Room-temperature local ferromagnetism and its nanoscale expansion in the ferromagnetic semiconductor Ge1–xFex

We investigate the local electronic structure and magnetic properties of the group-IV-based ferromagnetic semiconductor, Ge1−xFex (GeFe), using soft X-ray magnetic circular dichroism. Our results show that the doped Fe 3d electrons are strongly hybridized with the Ge 4p states, and have a large orbital magnetic moment relative to the spin magnetic moment; i.e., morb/mspin ≈ 0.1. We find that nanoscale local ferromagnetic regions, which are formed through ferromagnetic exchange interactions in the high-Fe-content regions of the GeFe films, exist even at room temperature, well above the Curie temperature of 20–100 K. We observe the intriguing nanoscale expansion of the local ferromagnetic regions with decreasing temperature, followed by a transition of the entire film into a ferromagnetic state at the Curie temperature.


Results and Discussion
Basic properties of our GeFe films. We carried out XMCD measurements on two samples (labeled A and B) consisting of a 120-nm-thick Ge 0.935 Fe 0.065 layer grown on a Ge(001) substrate by low-temperature molecular beam epitaxy (LT-MBE) [ Fig. 1(a,b)] (see Methods). The Ge 0.935 Fe 0.065 layer of sample A was grown at 160 °C, whereas that of sample B was grown at 240 °C. These samples are the same as those studied in ref. 6. From the Arrott plots of the H dependence of the magnetic circular dichroism (MCD) measured with visible light with a photon energy of 2.3 eV (corresponding to the L-point energy gap of bulk Ge), we found T C = 20 K and 100 K for samples A and B, respectively. Detailed crystallographic analyses, including in situ reflection high-energy electron diffraction (RHEED), high-resolution transmission electron microscopy (TEM), spatially resolved transmission-electron diffraction (TED) combined with energy-dispersive X-ray spectroscopy (EDX) and X-ray diffraction (XRD), showed that the GeFe films have a diamond-type single-crystal structure without any ferromagnetic precipitates and with nanoscale spatial Fe concentration fluctuations of 4-7% (sample A) and 3-10% (sample B) 6 . We found that T C is higher when the fluctuations in the Fe concentration are larger 6 . In addition, channeling Rutherford backscattering (c-RBS) and channeling particle-induced X-ray emission (c-PIXE) measurements showed that ~85% (~15%) of the doped Fe atoms exist at the substitutional (tetrahedral interstitial) sites in both samples A and B, and that the interstitial Fe concentration is not related to T C 6 . This also indicates that there are no ferromagnetic precipitates with different crystal structures in our films.
XAS and XMCD measurements. We measured the Fe L 2,3 -edge XAS spectra [μ + , μ − and (μ + + μ − )/2] of samples A [ Fig. 1 Fig. 1(d)] at 5.6 K with μ 0 H = 5 T applied perpendicular to the film surface. Here, μ + and μ − refer to the absorption coefficients for photon helicity parallel and antiparallel to the Fe 3d majority spin direction, respectively. In both films, three peaks a, b and c are observed at the Fe L 3 edge in the XAS spectra [see also the insets in Fig. 1(c,d)]. We found that the small peak c was suppressed by etching the surface with dilute HF, indicating that this peak, which can be assigned to the Fe 3+ state, originates from a small quantity of surface Fe oxide 16 , which remains even after surface cleaning. Meanwhile, peaks a and b are assigned to the Fe atoms in GeFe. Peaks a and b can be assigned to the Fe 2+ state 17,18 .

(c)] and B [
We measured the Fe L 2,3 -edge XMCD (= μ + − μ − ) spectra of samples A [ Fig. 1(e)] and B [ Fig. 1(f)] at 5.6 K with various H applied perpendicular to the film surface. Here, we discuss the XMCD intensities at 707.66 eV (X) and 708.2 eV (Y), which correspond to the photon energies of peaks a and b in the XAS spectra, respectively. When normalized to 707.3 eV, the XMCD spectra with various H differ, and the intensity at X grows faster than that at Y as H increases, as shown in the insets of Fig. 1(e,f). As shown in Fig. 1(c,d), the shapes of the XAS spectra at the Fe L 3 edge are similar between samples A and B, which have almost the same interstitial Fe concentrations (i.e., 15% of the total Fe content 6 ); therefore, we can assign the XMCD intensity at X to the substitutional Fe atoms and the paramagnetic component of the XMCD intensity at Y to the interstitial Fe atoms. We do not observe fine structures due to multiplet splitting at the Fe L 3 edge in both samples, which would be observed if the 3d electrons were localized and were not strongly hybridized with other orbitals 19 . These observations indicate that the Fe 3d electrons are strongly hybridized with the Ge 4p states 20 . Determination and analyses of the orbital and spin magnetic moments. We determine the orbital magnetic moment, m orb , and the spin magnetic moment, m spin , the orbital magnetic moment relative to the spin magnetic moment, m orb /m spin , and the total magnetic moment, M = m spin + m orb , of the substitutional Fe atoms in accordance with the well-established procedure using the XMCD sum rules [21][22][23][24][25] . Figure 2(a) shows the XAS spectra (solid curves) and the XAS signals integrated from 690 eV (dashed curves) of sample A. Figure 2(b) shows the XMCD spectra (solid curves) and the XMCD signals integrated from 690 eV (dashed curves) of sample A. Here, the measurements were carried out with a magnetic field μ 0 H = 5 T applied perpendicular to the film surface at various temperatures. Figure 2(c,d) shows the same data measured for sample B. For the XMCD sum-rules analyses, we define r, p and q as the following equations at each temperature.
