Electronic properties of Co 2 FeSi investigated by x-ray magnetic linear dichroism
Mirko Emmel, Alexey Alfonsov, Dominik Legut, Andreas Kehlberger, Enrique Vilanova, Ingo P. Krug, Daniel M. Gottlob, Marilena Belesi, Bernd Büchner, Mathias Kläui, Peter M. Oppeneer, Sabine Wurmehl, Hans-Joachim Elmers, Gerhard Jakob
EElectronic properties of Co FeSi investigated by x-ray magnetic linear dichroism
M. Emmel, A. Alfonsov, D. Legut, A. Kehlberger, E. Vilanova, I. P. Krug, D. M. Gottlob,
4, 5
M.Belesi, B. B¨uchner,
2, 6
M. Kl¨aui, P. M. Oppeneer, S. Wurmehl,
2, 6
H. J. Elmers, and G. Jakob Institut f¨ur Physik, Johannes Gutenberg-Universit¨at Mainz, Staudinger Weg 7, D-55128 Mainz, Germany IFW Dresden, Institute for Solid State Research, D-01069 Dresden, Germany VSB - Technical University of Ostrava, 17. Listopadu 15, CZ-70833 Ostrava, Czech Republic Peter Gr¨unberg Institut PGI-6, Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany Fakult¨at f¨ur Physik and Center for Nanointegration Duisburg-Essen (CeNIDE), D-47048 Duisburg, Germany Institut f¨ur Physik, TU Dresden, D-01062 Dresden, Germany Department of Physics and Astronomy, Uppsala University, P. O. Box 516, S-751 20 Uppsala, Sweden (Dated: July 18, 2018)We present experimental XMLD spectra measured on epitaxial (001)-oriented thin Co FeSi films,which are rich in features and depend sensitively on the degree of atomic order and interdiffusion fromcapping layers. Al- and Cr-capped films with different degrees of atomic order were prepared by DCmagnetron sputtering by varying the deposition temperatures. The local structural properties of thefilm samples were additionally investigated by nuclear magnetic resonance (NMR) measurements.The XMLD spectra of the different samples show clear and uniform trends at the L , edges. TheAl-capped samples show similar behavior as previous measured XMLD spectra of Co FeSi . Al . .Thus, we assume that during deposition Al atoms are being implanted into the subsurface of Co FeSi.Such an interdiffusion is not observed for the corresponding Cr-capped films, which makes Cr thematerial of choice for capping Co FeSi films. We report stronger XMLD intensities at the L , Coand Fe egdes for films with a higher saturation magnetization. Additionally, we compare the spectrawith ab initio predictions and obtain a reasonably good agreement. Furthermore, we were able todetect an XMCD signal at the Si L -edge, indicating the presence of a magnetic moment at the Siatoms. PACS numbers: 75.70.-i, 78.70.Dm, 71.20.Lp, 75.50.-y,
I. INTRODUCTION
Materials with a high spin polarization at the Fermiedge are promising for spintronic devices. Heuslercompounds, which have been predicted to be half-metallic ferromagnets, are currently considered as po-tentially interesting materials for this purpose. Heuslercompounds have a distinctive stoichiometry and crystal-lize in the L2 -structure X YZ, where X and Y are tran-sition metals and Z is a main group element. Amongthe Heusler compounds, Co FeSi has shown the highestmagnetization of 6 µ B per formula unit, in agreementwith the Slater-Pauling rule m = N v −
24, where N v isthe number of valence electrons. Moreover, Co FeSi isthe Heusler compound with the highest Curie tempera-ture. Therefore, Co FeSi might be an ideal material forspintronics applications, provided that the prediction ofhalf-metallic ferromagnetic properties is correct, as wasindeed recently suggested by Ref. 5.However, Co FeSi is predicted to be a half-metalliccompound only if electron correlations are considered inthe form of the on-site repulsion energy U . Neglecting theelectron correlations, Co FeSi is predicted to be a con-ventional ferromagnet. Hence, a reliable probe of half-metallic ferromagnetism in Co FeSi is still needed. Thecalculations reported in Ref. 6 show a significant changein the x-ray magnetic linear dichroism (XMLD) spectra ifelectron correlation effects are considered. Thus, XMLDmay serve as a crucial test for band structure calcula-tion schemes as the XMLD, in a single-particle picture, is roughly speaking proportional to the first derivative ofthe minority density-of-states function (PDOS) in con-trast to the x-ray magnetic circular dichroism being di-rectly proportional to the DOS. Meinert et al. alreadyinvestigated XMLD for Co FeSi and compared it to a va-riety of density functional theory-based calculations. Al-though the comparison, shown in Ref. 8, rules out someband structure models, qualitative differences betweenexperiment and theoretical predictions still remained.In this article, we present XMLD spectra measured ona series of Co FeSi film samples with systematically var-ied atomic order. The increase of atomic order results inan increase of magnetization, which suggests a concomi-tant transition from metallic to half-metallic ferromag-netic behavior. Thus, according to theoretical calcula-tions, a considerable altering of the spectra is expected.To address the relation between the measured XMLDspectra and the underlying electronic structure, we em-ployed various exchange-correlation functionals, used afew different values of the Hubbard U ( U eff ) parameterand performed a number of calculations using the so-called non-selfconsistent fixed spin moment technique.Although the overall spectrum is well given, the finestructure appearing predominantly at the L edge is notsufficiently captured. a r X i v : . [ c ond - m a t . m t r l - s c i ] J a n II. EXPERIMENTAL
Epitaxial (001)-oriented Co FeSi films were grown byDC magnetron sputtering onto MgO(001) substrates ina UHV system with a base pressure of 1 · − mbar. Thedistance between the film and the stoichiometric targetof Co FeSi was 10 cm, while the Ar working pressure was7.77 · − mbar. Different degrees of local atomic order inthe films were achieved by setting different substrate tem-peratures at each film deposition in the range of 470 ◦ C to730 ◦ C. The substrate temperature was determined with apyrometer set to an emissivity of 0.31. To prevent oxida-tion the films were capped immediately after depositionwith a 3 nm thick capping layer grown at room temper-ature. We used both Al and Cr as a capping layer.The saturation magnetization of each film was deter-mined with a superconducting quantum interference de-vice (SQUID) magnetometer (Quantum Design, MPMS-XL-5) at 20 K and 300 K with magnetic fields up to 3 T.Thickness determination and structural characterizationwere performed by x-ray reflection/diffraction with aPhillips X’pert diffractometer.The x-ray absorption spectra (XAS) were recordedat the synchrotron light source BESSY II (beamlineUE56/1-SGM). The samples were mounted perpendic-ular to the beam and were magnetically saturated byan external field parallel to the film surface. The de-gree of linear polarization of the synchrotron radiationwas close to 100 %. All measurements were performed atroom temperature with the total-electron-yield (TEY)technique where the specimen current is measured. Thephoton intensity was measured by a gold mesh. The po-larization of the photon beam was switched between lin-ear vertical and linear horizontal while the magnetic fieldwas kept constant. The linear dichroism is calculated asthe difference between spectra measured with horizontaland vertical polarization.The NMR experiments were performed in an auto-mated, coherent, phase sensitive and frequency tunedspin-echo spectrometer provided by NMR Service Erfurt,Germany. The NMR spectra were recorded at a temper-ature of 5 K and in the frequency range of 120-200 MHzwith steps of 0.5 MHz. No external magnetic field was ap-plied during the measurements. All NMR spectra werecorrected for the magnetic enhancement factor as wellas the ω dependence, resulting in relative spin-echo in-tensities, which are proportional to the number of nucleiwith a given NMR resonance frequency. The procedureof the enhancement correction is described in Refs. 9 and10. A. Ab initio calculations
The electronic structure of the Co FeSi was calculatedwith the WIEN2k code in the density-functional the-ory (DFT) framework, employing the local spin densityapproximation and the general gradient appoximation (GGA), the latter as parameterized by Perdew-Burke-Ernzerhof for the exchange-correlation term. Elec-tronic correlations were included by using the so-calledHubbard U approach (LSDA+ U , GGA+ U ) in the self-interaction corrected formulation. Calculations on thebasis of the conventional usual local spin density ap-proximation or the GGA alone, i.e. without additionalHubbard U , do not give a correct magnetic moment forCo FeSi as was already pointed out before by several au-thors (see Refs. 6 and 8 and references therein). All calcu-lations presented here were done for the lattice parameter a = 5 .
