Magnetism in Re-based ferrimagnetic double perovskites

We have investigated spin and orbital magnetic moments of the Re 5d ion in the double perovskites A2FeReO6 (A = Ba, Sr, Ca) by X-ray magnetic circular dichroism (XMCD) at the Re L(2,3) edges. In these ferrimagnetic compounds an unusually large negative spin and positive orbital magnetic moment at the Re atoms was detected. The presence of a finite spin magnetic moment in a 'non-magnetic' double perovskite as observed in the double perovskite Sr2ScReO6 proves that Re has also a small, but finite intrinsic magnetic moment. We further show for the examples of Ba and Ca that the usually neglected alkaline earth ions undoubtedly also contribute to the magnetism in the ferrimagnetic double perovskites.

We have investigated spin and orbital magnetic moments of the Re 5d ion in the double perovskites A2FeReO6 (A = Ba, Sr, Ca) by X-ray magnetic circular dichroism (XMCD) at the Re L2,3 edges. In these ferrimagnetic compounds an unusually large negative spin and positive orbital magnetic moment at the Re atoms was detected. The presence of a finite spin magnetic moment in a 'nonmagnetic' double perovskite as observed in the double perovskite Sr2ScReO6 proves that Re has also a small, but finite intrinsic magnetic moment. We further show for the examples of Ba and Ca that the usually neglected alkaline earth ions undoubtedly also contribute to the magnetism in the ferrimagnetic double perovskites. Ordered double perovskites of the composition A 2 M N O 6 (with A an alkaline earth, M a magnetic transition metal ion, and N a non-magnetic ion) have come again into the focus of research because of their interesting magnetic properties. First, in Sr 2 FeMoO 6 a large room-temperature magnetoresistance was observed [1]. Second, within the group of ferrimagnetic double perovskites materials with higher Curie-temperatures, T C , than in the simple perovskites (e.g. doped manganites) can be obtained. At the moment the highest T C values have been reported for Sr 2 CrReO 6 (T C ≈ 635 K) [2,3,4] and Sr 2 CrOsO 6 (T C ≈ 725 K) [5,6,7]. Third, the mechanism leading to magnetic coupling is believed to be associated with a strong tendency to a half-metallic nature of the charge carriers at the Fermi level [8,9,10]. Clearly, these materials are interesting candidates for spintronic applications [11], in particular when having in mind fully epitaxial structures based on perovskite materials.
Recently, Majewski et al. and Sikora et al. have proposed a simple scaling law between the Curietemperature and the induced magnetic moment at the non-magnetic site in the double perovskite structure [4,12,13]. Philipp et al. have discussed that a high Curie-temperature is associated with a tolerance factor close to one for the corresponding crystal [14]. The only exception for this rule is found in the series A 2 FeReO 6 (A = Ba, Sr, Ca). In this particular FeRe-system it is the strongly monoclinically distorted Ca-based compound having an anomally high T C , namely about 540 K [15,16,17] (comparing to about 400 K for Sr 2 FeReO 6 [16] and 325 K for Ba 2 FeReO 6 [18,19]). The dimen- * Electronic address: alff@oxide.tu-darmstadt.de sionless tolerance factor, f , in A 2 FeReO 6 whose deviation from unity implies structural distortion varies from about f = 1.057 for A = Ba over f = 0.997 for A = Sr to f = 0.943 for A = Ca [14]. In general, the Ba-based ferrimagnetic double perovskites are close to a structural transition into a hexagonal lattice where ferro(i)magnetism is not allowed for symmetry reasons; the Sr-based compounds are always close to a perfect cubic structure with maximal T C , and the Ca-based double perovskites are orthorhombically or monoclinically distorted, with still a large but -due to the reduced exchange -clearly reduced ferrimagnetic transition temperature. The exceptional large T C of Ca 2 FeReO 6 is accompanied by an insulating state at low temperatures, in contrast to Sr 2 FeReO 6 or even the similarly monoclinically distorted Ca 2 FeMoO 6 which both are metallic [20]. The metal-insulator transition in Ca 2 FeReO 6 has been reported to occur between 100 and 150 K [15,16,20]. This behavior has been attributed to strongly enhanced electron-electron correlations on the Re site due to a reduced transfer integral between Fe and Re corresponding to an extremely large effective Coulomb repulsion, U eff , of about 4 eV on both ions [20]. This, however, is in some contradiction to the observed high Curie-temperature, which is believed to be a consequence of a kinetic energy gain due to the hybridization of the Fe 3d and Re 5d t 2gorbitals. The prediction that a decreased band-filling is favorable for T C [21], which could be used to conciliate a high T C with a reduced Re-Re overlap, has turned out to be not valid: an increased band-filling actually leads to a strong T C enhancement for both the FeMo-system [22] and the CrW-system [23]. Within the kinetically driven exchange model [8,9,10], the increase of T C is more naturally explained as a consequence of increased band-filling. Note, that the cases of Ca 2 FeReO 6 and Sr 2 CrOsO 6 , both being insulating and having a high T C at the same time, are completely different: In the case of Sr 2 CrOsO 6 having Table I: Summary of sample properties from x-ray diffraction at 300 K (calculated by Rietfeld-refinement) and SQUID magnetometry.
only a tiny rhombohedral distortion, the Os 5d t 2g band is completely filled, while for Ca 2 FeReO 6 it is the structural distortion that drives the metal-insulator transition. Recently, it was suggested that in double perovskites with heavy ions as Re a large orbital contribution to the magnetic moment leads to an enhanced total magnetization above the integer value that is expected for a half-metallic material [25]. This elsewhere predicted and calculated [26] strong influence of spin-orbit coupling leads to a quasi-half metallicity which still is from the view point of applications in spintronics very high (above 90%). Another point of interest is the possibility of an intrinsic enhancement of the Re spin magnetic moment due to the peculiar Re 5+ state in the ferrimagnetic double perovskites. In this study, we present the XMCD analysis of the system A 2 FeReO 6 (A = Ba, Sr, Ca), compare the experimental data to theoretical predictions calculated within the full-potential linear muffin-tin orbital method (FP-LMTO) [27] with included spin-orbit coupling, and complete the so far suggested scaling law [4] by using the identical method to extract separately spin and orbital magnetic moments. Furthermore, we search for a contribution of the alkaline earth element to the magnetic behavior, and also look for an intrinsic Re moment in a suited double perovskite compound with M being a non-magnetic ion: Sr 2 ScReO 6 .

