may strongly affect the XANES. However, the contribution of
c-FeSi or other Fe-Si compounds to the XMCD is negligible
since they do not exhibit any ferromagnetic order. Thus, the Si
atoms near the surface will not measurably contribute to the
XMCD asymmetry if the composition significantly deviates
in this region. The XMCD signal compared to the XANES
intensity would be reduced as a consequence. Note that a
difference in the intensities of the double-peak structure for
annealed and nonannealed samples could not be obtained. The
annealing appears not to change the composition along the
depth if we follow the arguments above.
At higher photon energies, e.g., at the Si K edge, the
measurement is less surface sensitive and the contribution of
the bulk of Fe3Si to the total signal is larger. However, the
TEY detection mode of XANES and XMCD still leads to
an emphasis of the signal arising from surface atoms due to
self-absorption effects. Therefore, it is also reasonable to scale
experimental XANES and XMCD with different factors for
comparison to theory.
From computational aspects, there is also a distinct uncer-
tainty in the amplitude of XANES because of the exclusion
of final state effects as mentioned before. Better quality of
comparison for the XMCD spectra is due to cancellation of
this effect yielding different scaling factors for XANES and
XMCD to match experimental data. In addition, it seems to
be a general trend in such alloys, that theory underestimates
the orbital contributions to the total magnetic moments and
often overestimates spin moments whereby the overestimation
of the spin moments is produced by the GGA and the small
orbital moments are related to correlation effects. All these
effects discussed here are reflected in the large error bars of
the magnetic moments estimated from the experimental data.
V. CONCLUSION
In summary, we were able to detect the XMCD signal
at both the Si L3,2and Si K absorption edge respectively
for highly ordered Fe3Si films on a MgO tunnel barrier.
Orbital and spin magnetic moments are aligned antiparallel
to the magnetic moments of Fe and could be quantified by
comparison to calculated spectra. While the spin magnetic
moment of Si μeff
s=(0.011 ±0.005) μBis estimated to be
smaller than predicted by theory, the orbital magnetic moment
μl=(0.003 ±0.003) μBis about twice as large as the
theoretically expected value. Both reduced spin and enhanced
orbital magnetic moment may be explained by the surface
sensitivity of the TEY mode employed in this work, a possible
Si-enrichment in the surface layer of Fe3Si, and uncertainties
in the calculated XANES amplitudes.
In addition, the field dependence of the XMCD at the Si
K edge as a measure of the change of orbital magnetization
with the applied external magnetic field could be obtained. Our
findings demonstrate the possibility to detect extremely weak
induced magnetic moments and use them for the determination
214432-7
C. ANTONIAK et al. PHYSICAL REVIEW B 85, 214432 (2012)
of local atomic structures through synergistic theoretical and
experimental work.
ACKNOWLEDGMENTS
We would like to thank P. Wulkow (U. Duisburg-Essen)
for help in the measurements and the HZB BESSY II staff,
especially H. Pfau and R. Schulz for their kind support. Funded
by BMBF (05 ES3XBA/5) and DFG (SFB 491). Work in the
UCI was supported by US-DOE grant DE-FG02-05ER46237.
Calculations were performed on parallel computers at NERSC.
J.L. thanks the Alexander von Humboldt Foundation for
support through the Feodor Lynen program.
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214432-8
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