64 ˚A.The core electrons were treated fully relativistically(Dirac equations) and for the semicore and valence statesthe spin-orbit interaction (SOI) was included through avariational scheme. The convergence of the electronicstructure calculations was ensured by the following pa-rameters: the convergence criterion of the total energywas better than 10 − Ry/atom; the energy cutoff givenas the product of the muffin-tin radius and the maximumreciprocal space vector R MT K max was 8.5, the largest re-ciprocal vector in the charge Fourier expansion, G max ,was set to 12 Ry / , the maximum angular momentumvalue of partial waves inside the muffin-tin spheres l max was 10, and a grid of 20 × × k -points was applied tosample the 1 st Brillouin zone. The same k -point meshwas used to determine dipolar squared momentum ma-trix elements, which occur in the Kubo formula for thepermittivity tensor. To account for lifetime effects abroadening with a Lorentzian with a width of 0.3 eVwas applied for the x-ray spectra from core (localized)to unoccupied states (delocalized states). The core levelexchange splitting was also included. The Kramers-Kronig transformations were performed and the complexvalues of permittivity tensor elements (cid:15) ij were obtained.Subsequently, permittivity elements served as input forour in-house optical code solving Fresnel equations us-ing 4-vector Yeh’s formalism as extended for magneticmultilayers. We hence obtain the reflectivity and trans-mittivity matrices ( R pp , R ss , R ps , R sp , T pp , T ss , T ps , T sp )for each magnetization direction M . The absorbance A b is defined as A b = − ln( T ) = − ln(1 − A − S − R ) , (1)where A is absorptance, S denotes scatter and R reflec-tion of the material. The thickness dependent reflectivityand transmittivity matrices then lead to the attenuationcoefficient µ , which for both polarizations E (cid:107) M and E ⊥ M is calculated according to the Beer-Lambert law I ( d ) = I e − µ p ( ω ) d , (2)where the incident intensity I = 1 and the attenuatedintensity for the first (second) polarization P = E ( E )is I pp ( ss ) ( d ) = [ T pp ( ss ) − R pp ( ss ) ] /d , where d is the samplethickness. Note, that the absorption coefficient µ differsfrom absorptance A defined as A = I − II , i.e. incom-ing and absorbed intensity. Finally, the linear dichroismis computed here as XMLD = ( µ ( I pp ) − µ ( I ss )) /norm .Note, that this holds only for normal incidence. The nor-malization factor used was norm = max ( µ E + µ E ). III. STRUCTURAL PROPERTIES
The long range order of the atomic structure of thefilms was determined with 4-circle x-ray diffraction. Theobtained lattice constant of the films is 5.64 ± FeSi thinfilms as well as bulk material. The rocking curves re-veal widths ∆ ω between 0.29 ◦ and 0.73 ◦ . To determinethe L2 structure within the sample series, it is not suffi-cient to compare the maximum intensities of the (202) -and (111) - film reflections. Rather the ratio of the inte-grated peak areas of ω - scans A /A provides a betterestimation of the real intensity ratios. We measured therocking curves of the (202) - and (111) - reflections, whichwere fitted with Gaussian functions to determine the en-closed areas of the reflections. We compare our valueswith results calculated for powder diffraction correctedwith the geometry factor according to Bragg Brenatoand multiplicity. The ratio of the individual reflections isgiven by the program PowderCell as I /I = 12 . A /A are due to Fe atoms located onSi sites and vice versa. Structural data and magnetiza-tion values measured by a SQUID magnetometer, as wellas NMR results, are summarized in Table I. We see anincrease of the saturation magnetization with higher sub-strate temperatures, except for CFS(Cr2), which exhibitsthe lowest value. In the Al-capped series we find the samefor CFS(Al3). In general a systematic dependency for allvalues on the substrate temperature is observed. IV. RESULTSA. Experimental results
1. XMLD spectra
The absorption intensity is measured for the electricfield vector of the linearly polarized beam parallel I (cid:107) andperpendicular I ⊥ to the magnetization vector. The differ-ences I (cid:107) − I ⊥ result in the corresponding XMLD spectra.The XMLD spectra were measured for each sample atthe Co and Fe L , edges with the magnetization vec-tor along the in-plane directions [100] and [110]. EachXMLD spectrum was normalized by the maximum valueof the respective L edge I max of the averaged XAS spec-trum. Fig. 1 shows exemplarily two XAS spectra mea-sured in [100] orientation at the Fe (a) and Co (b) edgewith the corresponding XMLD spectra. At the Co [100]XAS spectra the maximum at the L edge is followed bya shoulder with a distance of 4 eV. This is typical for theHeusler structure and was already observed for different Heusler compounds (Refs. 18–20). An analogous shoul-der is visible for the Co edge at the energy 798.1 eV abovethe L peak, which is smaller due to lifetime broadeningeffects. The complete set of XMLD spectra for each film ispresented in Fig. 2 (for the case of (cid:126)M (cid:107) [100]) and Fig. 3(for the case of (cid:126)M (cid:107) [110]). For direct comparison, theXMLD spectra for Cr- and Al-capped films are displayedon the left- and right-hand side, respectively. The spec-tra measured at the Co L -edge are presented in the toppanels and those measured at Fe L -edge in the bottompanels.The structure of the XMLD spectra clearly exhibitsmore features at the L , edge than the XMCD spec-tra of Co FeSi, which was already predicted by Ref. 6and reported in Ref. 8. The spectra measured forthe Co FeSi(Cr4) film with the deposition temperatureof 730 ◦ C (Fig. 1 and Fig. 2 a,e) agree in all details ofthe spectra with the spectra reported in Ref. 8. Thelargest XMLD signal is observed for the Co FeSi(Cr)film with the highest magnetization (5.8 µ B /f.u.). Max-imum XMLD values of 4.1 % at the Fe L edge for (cid:126)M (cid:107) [100] (Fig. 2 e) and 3.4 % at the Co L edge for (cid:126)M (cid:107) [110](Fig. 3 e) are obtained.