E E 3 2 where E 3 (690-718 eV) and E 2 (718-760 eV) represent the integration energy ranges for the L 3 and L 2 absorption edges, respectively. Here, E represents the incident photon energy. We can obtain m spin and m orb of substitutional Fe atoms using the XMCD sum rules, which are expressed as follows: where n 3d and m T are the number of 3d electrons on the Fe atom and the expectation value of the intra-atomic magnetic dipole operator, respectively. We neglect m T because it is negligibly small for Fe atoms at the T d symmetry site 24 . By dividing equation (4) by equation (5), m orb /m spin is expressed by orb spin Thus, we can obtain m orb /m spin directly from the XMCD spectra without any assumptions. By the above calculations with equations (2), (3) and (6) using the temperature dependence of XMCD spectra shown in Fig. 2, we obtained the temperature dependence of m orb /m spin of substitutional Fe atoms as shown in Fig. 3(a,b). For sample A, m orb /m spin = 0.12 ± 0.02, and for sample B, m orb /m spin = 0.11 ± 0.03, both of which are positive and larger than that of bulk Fe (where m orb /m spin ~ 0.043 19 ); the orbital angular momentum in GeFe is not quenched. The observation that the spin and orbital angular momentum are parallel suggests that the Fe 3d shell is more than half filled. This implies that the Fe atoms are in the 2 + state rather than in the 3 + state, in which the Fe 3d shell is half-filled and the orbital angular momentum vanishes. This result is consistent with the peak positions of the XAS spectra (see Fig. 1(c,d)). The large m orb is a characteristic property of GeFe, and excludes the possibility of the existence of ferromagnetic Fe metal precipitates in our films.
We describe the derivation of m spin and m orb using equations (4) and (5). Figure 3(c,d) shows the XMCD spectra of samples A (c) and B (d) normalized to 707.3 eV measured at 5.6 and 300 K with magnetic fields of 0.1 and 5 T applied perpendicular to the film surface. In both films, all the line shapes of the XMCD spectra are almost the same, which means that the paramagnetic component observed at Y in Fig. 1(e,f) is negligibly small in comparison with the entire XMCD spectra and almost all XMCD intensities are composed of the absorptions by the substitutional Fe atoms observed at X in Fig. 1(e,f). This result means that the integrated values of the XMCD spectra p [equation (2)] and q [equation (3)] can be attributed only to the substitutional Fe atoms. Meanwhile, because the XAS signals have both contributions of the substitutional and interstitial Fe atoms, we reduced the integrated XAS intensity r [equation (1)] to 85% of its raw value (85% is the approximate ratio of the substitutional Fe atoms to that of the total Fe atoms in both samples A and B 6 ) when using the XMCD sum rules. We note that this assumption, that each substitutional Fe atom and each interstitial Fe atom contribute equally to the integrated XAS intensity [r value (equation (1))], does not affect our main conclusions in this paper (see Supplementary Discussion S1). We took n 3d to be 6 and the correction factor for m spin to be 0.88 25 for Fe 2+ in equations (4) and (5). By the above calculations using the temperature dependence of XAS and XMCD spectra shown in Fig. 2, we obtained the temperature dependence of m spin , m orb and m spin + m orb (= M) of substitutional Fe atoms shown in Fig. 3(a,b). The M values obtained by the XMCD measurements are 1.00 μ B /Fe for sample A and 1.43 μ B /Fe for sample B when a magnetic field μ 0 H = 1 T is applied perpendicular to the film surface at 5.6 K. The magnetizations measured by superconducting quantum interference device (SQUID) under the same condition at 5 K are 0.7 μ B /Fe for sample A and 1.3 μ B /Fe for sample B 6 . These values are close to those obtained by XMCD. The slight differences may originate from the unavoidable inaccuracy of the subtracting procedure of the large diamagnetic response of the substrate in the SQUID measurements. We see that both m spin and m orb (and therefore the total magnetic moment M = m spin + m orb ) are larger in sample B (T C = 100 K) than in sample A (T C = 20 K) over the entire temperature region when μ 0 H = 5 T. Figure 4 shows the H dependence of the XMCD intensity at energy X and a temperature of 5.6 K, the MCD intensity measured with visible light of 2.3 eV at 5 K, and the magnetization measured using a SQUID at 5 K for sample B. The shapes of these curves show excellent agreement with each other; it follows that the spin splitting of the valence band composed of the Ge 4p orbitals is induced by the Fe 3d magnetic moment, which originates from the substitutional Fe atoms, through the p-d hybridization. The MCD hysteresis curve did not depend on the sweeping speed of the magnetic field unlike superparamagnetic materials with spin blocking [see Supplementary Discussion S2 26,27 ]. This result supports our understanding that the GeFe films are ferromagnetic below T C .
