Nonlocal Interactions in the Double Perovskite Sr 2 FeMoO 6 from Core-Level X ‑ ray Spectroscopy

: The valence electronic structure of the half-metallic double perovskite Sr 2 FeMoO 6 forms from a strongly hybridized band in the spin-down channel of Fe 3d and Mo 4d states that provides metallic conductivity and a gapped spin-up channel. The ground-state description has previously been explored in terms of many-body interactions where local and nonlocal interactions produce states with a combination of a charge-transfer con ﬁ guration and intersite charge ﬂ uctuations. Here, we provide a qualitative understanding on nonlocal e ﬀ ects in Sr 2 FeMoO 6 using a combination of core-level X-ray spectroscopies, speci ﬁ cally X-ray absorption, emission, and photoelectron spectroscopies. Our spectroscopic data indicate intersite Fe 4p − O 2p − Mo 4d interactions to be the origin of these nonlocalized transitions. Close to the Fermi level, this interaction is dominated by Mo 4d − O 2p character. When our data are compared against ﬁ rst-principles electronic structure calculations, we conclude that a full understanding of the nature of these states requires a spin-resolved description of the hybridization functions and that the nonlocal screening occurs predominantly through hybridization in the minority spin channel of the Mo 4d bands.


■ INTRODUCTION
Double perovskite (DP) oxides offer a unique material framework to engineer a wide range of physics with a multitude of functionalities. In its simplest form, the DP structure (A 2 BB′O 6 ) consists of two transition metal (TM) ions interspersed by corner-sharing octahedra that can be arranged in a rock-salt, layered, or columnar order. 1 This means that this type of perovskite oxide can accommodate a range of suitable A-and B-type cations, altering its microscopic interactions and, in turn, dramatically affecting a material's macroscopic properties. More specifically, the choice of the B/ B′ cations can profoundly alter a material's electronic structure, creating materials with desired functionalities ranging from spin-polarized metals to strongly correlated systems, spin− orbit effects, ferroelectricity, and complex magnetic properties, to name a few examples. 2−7 The proximity effects of two separated octahedra of B cations in DP oxides with varying ionic size and valence states produce materials with different structural and electronic characteristics. The electronic and magnetic properties are governed by the spatially extended TM d orbitals and therefore by the balance between bandwidth, crystal-field splitting of the d orbitals, electron−electron correlations, and spin−orbit coupling in 4d/5d elements, making the prediction of DP's properties complex. 1 The interaction between neighboring metal components is simultaneously active and has encouraged research to uncover new fundamental properties as well as materials with properties that can be engineered for use in a range of applications from spintronics to catalysis. 8 One of the most studied materials in this class is the halfmetallic and ferrimagnetic Sr 2 FeMoO 6 (henceforth termed SFMO). 9 It is known to have a purely spin-polarized band structure where only one-spin direction is present at the Fermi level. 9−11 The large room-temperature magnetoresistance is noteworthy for its potential use in spintronic devices based on the high spin polarization of charge carriers. 7,12−15 In the ionic picture, the electronic structure is understood to have a Fe 3+ (3d 5 ) sites as localized with a high-spin S = 5/2 configuration together with Mo 5+ (4d 1 ) sites with one conduction electron that can hop between Mo and Fe sites in the exchange split t 2g orbitals. 16 20 This intricacy arises from the antiferromagnetic coupling between Fe and Mo sites, e.g., unlike the ferromagnetic coupling in manganites. In contrast to manganites like La 1−x Sr x MnO 3 , the strong local coupling in SFMO only applies to every other site since Mo is paramagnetic. 19 Unlike most common half-metals such as Heuslers or manganites, SFMO has a large localized moment associated with the Fe 3d shell and antiparallel moment associated Mo 4d states. Thus, an antiferromagnetic (AFM) exchange interaction results between Fe localized moments and conduction electrons. This relationship of interatomic electronic and magnetic structures and competition between electron localization and hybridization are relevant ingredients in determining a material's Curie temperature and ferromagnetic state. 15 This nonlocal interaction between every other Fe site produces interesting coupling schemes that constitute the basis of this study and relevant to other magnetic perovskite oxides.