2. Influence of the capping layer
Due to the surface sensitivity of the TEY method dif-ferent interface properties for different capping materialscan be detected. The information depth of TEY is givenby the mean free path of the emitted secondary electronsand typically amounts to 2.5 nm. We compare two seriesof samples prepared with identical conditions except forthe different capping materials Al and Cr. Both cappingmaterials do not contribute to the absorption spectra inthe investigated energy range. Thus, we anticipated nochange in the measured XMLD spectra of the films withdifferent capping layers. Contrarily, the two sets of spec-tra show pronounced differences, as discussed in the fol-lowing.The XMLD spectra of the Co FeSi(Cr) films (see leftcolumn of Fig. 2 and Fig. 3) show similar features withinthe film series at a given field and beam geometry. Incontrast, the XMLD spectra of Al-capped films (see rightcolumn of Fig. 2 and Fig. 3) show pronounced variationsfor different samples.The most striking differences between Cr- and Al-capped films are observed for (cid:126)M (cid:107) [100] at the Co edge(Fig. 2 a and Fig. 2 m). For the Co FeSi(Cr) series at the L edge, we note a sharp minimum (A) followed by asharp maximum (B). For the Co FeSi(Al) samples, in-stead, the XMLD spectra starts with a maximum (A’)followed by the minimum A (Fig. 2 m,n). Samples withlower magnetization (Fig. 2 o,p) show a minor (A) but donot show a positive maximum (B).We assume that the Al atoms interdiffuse into the film.
Table I. Deposition temperature, thickness of capping layer, saturation magnetization at 20 K and width of the rocking curveof the 400-film reflex, area ratio A / A , and NMR parameters for the epitaxial Co FeSi/MgO films.Film T
Sub d capping m sat ∆ ω I /I NMR freq. NMR linewidth NMR spacing Fe-Si off-( ◦ C) (nm) ( µ B /f.u.) ( ◦ ) (MHz) (MHz) (MHz) stoichiometry (%)CFS(Cr1) 470 3.0 Cr 4.89 0.87 21.7 144.85 ± .
03 8.59 ± .
07 33 ± ± . ± .
03 8.03 ± .
07 33 ± ± . ± .
03 8.03 ± .
07 31 ± ± . ± .
03 7.90 ± .
07 27 ± ± . ± .
03 8.39 ± .
07 33 ± ± . ± .
03 7.68 ± .
07 30 ± ± . ± .
05 8.75 ± .
14 31 ± ± . ± .
00 6.57 ± .
50 28 ± ± . a) b)
705 710 715 720 725-0.020.000.020.04 ( I || - I ⊥ ) / I max X M L D Photon energy (eV) I || I ⊥ I || , I ⊥ ( a r b . un it s )
775 780 785 790 795 800-0.010-0.0050.0000.005 ( I || - I ⊥ ) / I max X M L D Photon energy (eV) I || I ⊥ I || , I ⊥ ( a r b . un it s ) Fig. 1. (Color online) X-ray absorption spectra measured on the Co FeSi(Cr4) sample at the L , edge of Fe (a) and Co(b) with the polarization vector parallel ( I (cid:107) ) and perpendicular ( I ⊥ ) to the film magnetization along the [100] direction. Theresulting XMLD spectra ( I (cid:107) − I ⊥ )/ I max are shown in the lower panels, where I max is the maximum value of the correspondingmean L absorption edge. To support our assumption we recorded XMLD spectra(Fig. 4) of a Co FeSi . Al . film, which was deposited at700 ◦ C and capped with a 3 nm Al layer. Co FeSi . Al . was chosen to mimic a Co FeSi film with an interdiffu-sion of Al atoms in the subsurface for the surface-sensitiveTEY method. The spectra reveal the same features asfor the Al-capped Co FeSi films for both Fe and Co anddirections [100] and [110]. Especially at Co and for di-rection [100] we see that a maximum A (cid:48) is followed by aminimum A, like discussed before. Given the similarityof the XMLD spectra of the Co FeSi . Al . film and theCo FeSi(Al) series, we assume that during the deposi-tion of the capping layer, Al atoms interdiffuse into theCo FeSi film. Even though we grew each capping layer atroom temperature, our results suggest intermixing, alsobeing partially due to resputtering of the Co FeSi atomswith the result of Al atoms being implanted into the firstatomic layers. As a consequence, the subsurface of theprepared Co FeSi(Al) films is similar to Co FeSi . Al . .Since the TEY method is surface sensitive, the measuredXMLD on the Co FeSi(Al) films resemble the XMLDspectra of the Co FeSi . Al . film. The interdiffusion ofthe Al atoms manifests in each XMLD spectra differently with respect to the orientation (i.e. the excitation geom-etry which the sample was measured in). Additionally,the probed element (Co, Fe) plays a role, as the influenceof the Al atoms in the upper layer can be clearly observedat the Co edge, whereas the capping has hardly any influ-ence on the XLMD spectra of Fe edge. This is easily un-derstood by taking into account the following argument:The Al capping atoms intermix with Si atoms. This in-terdiffusion changes the first nearest neighboring shell ofCo atoms and only the second nearest neighbor shell ofFe. The non systematic variation can be explained byunknown temperatures of the sample during the deposi-tion of the capping layer. This took place a temperaturesbetween room temperature and 50 ◦ C, where we did notexpect any interdiffusion and therefore did not monitorexact temperatures and waiting times. Thus different de-grees of intermixing of Al atoms with the film occur. Ingeneral it is possible to show interdiffusion via neutronreflectivity measurements of multilayer sample (see Ref.21). However, to show interdiffusion on a single layer ismuch more demanding due to the small sample volumeand the unknown partial oxidation of the capping layer.As mentioned above, we encounter no large variations
700 705 710 715 720 725 730-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04700 705 710 715 720 725 730
Photon energy (eV) µ Β /f.u.4.89 µ Β /f.u.5.37 µ Β /f.u. N o r m a li ze d X M L D CFS(Cr) Fe [100] µ Β /f.u.