II. EXPERIMENTAL
A summary of the sample properties is given in Table I. All values where a comparison can be made to literature values are in good agreement with these data [2,15]. Note that the small amount of antisite disorder does not affect our results. The XMCD measurements on the Re L 2,3 edges were performed at the European Synchrotron Radiation Facility (ESRF) at beam line ID12 [29]. The spectra were recorded within the total fluorescence yield detection mode. The XMCD spectra were obtained as direct difference between consecutive XANES scans (X-ray Absorption Near Edge Spectrum) recorded with opposite helicities of the incoming x-ray beam. To ensure that the XMCD spectra are free from any experimental artefacts the data were collected for both directions of the applied magnetic field of 6 T (parallel and antiparallel to the x-ray beam). The degree of circular polarization of the monochromatic x-ray beam was 98%. The measurements were performed at about 10 K for all samples (T ≪ T C ), if not indicated otherwise. Since the samples measured in backscattering geometry were very thick, the spectra were first normalized to the edge jump of unity and then corrected from self-absorption effects. The edge jump intensity ratio L 3 /L 2 was then normalized to 2.19/1 [30]. This is different from the statistical 2:1 branching ratio due to the difference in the radial matrix elements of the 2p 1/2 to 5d(L 2 ) and 2p 3/2 to 5d(L 3 ) transitions. The XMCD measurement as a function of applied field suggests that our samples are closer to saturation at 6 T as is concluded by de Teresa at al. [25] from high-field SQUID measurements. This issue has to be clarified in future by high-field XMCD measurements.