In this article, we provide a detailed view of the local and nonlocal Fe energy levels of Sr 2 FeMoO 6 comparison to several Fe-based oxides to show how nonlocal effects are important to understand this material. Core-level X-ray spectroscopic methods are extensively used for studying 3d electrons and their local and nonlocal effects. 21 Nonlocal effects, sensitive to aspects of intersite interactions, leave signatures in the X-ray absorption, emission, and photoemission spectra. Here, we employ Fe K-edge X-ray absorption (XAS) and X-ray emission spectroscopy (XES) to gain valuable information about the spin density of Sr 2 FeMoO 6 and use a partial fluorescence absorption spectrum to reveal features related to this intersite hybridization. The pre-edges region of a K-edge XAS is typically comprised of relatively low-intensity structures due to weak 1s → 3d quadrupole transitions. For Sr 2 FeMoO 6 , this feature has larger intensity when compared with other similar oxide perovskites where Fe 3+ remains octahedrally coordinated by O 2 − ions. We furthermore find that hard X-ray photoemission spectroscopy (HAXPES) for the Fe 2p core-level spectra show structures characteristic of nonlocal screening channels. Calculations from local density approximation (LDA) with density functional theory (DFT) can explain these features by examining the hybridization potential function which can be used to investigate the amount and intensity of hybridized Fe 3d−O 2p−Mo 4d states, especially near the Fermi level.

■ EXPERIMENTAL SECTION
Polycrystalline Sr 2 FeMoO 6 , α-Fe 2 O 3 , and LaFeO 3 pellets were prepared by conventional solid-state synthesis as described in ref 22. SrCO 3 is preheated at 150°C to remove any absorbed water. The stoichiometric mixture of highly pure SrCO 3 , α-Fe 2 O 3 , and MoO 3 is first heated at 900°C for 12 h for calcination. The obtained powder is then annealed to 1500°C in a reducing atmosphere 98% Ar/2% H 2 gas for 12 h. The powder was finally pressed to 5 GPa to form a 5 mm diameter pellet and subsequently sintered for 6 h at 1500°C. Polycrystalline Ca 2 FeReO 6 was prepared by solid-state reaction as previously reported. 23 The phase purity and ordering were checked by laboratory X-ray diffraction (PANanalytical MRD II). The X-ray diffraction pattern was indexed with the (111) and (311) Bragg peaks that are due to the alternating order of the Fe and Mo sites. The sample is highly ordered, and no impurity peaks are found in the XRD pattern.
X-ray absorption and emission measurements at the Fe Kedge edge were performed at the CLAESS beamline 24 of the ALBA Synchrotron (Barcelona, Spain) using a Si (311) double-crystal monochromator. The spectra were recorded by monitoring the emission of the Kβ 1,3 (≈ 7058 eV) or Kβ′ (≈ 7045 eV) emission lines and scanning the incoming energy across the Fe K-edge absorption edge. The Fe fluorescence energy was selected by using a Si (333) dynamical bent diced analyzer crystal and an energy dispersive one-dimensional (1D) detector in Rowland circle geometry (Rowland radius = 1 m). The overall energy resolution was determined to 0.8 eV from the full width at half-maximum (fwhm) of the quasielastic peak collected from a Kapton tape. The spectrometer energy window around the Fe Kβ 1,3 emission line window was 15 eV. Spin-selective high-resolution fluorescence detected Xray absorption (HERFD-XANES) was acquired by selecting Kβ 1,3 and Kβ′ fluorescence lines, which correspond to final states with the unpaired spin in the 3p shell either parallel or antiparallel to the unpaired spin in the 3d shell. 25 Our fitting procedure is applied in the range 7110−7119 eV with Gaussian peaks whose widths are constrained to the experimental resolution. The background was fitted by using an arc-tangent function having a fwhm of ∼1.8 eV and a centroid energy of ∼7120 eV to account for the leading edge of the intense dipolar transition. Oxygen K-edge XAS were measured at the 8.0.1 beamline 26 at the Advanced Light Source (Berkeley, CA). The X-ray absorption spectrum was acquired in both total electron yield (TEY) and total fluorescence yield (TFY) modes at room temperature and under a high vacuum of 10 −10 mbar. Spectra obtained by TEY and TFY were qualitatively similar. Oxygen K-edge XAS data were calibrated by using the offset determined from the TiO 2 O K-edge.