770 775 780 785 790 795 800 805-0.010-0.0050.0000.005-0.010-0.0050.0000.005-0.010-0.0050.0000.005-0.010-0.0050.0000.005770 775 780 785 790 795 800 805
Photon energy (eV)CFS(Cr) Co [100] µ Β /f.u. N o r m a li ze d X M L D µ Β /f.u.5.37 µ Β /f.u.5.80 µ Β /f.u. 770 775 780 785 790 795 800 805-0.010-0.0050.0000.005-0.010-0.0050.0000.005-0.010-0.0050.0000.005-0.010-0.0050.0000.005770 775 780 785 790 795 800 805 Photon energy (eV)CFS(Al) Co [100] µ B /f.u. N o r m a li ze d X M L D µ B /f.u. M C D µ B /f.u.6.10 µ B /f.u.
700 705 710 715 720 725 730-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04700 705 710 715 720 725 730
Photon energy (eV) µ Β /f.u.5.02 µ Β /f.u.5.31 µ Β /f.u. N o r m a li ze d X M L D CFS(Al) Fe [100] µ Β /f.u. AB C D EF ABC D EFA' a)b)c)d)e)f) g)h) i)j)k)l) m)n)o)p)q)r)s)t)
AB CD E F ABCD E F X M L D m sat ( µ Β /f.u.)CFS(Al) Co [100] X M L D m sat ( µ Β /f.u.)CFS(Al) Fe [100] X M L D m sat ( µ Β /f.u.)CFS(Cr) Co [100] CFS(Cr) Fe [100]
A-BB-CC-DE-F X M L D m sat ( µ Β /f.u.) Fig. 2. (Color online) X-ray magnetic linear dichroism spectra measured on the Co FeSi films with Cr capping layer (a - h)and Al capping layer (m - t) taken at [100] orientation. First row: Results with photon energies at the Co edge. Second row:Results with photon energies at the Fe edge. The saturation magnetization of each film is displayed in the upper right corner.Middle row: Four graphs (i - l), each related to a series of XMLD spectra (indicated by the arrows), showing the strength ofthe XMLD depending on the magnetization of the film. In the legend A-B, C-D, E-F and E-F relate to the difference of theXMLD signal between the respective points. Colored dashed lines represent a quadratic fit of the XMLD values of the samecolor. for the Cr-capped films. Hence, we conclude that Cr doesnot interdiffuse with the Co FeSi film. A non continuouscapping layer would result in a partially oxidized film,which clearly would change the XMLD spectra. We canexclude this as we already showed XMCD spectra of sam- ples without oxidation in Ref. 22 that were capped withthe same material and procedure.
770 775 780 785 790 795 800 805-0.010.000.010.02-0.010.000.010.02-0.010.000.010.02-0.010.000.010.02770 775 780 785 790 795 800 805
Photon energy (eV)CFS(Al) Co [110] µ B /f.u. N o r m a li ze d X M L D µ B /f.u. M C D µ B /f.u.6.10 µ B /f.u.770 775 780 785 790 795 800 805-0.010.000.010.02-0.010.000.010.02-0.010.000.010.02-0.010.000.010.02770 775 780 785 790 795 800 805 Photon energy (eV)CFS(Cr) Co [110] µ Β /f.u. N o r m a li ze d X M L D µ Β /f.u.5.37 µ Β /f.u.5.80 µ Β /f.u.
700 705 710 715 720 725 730-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04700 705 710 715 720 725 730
Photon energy (eV) µ Β /f.u.4.89 µ Β /f.u.5.37 µ Β /f.u.5.80 µ Β /f.u. N o r m a li ze d X M L D CFS(Cr) Fe [110]
700 705 710 715 720 725 730-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04-0.020.000.020.04700 705 710 715 720 725 730
Photon energy (eV) µ B /f.u.5.02 µ B /f.u.5.31 µ B /f.u. N o r m a li ze d X M L D CFS(Al) Fe [110] µ B /f.u. X M L D m sat ( µ Β /f.u.)CFS(Al) Fe [110] a)b)c)d) i)j) m)n)o)p)e)f) g)h) k)l) q)r)s)t) A B C D A B C DA B C DA B C D
A-BC-D X M L D m sat ( µ Β /f.u.)CFS(Cr) Co [110] X M L D m sat ( µ Β /f.u.)CFS(Al) Co [110] A-BC-D X M L D m sat ( µ Β /f.u.)CFS(Cr) Fe [110] Fig. 3. (Color online) X-ray magnetic linear dichroism spectra measured on the Co FeSi films with Cr capping layer (a - h)and Al capping layer (m-t) taken at [110] orientation. First row: Results with photon energies at the Co edge. Second row:Results with photon energies at the Fe edge. The saturation magnetization of each film is displayed in the upper right corner.Middle row: Four graphs (i - l), each related to a series of XMLD spectra (indicated by the arrows), showing the strength ofthe XMLD depending on the magnetization of the film. In the legend A-B and C-D relate to the difference of the XMLD signalbetween the respective points. Colored dashed lines represent a quadratic fit of the XMLD values of the same color.