Room-temperature local ferromagnetism and the nanoscale expansion of the local ferromagnetic regions in the GeFe films. Figure 5(a,b) shows the effective magnetic-field (H eff ) dependence of the   . (a,b) The dependence of the XMCD intensity measured at X on the effective magnetic field H eff for sample A (a) and sample B (b) at various temperatures. The total magnetization (M = m spin + m orb ) obtained using the XMCD sum rules is also plotted (filled red symbols). We scaled the vertical axis of the XMCD intensity so that it represents M at each temperature. In all measurements, H was applied perpendicular to the film surface.
Scientific RepoRts | 6:23295 | DOI: 10.1038/srep23295 XMCD intensity measured at X for samples A (a) and B (b) at various temperatures. Here, M is also plotted (filled red symbols), and μ 0 H eff is obtained by subtracting the product of M and the density of the substitutional Fe atoms from μ 0 H to eliminate the influence of the demagnetization field (see Supplementary Discussion S3). The insets show clear hysteresis below T C in both samples. The XMCD-H eff curves show large curvature above T C in both samples [see the main panels of Fig. 5(a,b)], indicating that part of the film is superparamagnetic (SPM) above T C . It indicates that local ferromagnetic regions form in nanoscale high-Fe concentration regions at temperatures above T C , and thus M can be described by  Fig. 3(a,b)] when all the substitutional Fe atoms are magnetically active. Here, the Curie constant per substitutional Fe atom is obtained using the following equations: where μ B , k B , n B , S, L and J represent the Bohr magneton, the Boltzmann constant, the effective Bohr magneton number, the spin angular momentum, the orbital angular momentum and the total angular momentum, respectively. Here, S = 2 (for Fe 2+ ), and L = 0.4 (L = 2 S × m orb /m spin , where m orb /m spin ≈ 0.1 as shown in Fig. 3(a,b)), and J = 2.4 (= L + S because the spin and orbital angular momenta of a substitutional Fe atom are parallel) in equation (9). Thus, n B is estimated to be 5.24. The first and second terms in equation (7) correspond to the SPM and paramagnetic components, respectively. In Fig. 5(a,b), the thin black solid curves correspond to the best fit obtained with equation (7). For sample B, the M-H eff curves at temperatures in the range 100-300 K are well reproduced by equation (7), which indicates that the ferromagnetic -SPM transition occurs at T C = 100 K. With sample A, the M-H eff curves at temperatures above T C (i.e., T ≥ 20 K) are well reproduced by equation (7), except for T = 20 K, which is probably due to the onset of ferromagnetism. These good fits up to room temperature indicate that ferromagnetic interactions within the nanoscale high-Fe concentration regions remain at room temperature in both samples.
Here, we estimate the ratios of the substitutional ferromagnetic, paramagnetic, and magnetically inactive Fe atoms to the total number of substitutional Fe atoms at 5.6 K in samples A and B. In this discussion, we only consider substitutional Fe atoms. The obtained results are summarized in Table 1  dependence of M (= m spin + m orb ) of one substitutional paramagnetic Fe atom is expressed by the Langevin function. Thus, theoretically, the H eff dependence of M of one substitutional paramagnetic Fe atom at 5.6 K is obtained by substituting 4.4 μ B , 1 and 5.6 K in m SPM , f SPM and T of equation (7), respectively (Fig. 6). Here, the experimental M-H eff curves at 5.6 K shown in Fig. 5(a,b) can be approximately expressed by the sum of the square hysteresis curve originating from substitutional ferromagnetic Fe atoms and the Langevin function originating from substitutional paramagnetic Fe atoms. From the high-field magnetic susceptibility value is estimated to be 0.33 μ B /T per one substitutional paramagnetic Fe (slope of the black dashed line in Fig. 6). As shown in Fig. 5(a,b), the experimental µ ∂ ∂ M H / ( ) 0 eff values at 5.6 K in samples A and B are 0.08 μ B /T and 0.06 μ B /T, respectively; it follows that the ratios of the substitutional paramagnetic Fe atoms to the total number of substitutional Fe atoms are ~24% (= 0.08/0.33) in sample A and ~18% (= 0.06/0.33) in sample B. Next, we estimate the fraction of substitutional ferromagnetic Fe atoms. The extrapolated M value from the high magnetic field region to H eff = 0 in Fig. 5(a,b)  magnetization. We think that some fraction of these substitutional magnetically inactive Fe atoms couple antiferromagnetically. This is also supported by the weak spin-glass behaviour observed in GeFe at very low temperatures 7 .