Hard X-ray photoelectron spectroscopy measurements were performed at the P22 beamline 27 of the PETRA-III synchrotron in Hamburg, Germany. The incident photon energy was set to 4750 eV. The Fermi level was calibrated by using a clean Au foil in contact with the sample holder. The overall instrumental resolution was set to 300 meV. The photoelectrons were collected by using a SPECS 225 HV hemispherical analyzer at a near normal emission geometry with the incident X-ray at a 15°angle to the sample. The pressure in the main chamber was ∼10 −10 mbar, and measurements were carried at room temperature (300 K).

■ COMPUTATION DETAILS
The density functional theory (DFT) calculations are performed in the generalized gradient approximation + Hubbard U (GGA+U) approach by means of a full potential linearized muffin-tin orbital method (FP-LMTO) 28,29 as implemented in the RSPt code. 30 The Brillouin-zone (BZ) integration is performed by using the thermal smearing method with 10 × 10 × 10 k-mesh which corresponds to 144 k-points in the irreducible part of the BZ. For the charge density and potential angular decomposition inside the MT spheres, the value of maximum angular momentum was taken equal to l max = 8. To describe the electron−electron correlation within the GGA+U approach, we have used U = 3 eV and J = 0.8 eV for Fe d states. We note that our choice of U is guided by the recent study where such values of correlation The Journal of Physical Chemistry C pubs.acs.org/JPCC Article parameters were used to study SFMO in the GGA+U framework. 31 After self-consistency is achieved, we used the spin-polarized GGA+U solution to compute the energy-dependent hybridization function Δ(E) of Mo and Fe d orbitals. If G 0 is the site projected Green's function obtained from DFT and H is the hybridization-free impurity Hamiltonian, with the corresponding energy E QI , one obtains the following form of the hybridization function, Δ(E), via the Dyson equation: The preceding expression is used to compute the hybridization function from our converged DFT calculations. In a quantum impurity model, Δ(E) gives the properties of the bath surrounding the impurity cluster and thus describes the interaction of an impurity electron (in our case, d-electrons of either Fe or Mo ions) with the bath consisting of all other electrons.

■ RESULTS AND DISCUSSION
The spin sensitivity in Kβ XES (3p → 1s) stems from the exchange coupling between unpaired 3p and unpaired 3d electrons. Via this coupling, the XES process provides an indirect probe of the local magnetic moment at the Fe 3d site and is therefore sensitive to the Fe spin state. 32,33 Figure 1 shows the Kβ XES spectrum taken at an incident energy of 7300 eV, far above the Fe K-edge absorption threshold. As mentioned above, the splitting of the Kβ into the Kβ 1,3 line and Kβ′ originates from an exchange coupling between electrons in the 3d shells and a hole in the 3p shell. As is now established, the Kβ spectral shape and intensity are sensitive to the local spin state of the Fe ion and is more quantitatively estimated by comparing with references through the integral absolute difference (IAD) method. 34,35 From our IAD calculations, Sr 2 FeMoO 6 shows a high-spin S = 2.5, an assignment similar to that of hematite (α-Fe 2 O 3 , S = 2.5) and LaFeO 3 (S = 2.5). Fe in both SFMO and LaFeO 3 systems resulted in a high-spin configuration, with five unpaired electrons occupying the 3d levels. The inset shows the relative variation of determined magnetic moment and IAD values plotted as a function of references and SFMO, where qualitatively similar trends are observed. We see that IAD depends linearly formal Fe valence and tracks with the experimental magnetic moment. One can separate the Kβ X-ray emission spectrum into an internally referenced spin-up and spin-down channels to obtain a local-spin selectivity in the K-edge absorption spectrum. 