3. XMLD versus Magnetization
The XMLD is expected to increase with the square ofthe magnetization of the sample. To investigate this de-pendence systematically, the intensity differences of themarked maxima and minima (A, B, C, D, E, and F) were taken as a scale for the XMLD strength. The respec-tive XMLD values were plotted versus the correspond-ing saturation magnetization of the film (Fig. 2 i,j,k,l andFig. 3 i,j,k,l). The Co[100]-plot (Fig. 2 i) of the Cr-cappedseries exhibits an increase of B-C and E-F. The valueof A-B of the film with m sat = 5.37 µ B /f.u. does not A'A B D EF
700 705 710 715 720 725 730-0.06-0.04-0.020.000.020.040.060.080.10 magnification: 4xCo FeAl Si CFS(Al4) (as in Fig. 2 q) N o r m a li ze d X M L D Photon energy (eV)
770 775 780 785 790 795 800 805-0.06-0.04-0.020.000.020.040.060.080.10 magnification: 6xCo FeAl Si CFS(Al4) (as in Fig. 3 m) N o r m a li ze d X M L D Photon energy (eV)
700 705 710 715 720 725 730-0.08-0.06-0.04-0.020.000.020.040.060.080.10 magnification: 4xCo FeAl Si CFS(Al3) (as in Fig. 3 t) N o r m a li ze d X M L D Photon energy (eV)
Fe [100] Co [100]Co [110]Fe [110] ABB BAA C C CC D DD FE
770 775 780 785 790 795 800 805-0.020-0.015-0.010-0.0050.0000.0050.0100.0150.020 magnification: 4xCo FeAl Si CFS(Al2) (as in Fig. 2 n) N o r m a li ze d X M L D Photon energy (eV)
Fig. 4. (Color online) X-ray magnetization linear dichroism measured on a Co FeSi . Al . film, capped with 3 nm Al layer, atthe L , edge of Fe and Co with the film magnetization along the [100] and [110] direction. Each XMLD spectrum is comparedwith a spectrum measured on one of the Co FeSi(Al) films. match the general trend of an increase, even though theother samples depict an increase. C-D shows strongerXMLD values with rising saturation magnetization, ex-cept the last datapoint of C-D, which is slightly lowerthan the film with with m sat = 5.37 µ B /f.u.. However, atrend of increasing XMLD signal is visible, whereas at theCo[100]-plot for the Al-capped series (Fig. 2 j), no suchdependence can be observed. For the Fe[100]-plot withthe Cr-capped series (Fig. 2 k), the film with the lowestand the highest saturation magnetization have the small-est, respectively the highest XMLD values as expected.However, the film with 5.37 µ B /f.u. shows smaller valuesthan the film with 4.89 µ B /f.u.. The same can be ob-served for Co [110] (Fig. 3 i). The Al-capped series of theFe[100]-plot (Fig. 2 l) and Co[110]-plot (Fig. 3 j) do showvery similar values for the XMLD and thus again showno dependence on the saturation magnetization. For theCr-capped series at the Fe[110]-plot (Fig. 3 k), the valuefor A-B and C-D increases with the saturation magne-tization. For the Al-capped series (Fig. 3 l), it is foundthat the film with the lowest saturation magnetizationof 4.98 µ B /f.u. has the strongest XMLD features. Even the film with 6.10 µ B /f.u. does not exceed these values.Generally, comparing the XMLD spectra of the Cr- andAl-capped films, higher values for the Cr-capped film se-ries were observed.
4. NMR results
Nuclear magnetic resonance (NMR) probes all the Co nuclei in the film samples due to a rather largepenetration depth of the radio frequency wave (typi-cally on the order of µ m). The surface effects seen inXMLD, namely the formation of a few monolayers ofCo FeSi . Al . at the Co FeSi/Al interface, are not ob-servable by NMR due to a lack of sensitivity, as the signalwas optimized to reveal the NMR signals stemming fromthe bulk of the films. Note that the NMR spectra ofCo FeSi . Al . (at about 160 MHz) may be hidden inthe broad signal. NMR allows to investigate the localenvironments of Co nuclei in the bulk of the film sam-ples, and enables to determine the degree of order as wellas possible existence of off-stoichiometry.
The Co NMR spectra measured on all samples(representatives are shown in Fig. 5) have a main lineat around 145 MHz with one satellite on the high-frequency side. A similar Co NMR spectrum with high-frequency satellites was reported for off-stoichiometricCo FeSi films (Ref. 23). In the present case, the averagelinewidths (7.99 MHz) are smaller than those reportedin the previous data (11.8 MHz, Ref. 23), which alreadyindicates a higher degree of order and smaller degree ofoff-stoichiometry in the present films. This interpreta-tion is consistent with the overall shift of the main line(145 MHz) towards lower frequencies compared to previ-ous NMR data on Co FeSi films (150 MHz ), the mainline of the Co FeSi films now shifting towards the sin-gle NMR line observed for highly-ordered bulk Co FeSi(139 MHz ). The intensity of the high-frequency satel-lite lines is lower compared to the satellite lines presentedin Ref. 23, indicating that the films investigated here areof much higher structural quality. The improved shortrange order of the L2 structure visible in the NMR pa-rameters correlates with the improved long range orderseen in the X-ray investigations, i.e. an increased inten-sity of the (111) ordering peak.To quantitatively analyze the spectra we fitted themusing a sum of Gaussian lines representing different num-bers of Fe and Si next nearest neighbors in the first co-ordination shell of Co (compare Ref. 23). The represen-tative fit of the Co FeSi(Al1) sample is shown in Fig. 6.However, the fit matches much better to the data if athird broad line is included. Interestingly, the resonancefrequency of this broad line coincides with the one ob-served for the main line in Co FeSi . Al . . However,this line is observed for both types of capping layers, Aland Cr. This excludes the formation of Co FeSi . Al . as origin of the broad NMR line. We suggest the originof the broad line to be strain within the film, induced bythe substrate as explained in the following: The broadline has the same frequency and the same linewidth forall samples, the only difference is its relative contribu-tion to the total spectrum, which slightly varies fromsample to sample. The contribution of the broad line isstronger for thinner films, e.g. in the case of the 45 nmCr-capped Co FeSi film the ratio between intensities ofthe broad line and the main line is 0 . ± .
05, whereasin the case of the 75 nm thick Cr-capped Co FeSi filmit is 0 . ± .
05. This finding suggests that this broadcontribution is probably from the so called “dead layer”near the substrate. It is well known that there is a sub-stantial difference between lattice parameters of the MgOsubstrate (4.21 ˚A ·√ FeSi (5.64 ˚A),which may yield a monotonous change in the structureof the Heusler film within a certain distance from thesubstrate. The factor √ FeSi unit cell by 45 ◦ with respect to the MgOunit cell. The bulk of the film sample has an ideal L structure with a slight amount of Fe-Si off-stoichiometry,represented by the parameter x in Co Fe x Si − x . Thevalues of x in percent are listed in Table I. All x values
120 130 140 150 160 170 180 1900.00.20.40.60.81.0
CFS(Al1)CFS(Cr4)Data taken from Ref. 13 C o N M R s p i n ec ho i n t e n s it y ( a r b . u . ) Frequency (MHz)
Fig. 5. (Color online) Co NMR spectra of CFS(Al1) andCFS(Cr4) samples plotted together with previous data onsimilar Co FeSi sample, data taken from Ref. 23. The upperinset shows the L type Heusler structure with the corre-sponding Wyckhoff positions of Co (blue), Fe (green) and Si(red). Please note that the first coordination shell of Co inthe L type structure with the 2:1:1 stoichiometry consists of4Fe+4Si atoms; the resonance line at 145 MHz corresponds to Co nuclei with this specific local environment. The satelliteat higher frequencies originates in an Fe-rich stoichiometrywith the first coordination shell of Co consisting of 5Fe+3Siatoms (compare Ref. 23). were calculated by fitting a binomial distribution func-tion to the relative areas of the NMR resonance lines,as discussed in detail in Ref. 23. Fig. 7 summarizes therelations between the different film characteristics (de-position temperature and saturation magnetization) andthe results of the NMR analysis (linewidth, amount ofoff-stoichiometry and resonance frequency). For bothtypes of capping layers, the amount of off-stoichiometry x depends on the deposition temperature, specifically:the degree of off-stoichiometry decreases with increas-ing deposition temperature and hence with the degreeof order (Fig. 7(a,b)). Generally, the NMR linewidth isalso a good measure of the structural order of a system.Fig. 7 c,d demonstrate a clear correlation between themagnetic moment of a given film and the NMR linewidth.Samples prepared at higher deposition temperatures gen-erally have a larger moment and smaller NMR linewidth,which is an indication of higher local order. In addi-tion, there is a dependence of the resonance frequency ofthe main NMR line on the magnetic moment, sampleswith higher magnetic moment show a signal at lowerfrequencies, with the frequency closer to bulk Co FeSi(6 µ B /f.u.). Such a trend is typically seen for NMR linesof Heusler compounds (compare Refs. 25 and 26).