III. RESULTS AND DISCUSSION
In this paper, the XANES spectra themselves are not further discussed. As shown in Fig. 1, for FeRecompounds at both absorption edges we find a rather intense XMCD signal. This is a clear evidence for the existence of a magnetic moment at the Re 5d shell. For all three compounds, the XMCD spectra at the L 2 edge are largest (as expected for m = 1 orbitals) and similar in shape. In Ca 2 FeReO 6 the size of the XMCD signal is by a factor of 2 smaller compared to the two other FeRe compounds. At the L 3 edge, the Ca-based double perovskite again stands out by a pronounced peak with negative XMCD signal which is absent for Sr 2 FeReO 6 and Ba 2 FeReO 6 . The data at the L 3 edge look slightly different in amplitude as compared to previously published data [13]. However, the data are consistent in that the integrated XMCD intensity at the L 3 edge is negative only in the case of Ca 2 FeReO 6 . In this sense, all data support the unusual behavior of Ca 2 FeReO 6 , which cannot only be attributed to the different ionic size of the Table II: Measured (exp., normalized to 5 K) and calculated (th., calculated within the generalized gradient approximation including spin-orbit coupling (GGA+SO)) magnetic moments at the Re site for different double perovskites at about 10 K. For a detailed discussion of the applied band-structure calculation see e.g. [26,28]. Calculation in [31] is GGA with spin-orbit coupling. The number of d-holes was taken from the band-structure calculation. In our case this number was around 5.3. The error of the measured values is estimated as 2.5%.  A site ions.
In Fig. 2 we show XANES and XMCD spectra for the compound Sr 2 ScReO 6 . This compound is important because the absence of any free electrons at Sc 3+ which has a 3d 0 configuration will lead to a complete breakdown of the induced magnetic moment at the Re site. This compound therefore allows the measurement of the intrinsic magnetic moment of Re 5+ (also in contrast to Re 6+ compounds as Sr 2 MgReO 6 ). Previously, Kato et al. have calculated from a Curie-Weiss fit to the susceptibility an effective magnetic moment of Re in Sr 2 ScReO 6 of about 1.1 µ B /f.u., as expected within the ionic picture [32]. In contrast, our data show the existence of a much smaller, but finite intrinsic moment at the Re site, indicating an increased tendency to magnetic ordering of Re 5+ . Since this moment is present above the antiferromagnetic transition temperature, it is not related to spin glass behavior. The spin magnetic moment is about 50 times smaller than corresponding induced moments on Re 5+ , and the orbital magnetic moments even by a factor of 100. However, due to the high sensitivity of the set-up at ESRF, one can unambiguously prove the existence of this moment. In contrast to the opposite sign of the induced magnetic moment with respect to the applied field, the spin magnetic moment at the Re in Sr 2 ScReO 6 is aligned with the field. This is expected because the kinetic exchange via fully polarized spin down is not at work. This intrinsic moment of Re 5+ therefore has to be considered as an indicator of the tendency to unusually high magnetization of Re based double perovskites.
As a last point, we address magnetism in the earth alkaline ions itself, which usually are completely neglected in the magnetic scenario. The XANES and XMCD spectra of the Ba L 2 and L 3 edges of Ba 2 FeReO 6 and of the Ca K-edge of Ca 2 FeReO 6 are shown in Fig. 3. The 5d spin magnetic moment (calculated with 9 as the number of d-holes corresponding to the band-structure calculation) of Ba is µ S = −0.0065 and the 5d orbital magnetic moment µ L = −0.0013 (both in µ B /f.u.), |µ L /µ S | ≈ 0.2. The theoretical predictions calculated as described elsewhere [26,28] are µ S = −0.0084 and µ L = −0.0014 which is in fair agreement with our experimental data. For Ca 2 FeReO 6 we can only qualitatively say that a finite magnetic moment is observed, because the K-edge probes only the 4p orbital magnetism. Since the L edges are experimentally not accessible, a quantative analysis cannot be done. The observation of a magnetically polarized density of states gives clear evidence for a magnetic interaction of the earth alkaline ions with the other ions. The magnetic contribution of Ba in this case is a factor of 2 smaller than the contribution of the intrinsic Re moment. Naturally, one expects that the magnetic con-tribution increases with ionic size due to the increased exchange with the neighboring ions. The clear orbital contribution in Ba 2 FeReO 6 is not unexpected due to the heavy ionic mass. Our data provide a test for a detailed theoretical study of the magnetism in the double perovskites, and underlines the importance of taking spinorbit coupling into account. Note, that for example in CrO 2 , where the importance of oxygen in the magnetic mechanism is undoubted, comparable values of spin and orbital moments of the oxygen ion have been measured [33] as compared to our results on Ba in Ba 2 FeReO 6 .
In Table II we summarize our results for the spin and orbital magnetic moments at the Re site as derived from the XMCD measurements by applying the standard sum rules [34,35] and compare them to theoretical values. Also, the ratio | m L /m S | is calculated, since this quantity is not affected by possible uncertainties in the calculated number of holes. In general, the calculated data are in surprisingly good agreement with the measured data. One of the main reasons certainly is, that spin-orbit coupling is taken into account from the beginning. Note, that in the hard x-ray range the sum rules apply with high validity due to the large spin-orbit splitting of the core level.
Let us finally discuss again our data for the three FeRebased compounds. Our data are in good qualitative and quantitative agreement with literature data with one exception: Ca 2 FeReO 6 . While Sikora et al. [13] find, that the spin magnetic moment of Re in Ca 2 FeReO 6 scales with the high T C , in our case it has the lowest spin magnetic moment, letting Ca 2 FeReO 6 stand out from the scaling law [4,12,13] which so far holds in all other cases. This behavior is certainly more natural, since one expects that a reduced exchange will also lead to a reduced spin magnetic moment on the Re site. Note that the ratio of orbital and spin magnetic moments are consistent with the previous data. As suggested previously by Kato et al. [16], a Re t 2g orbital ordered state or its glass-state analog associated with the monoclinic lattice distortion occurs, pointing out the importance of correlation effects in this compound. Recently, Sikora et al. [36] proposed a scenario with a complex competition between two phases with different electronic and crystallographic structure. Our data give further indication that Ca 2 FeReO 6 is exceptional among the double perovskites due to the strong octahedral-site distortions.

IV. SUMMARY
In summary, we have elucidated the Re magnetic moments in the FeRe-based series of double perovskites as a function of the earth alkaline ion, confirming the exceptional position of Ca 2 FeReO 6 . We have measured a finite intrinsic magnetic moment at the Re 5+ site in Sr 2 ScReO 6 indicating the tendency to enhanced magnetic moments observed in Re based double perovskites. Furthermore, for the first time we were able to measure by XMCD the magnetic moments directly at the alkaline earth site itself. Our result shows that the usually neglected Ca and Ba ions play a role in the magnetic scenario of the kinetically driven exchange model, comparable in size to the role of oxygen.