We see a similar trend in the temperature dependence of the fitting parameters f SPM and m SPM in both films; i.e., f SPM and m SPM both increase with decreasing temperature (Fig. 7(a,b)). This result implies that the ferromagnetic regions, which form only in the nanoscale high-Fe concentration regions at room temperature [ Fig. 7(c)], expand toward lower Fe concentration regions with decreasing temperature [ Fig. 7(d)], and finally the entire film becomes ferromagnetic at T C [ Fig. 7(e)]. This appears to be a characteristic feature of materials that exhibit single-phase ferromagnetism, despite the inhomogeneous distribution of magnetic atoms in the film 6,7 . As shown in Fig. 7(a,b), f SPM and m SPM are larger in sample B than in sample A, which can be attributed to the difference in spatial fluctuations of the Fe concentration, which are 4-7% in sample A and 3-10% in sample B 6 . The larger the nonuniformity of the Fe distribution is, the larger each local ferromagnetic region, f SPM , and m SPM become, and the local ferromagnetic regions can be more easily connected magnetically, resulting in a higher T C .

Summary.
We have investigated the local electronic structure and magnetic properties of the doped Fe atoms in the Ge 0.935 Fe 0.065 films, which have a diamond-type single-crystal structure without any ferromagnetic precipitates and with nanoscale spatial Fe concentration fluctuations, using XAS and XMCD. The Fe atoms appear in the 2 + state, with the 3d electrons strongly hybridized with the 4p electrons in Ge; this results in a delocalized 3d nature and long-range ferromagnetic ordering, leading to the excellent agreement between the H dependence of magnetization, MCD and XMCD. Using the XMCD sum rules, we obtained the M-H eff curves, which can be explained by the coexistence of SPM and paramagnetic properties at temperatures above T C . The fitting results clearly show that the local ferromagnetic regions, which exist at room temperature, expand with decreasing temperature, leading to a ferromagnetic transition of the entire system at T C . The nonuniformity of the Fe concentration seems to play a crucial role for the formation of the ferromagnetic regions, and our results indicate that strong ferromagnetism is inherent to GeFe, and persists at room temperature. Such a nanoscale expansion of the ferromagnetic regions is a key feature in understanding materials that exhibit single-phase ferromagnetism (i.e., where the film is free from any ferromagnetic precipitates) despite the inhomogeneous distribution of magnetic atoms in the film 6,7,14,15 .

Methods
Sample preparation. The Ge 0.935 Fe 0.065 thin films were grown on Ge(001) substrates by LT-MBE. The growth process is described as follows. After the Ge(001) substrate was chemically cleaned and its surface was hydrogen-terminated by buffered HF solution, it was introduced in the MBE growth chamber through an oil-free load-lock system. After degassing the substrate at 400 °C for 30 minutes and successive thermal cleaning at 900 °C for 15 min, we grew a 30-nm-thick Ge buffer layer at 200 °C, which was followed by the growth of a 120-nm-thick Ge 0.935 Fe 0.065 layer at T S = 160 (sample A) or 240 °C (sample B). After that, we grew a 2-nm-thick Ge capping layer at 200 °C to avoid the surface oxidation of the GeFe layer. The in situ RHEED was used to check the crystallinity and morphology of the surface during the growth. The diffraction pattern of the Ge 0.0935 Fe 0.065 showed intense and sharp 2 × 2 streaks with no extra spots, which indicate a 2-dimensional growth mode and exhibit a diamond-type single-crystal structure. To remove the oxidized surface layer, the samples were briefly etched in dilute hydrofluoric acid (HF) prior to loading into the XAS (XMCD) vacuum chamber.
XAS and XMCD measurements. We performed XAS and XMCD measurements at the soft X-ray beamline BL23SU of SPring-8 with a twin-helical undulator of in-vacuum type 28 . The monochromator resolution was E/ΔE > 10000. The XAS and XMCD spectra were obtained by reversing photon helicity at each energy point and were recorded in the total-electron-yield mode. The XMCD spectra were taken both for positive and negative applied magnetic fields and were averaged in order to eliminate experimental artifacts. Backgrounds of the XAS spectra at the Fe L 2,3 -edge were assumed to be hyperbolic tangent functions.