120 130 140 150 160 170 180 1900.00.20.40.60.81.0
CFS(Al1)Cumulative fit C o N M R s p i n ec ho i n t e n s it y ( a r b . u . ) Frequency (MHz)
Fig. 6. (Color online) Co NMR spectrum of Co FeSi(Al1)sample and its fit using three Gaussian lines. Thick solid linerepresents the total fit of the spectrum.
5. XMCD of Si L -edge Although the total magnetization in Co FeSi is dom-inated by the large moments located at the Co and Featoms, it has been predicted that a weak magnetic mo-ment of ca. 0.13 µ B (LSDA+ U ) is also induced at the Siatom with antiparallel orientation to the mean magne-tization direction. The element-specific detection of thissmall magnetic moment remained a challenge because theSi K - and L -edges’ signals are extremely weak. Recently,Antoniak et al . showed the occurrence of an antiparal-lel Si moment of -0.01 µ B in thin Fe Si films using x-rayabsorption at the Si K -edge and at the Si L , edges.Here, we investigated Co FeSi by using a similar tech-nique. Fig. 8 shows the XAS and XMCD data measuredat the Si L , edges. We verified the result with fieldswitching and polarization switching. In comparison tothe data for Fe Si the XAS is much less structured re-vealing only a smooth increase near 102 eV. The XMCDpeak at 103 eV shows a maximum value. The strength ofthe signal is given by the ratio of the difference of the in-tensities I + , I − (0.006) and the value of the XAS spectra(0.1) at 103 eV (values are extracted from Fig. 8). With( I + − I − ) /I = 0 . / . .
06, we calculate an asym-metry of 6 %. Calculation was performed according toRef. 27. Notably, this value is about seven times largerthan the value of 0.8 % obtained by Antoniak et al . Asin the case of Fe Si, we conclude from the positive asym-metry that the orientation of the Si moment is antiparal-lel to the mean magnetization, which is in agreement withthe prediction in Ref. 3. Assuming that the size of theasymmetry scales with the magnetic moment we obtainan induced magnetic moment of -0.07 µ B , which nicelyagrees with our calculated value of Si total magnetic mo-ment of -0.06 µ B , ( µ orb = − . µ B ). As we probe Si p- states, the magnetization is induced to the hybridiza- tion of the magnetic 3d orbitals of the neighbors. Sincewe could not measure at the K -edge we cannot concludeon the contribution from the orbital magnetic moment.Because the atomic structure in our case is cubic we mayassume that the orbital moment contribution will be anorder of magnitude smaller than the spin moment. B. Calculated results
1. XMLD at the L , edges of Fe and Co The calculation of adequate XMLD spectra at the Coand Fe L , edges of the full Heusler compound Co FeSiis still a challenging task. Using different exchange-correlation functionals, or employing additional parame-ters such as the Hubbard U , varying electronic structurescan be obtained, leading to magnetic moments differentfrom 6 µ B as well as to different x-ray spectra. Recently,the so-called fixed-spin method has been employed toconstrain the magnetic moment of Co FeSi to the maxi-mum measured value of 6 µ B ; the electronic structure wasthen computed selfconsistently under this constraint. However, it seems that the low lying bands exhibit a non-physical exchange splitting of 1 eV, see Fig. 6 of Ref. 8(cf. Ref. 5). Another possibility to describe the high-spinelectronic is to apply by the so-called Hubbard U tech-nique with the self-interaction correction and choosesuitable parameters, i.e. U eff (Co) = 4.8 eV and U eff (Fe)= 4.5 eV (see Ref. 6).Recent electronic structure investigations have shownthat the observed fine structure at the L edges is oftennot exactly reproduced by ab initio calculations, whereasthe L edges often show just a simple oscillation andhere the agreement with the first-principles calculationsis good. The experimentally observed fine structure atat L edge might stem from various, as yet unresolvedorigins. It might come from many-body effects or evenbe related to deficiencies of the sample. As the LSDA+ U approach has given the best agree-ment between experimental and computed data, we em-ploy here this approach. In Fig. 9 we show the computednormalized XMLD spectra for both Co and Fe atomsand for the magnetization directions parallel to [100] orto [110]. The positions of the calculated L edges havebeen aligned to the experimental L edge energy.Certain differences between the experimental and cal-culated spectra can be noted. For magnetization parallelto [100] the calculated XMLD spectrum at the Co L , edge does not exhibit a fine structure in contrast to themeasured spectra shown in Fig. 2. The calculations lackthe drop (C) and the drop (D) on the high-energy sideat the L edge. For the L edge the calculated XMLDspectrum exhibits a single oscillation with the same signof the asymmetry of the two lobes as in the experiment,compare Fig. 9 and Fig. 2. For magnetization parallel to[110] the XMLD spectrum again exhibits a single oscil-lation at both the L and L edges as seen in the ex-0
450 500 550 600 650 700 7500.00.20.40.60.81.01.21.41.61.82.0 F e - S i o ff- s t o i c h i o m e t r y x
450 500 550 600 650 700 7506.57.07.58.08.59.0 (a) N M R li n e w i d t h ( M H z ) deposition temperature (°C) Cr capping layer fr e qu e n c y o f N M R m a i n r e s on a n ce li n e ( M H z ) m sat ( µ B /f.u.)(c) N M R li n e w i d t h ( M H z )
450 500 550 600 650 700 7500.00.20.40.60.81.01.21.41.61.82.0 Al capping layer F e - S i o ff- s t o i c h i o m e t r y x (b)
450 500 550 600 650 700 7506.57.07.58.08.59.0 N M R li n e w i d t h ( M H z ) deposition temperature (°C) fr e qu e n c y o f N M R m a i n r e s on a n ce li n e ( M H z ) m sat ( µ B /f.u.) N M R li n e w i d t h ( M H z ) Al capping layer (d)
Fig. 7. (Color online) Relation between the results of the NMR analysis (amount of Fe-Si off-stoichiometry x (crosses)), width(squares) and frequency (triangles) of NMR main line) and the film characteristics (deposition temperature (a,b) and momentin saturation (c,d)). The data for the Cr capped films are shown in the left panels (a,c) while the data for the Al capped filmsare presented in the right panel (b,d).
98 100 102 104 106 108 110 112 -0.0020.0000.0020.0040.006 I + - I − X M C D Photon energy (eV) -0.10.00.10.20.30.4 I + I − I n t e n s it y ( a r b . un it s ) Fig. 8. (Color online) X-ray absorption spectra and X-raymagnetic circular dichroism of Co FeSi(Cr4) measured at theSi L , . periment having the correct asymmetry, i.e. the posi-tive peak is higher in magnitude than the negative peak.Moreover, the sign of the Co XMLD is inverted under
775 780 785 790 795 800-0.06-0.0300.030.06 [100][110]
705 710 715 720 725 730
Photon energy (eV) -0.2-0.100.10.20.3 N o r m a li z ed X M L D CoFe
Fig. 9. (Color online) X-ray magnetic linear dichroism ofCo FeSi calculated for the attenuation coefficient of the 75 nmthick sample at the L , edge of Co (upper panel) and of Fe(lower panel), for the magnetization along the [100] or [110] di-rections. The calculations were performed with the LSDA+ U technique, using U eff = 4.8 eV(Co) and U eff = 4.5 eV(Fe). Fordetails, see text. and withstudies of the pure 3 d elements. This inversion of theXMLD spectrum appears as a consequence of the crystal-field splitting of the t g and e g states of the respectivetransition metal atom, with different states being sensi-tively probed for different magnetization directions. Wenote that the XMLD spectra of Co in Fig. 4 of Ref. 8 ob-tained with the LSDA+ U differ from ours by more finestructures at the L and L edges for both magnetiza-tion directions. However, it seems that we can reproducesuch fine structures with calculations using the general-ized gradient approximation with the Hubbard U tech-nique (GGA+ U ) instead of LSDA+ U , but for the verysimilar value of U eff = 4 . L edge, whereas a single oscillationat the L edge exists for both magnetization directions,which again are inverted when changing the magnetiza-tion orientation from [100] to [110]. The experimentalspectra at the L edge exhibit similar features for mag-netization along [100], except for peak D (see Fig. 2 e).The main disagreement between calculations and experi-mental data is in the magnitude of the first negative peak.It seems that the best agreement between calculated andmeasured XMLD spectra is achieved for the spectrumshown in Fig. 2 f. However, still the D feature (positiveshoulder on the high-energy side) is not reproduced in thecalculation. This was observed also in Ref. 8, even whenvarious approximations for the exchange-correlation termwere used. The single oscillation in the XMLD spectrumat the L edge for magnetization along [100] is well re-produced.A poorer agreement between measured and calculatedXMLD spectra is found for both the Fe L , edges formagnetization along [110]. Experimentally, a single os-cillation is observed here, while in ours and other theoret-ical calculations, a three peak structure is found. Also,our calculated results differ from those of Kallmayer etal. For the L edge again a single oscillation is com-puted, whereas experimentally predominantly a positivepeak is detected, similar to Ref. 6 and 8, and the nega-tive peak is small. We ascribe this difference with Ref. 6to recent improvement of our calculations of the dielec-tric tensor elements (complex linear response formula)and the present use of a more sophisticated multilayermodel for describing the light-sample interaction (Fresneltheory using Viˇsˇnovsk´y’s formalism ) over the simplerapproach used in Ref. 6.The calculated XMLD spectra are about one order ofmagnitude larger than the experiment. This is under-standable in the TEY experiment, as we do not accountfor any loss due to scattering within the sample. Wehave tested the effect of substrate (150 nm MgO) as wellas 3 nm capping layer of Al or Cr, where in addition tothe ab initio calculated Co FeSi optical data, we adoptedfor the capping and substrate experimental data from thex-ray database. We found that none of those influence
XAS ( a r b . un i t s )
80 90 100 110 120 130 140 150
Photon energy (eV) -0.0002-0.000100.00010.0002 X M CD no t no r m . Fig. 10. (Color online) Calculated X-ray absorption spectraand X-ray magnetic circular dichroism (not normalized) atthe L , edges of Si in Co FeSi. See text for details. the spectra in the energy range of the Fe and Co L -edges.
2. XMCD at the L , edges of Si Using the LSDA+ U approach for the electronic struc-ture of Co FeSi, we also calculated the XAS and XMCDat the L , edges of Si. The results are given in Fig. 10.The XMCD strength is calculated analog to sectionIV A 5. From Fig. 10 at 103 eV we obtain 0 . / .
003 =0 .
1. It means that XMCD is about 10 % of the XAS mag-nitude, which is in agreement with the experimental find-ing of 6 %. Note that experimental XMCD spectrum ap-pears to exhibit a stronger broadening than the computedspectrum. The computed spectra only shows contribu-tion from Si, whereas experimentally we see contributionfrom Co and Fe, which create a huge background signaldue to the weak Si signal. We note that it is a generalproblem to subtract the background reliably. Consistentwith the experiment, we find that an L edge XMCDsignal is not present. The calculated XMCD spectrum isoverall similar in shape to that calculated for Si in Fe Siby first-principles methods in Ref. 27, except that here wedo not obtain a negative peak at the high-energy side.
V. SUMMARY AND CONCLUSION
In summary, magnetic properties of two series ofCo FeSi films, one capped with Cr and the other withan Al layer, were investigated. Both series comprise fourfilms, each exhibiting a different local order and variedsaturation magnetization. A comparison of the recordedXMLD spectra revealed that the Al-capped films showlarge variations, whereas the Cr-capped series exhibitconsistent features within the series. The XMLD spectraof a Co FeSi . Al . film showed similar features like Al-capped Co FeSi. Thus, an intermixing of Al atoms of the2Co FeSi subsurface during deposition was assumed. Thisis a finding which needs to be considered carefully whenmaking tunnel barriers for TMR devices, since it is im-portant to have a stoichometric structure at the interface.For a systematic investigation, certain points were takenas a scale for the XMLD strength and the values wereplotted versus the saturation magnetization of the films.An expected rise was noted for the Cr-capped Co FeSiseries, whereas the Al-capped series showed no depen-dence. All samples show a clear dependence of the filmquality on the deposition conditions, while the depositiontemperature has the highest impact on the film quality.By increasing the deposition temperature the films arebetter ordered and furthermore the off-stoichiometry isreduced.Comparison with ab initio calculated XMLD spectrashowed an overall good agreement, however, certain dif-ferences remain. Whether these are due to the residualoff-stoichiometry of the films or if further improvementof the calculation is needed is currently an open ques-tion. Experimentally, the feature-rich spectra of the Cr-capped samples change only qualitatively with disorder.This observation still needs to be reproduced in future calculations. The magnetic moment at the Si atom inCo FeSi could be detected with XMCD. A small mag-netic contribution aligned antiparallel to the Co momentswas observed, in agreement with ab initio calculations.
ACKNOWLEDGMENTS
We acknowledge support by DFG research group AS-PIMATT DFG Ja821/5-1 and Graduate School of Ex-cellence Materials Science in Mainz (MAINZ) - GSC266.We thank S. Cramm for support at BESSY. SW grate-fully acknowledges funding by Deutsche Forschungsge-meinschaft DFG under the Emmy Noether programmein project WU595/3-1. DL acknowledges support withinprojects Reg. No. CZ.1.07/2.3.00/20.0074 and Reg. No.CZ.1.05/1.1.00/02.0070, both supported by OperationalProgramme ’Education for competitiveness’ funded byStructural Funds of the European Union and state bud-get of the Czech Republic. AK acknowledges DFG(Graduate School of Excellence Materials Science inMainz (MAINZ) - GSC266). S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M.Daughton, S. von Moln´ar, M. L. Roukes, A. Y. Chtchelka-nova, and D. M. Treger, Science , 1488 (2001). R. A. de Groot, F. M. Mueller, P. G. v. Engen, and K. H. J.Buschow, Phys. Rev. Lett. , 2024 (1983). S. Wurmehl, G. H. Fecher, H. C. Kandpal, V. Ksenofontov,C. Felser, H.-J. Lin, and J. Morais, Phys. Rev. B ,1844341 (2005). G. H. Fecher, H. C. Kandpal, S. Wurmehl, C. Felser, andG. Sch¨onhense, J. Appl. Phys. , 08J106 (2006). D. Bombor, C. G. F. Blum, O. Volkonskiy, S. Rodan,S. Wurmehl, C. Hess, and B. B¨uchner, Phys. Rev. Lett. , 066601 (2013). M. Kallmayer, P. Klaer, H. Schneider, G. Jakob, H. J.Elmers, D. Legut, and P. M. Oppeneer, Phys. Rev. B ,054448 (2011). J. Kunes, P. M. Oppeneer, S. Valencia, D. Abramsohn,H.-C. Mertins, W. Gudat, M. Hecker, and C. Schneider, J.Magn. Magn. Mater. , 2146 (2004). M. Meinert, J.-M. Schmalhorst, M. Glas, G. Reiss,E. Arenholz, T. B¨ohnert, and K. Nielsch, Phys. Rev. B , 054420 (2012). S. Wurmehl and J. Kohlhepp, Topical review in J. Phys.D: Appl. Phys. , 173002 (2008). P. Panissod, in NATO ASI series High Tech, edited byV. G. Baryakhtar, P. E. Wigen, and N. A. Lesnik (KluwerAcademic, Dordrecht, 1997), vol. 48, p. 225. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka,and J. Luitz, An Augmented Plane Wave + Local OrbitalsProgram for Calculating Crystal Properties, Techn. Univ.Wien, Austria (2001). J. P. Perdew and Y. Wang, Phys. Rev. B , 13244 (1992). J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996). V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. Czyzyk,and G. A. Sawatzky, Phys. Rev. B , 16929 (1993). J. Kunes and P. M. Oppeneer, Phys. Rev. B , 024431(2003). ˇS. Viˇsˇnovsk´y, Czech. J. Phys. , 663 (1991). H. Schneider, G. Jakob, M. Kallmayer, H. J. Elmers,M. Cinchetti, B. Balke, S. Wurmehl, C. Felser, M. Aeschli-mann, and H. Adrian, Phys. Rev. B , 174426 (2006). N. D. Telling, P. S. Keatley, G. van der Laan, R. J. Hicken,E. Arenholz, Y. Sakuraba, M. Oogane, Y. Ando, andT. Miyazaki, Phys. Rev. B , 224439 (2006). P. Klaer, M. Kallmayer, C. G. F. Blum, T. Graf, J. Barth,B. Balke, G. H. Fecher, C. Felser, and H. J. Elmers, Phys.Rev. B , 144405 (2009). H. J. Elmers, G. H. Fecher, D. Valdaitsev, S. A. Nepi-jko, A. Gloskovskii, G. Jakob, G. Sch¨onhense, S. Wurmehl,T. Block, C. Felser, et al., Phys. Rev. B , 104412 (2003). H. Zabel, materialstoday , 42 (2006). M. Kallmayer, H. Schneider, G. Jakob, H. J. Elmers,B. Balke, and S. Cramm, J. Phys. D: Appl. Phys , 1552(2007). S. Wurmehl, J. Kohlhepp, H. Swagten, B. Koopmans,C. Blum, V. Ksenofontov, H. Schneider, G. Jakob,D. Ebke, and G. Reiss, J. Phys. D: Appl. Phys. , 084017(2009). C. G. F. Blum, K. Jenkins, J. Barth, C. Felser, S. Wurmehl,G. Friemel, C. Hess, G. Behr, B. B¨uchner, S. Riegg, et al.,Appl. Phys. Lett. , 161903 (2009). S. Wurmehl, J. Kohlhepp, H. Swagten, and B. Koopmans,J. Appl. Phys. , 043903 (2012). M. W´ojcik, E. Jedryka, H. Sukegawa, T. Nakatani, andK. Inomata, Phys. Rev. B , 100401 (2012). C. Antoniak, H. C. Herper, Y. N. Zhang, A. Warland,T. Kachel, F. Stromberg, B. Krumme, K. Weis, C. Fauth, W. Keune, P. Entel, et al., Phys. Rev. B , 214432 (2012). F. Nolting, D. Legut, J. Rusz, P. M. Oppeneer, G. Wolters-dorf, and C. H. Back, Phys. Rev. B , 184415 (2010). D. Legut (unpublished). B. L. Henke, E. M. Gullikson, and J. C. Davis, At. Dataand Nucl. Data Tables54