36−38 This is based on measuring partial fluorescence absorption spectrum by setting the emission energy selectively to either Kβ 1,3 or Kβ′ satellite lines that are sensitive to the local 3d moment. 25 The Kβ 1,3 emission line leaves the final state with a spin-down reference in the 3p state, and Kβ′ with a final state with a spin-up 3p state, as shown schematically in Figure 2a. Figure 2b shows the pre-edge region for spin-selective XANES spectra measured for Kβ 1,3 (spin-down) and Kβ′ (spin-up) lines for SFMO; the inset shows the full energy range. Figure  2b clearly shows a distinct pre-edge feature for the spin-down channel that is absent for the spin-up channel. This is a direct consequence of the high-spin configuration of SFMO 3d 5 (S = 2.5) as determined from our Kβ XES analysis discussed previously. Therefore, we expect only spin-down intermediate states to be available in the 1s → 3d transitions. This interpretation shows evidence for a purely spin-down band in SFMO's ground-state electronic structure.
The Fe K-edge 1s → 3p resonant X-ray emission (RXES) map for SFMO and related Fe 3+ oxides is measured as the incident energy and emitted energy are varied, yielding a twodimensional spectral surface as shown in Figure 3. The diagonal cut in a RXES map corresponds to the so-called high energy resolution fluorescence detection (HERFD) spectrum recorded as a partial fluorescence yield. In Figure 4a, we show HERFD spectra for SFMO and reference Fe 3+ oxides, obtained at the Kβ 1,3 emission line. The partial yield spectrum shows better resolved spectral features compared to Fe K-edge conventional XANES, 39 particularly in the pre-and near-edge range. The absorption spectrum is referenced against FeO  Although these references have different crystal structures, the local atomic coordination is also octahedral. We observe that the absorption edge shifts to higher energies for the Fe 3+ compounds as expected and reported previously for Fe oxides. 40 The pre-edge structure also evolves in spectral shape and intensity between Fe reference oxides and SFMO (Figure 4b  inset). SFMO exhibits two main pre-edge structures centered near 7115 and 7120 eV. These features are attributed to quadrupolar (1s → 3d) and dipolar (1s → 4p) transitions, resulting in overlapping lines, and therefore single transitions cannot be easily distinguished. However, general trends can be observed based on the intensity and energy position. The first pre-edge feature is assigned to a 1s → 3d quadrupolar transition that is localized at the Fe absorbing atom. 41 More than one feature can be identified in this energy range because of the splitting of the 3d orbital energy levels. In the crystal-field picture, the quadrupolar prepeak intensity distribution change systematically with spin state, oxidation state, and local geometry. 42 Because of differences in crystallographic symmetry, it is only appropriate to compare the pre-edge of structures of LaFeO 3 and SFMO, as FeO and α-Fe 2 O 3 assume rock-salt and corundum crystal structures, respectively. As shown in the bottom panel of Figure 3b, two well-resolved preedge features can be distinguished for LaFeO 3. They correspond to local quadrupolar 1s → 3d transition into unoccupied t 2g and e g states, although they have been suggested to carry some O 2p character as reported in previous studies, 25 . 43,44 The splitting of the two pre-edge peaks for LaFeO 3 is 1.53 eV, which correspond to the crystal-field splitting of 1.50 eV as reported by Haas et al. 43 For SFMO, we find that three peaks are necessary for a reasonable fit of the Fe K pre-edge. The first two features, labeled Peaks 1 and 2 in Figure 3b, are separated by 1.23 eV and can be readily accounted as transitions to crystal field split t 2g and e g states,  respectively, which is close to the crystal-field splitting of 1.25 eV from our calculations. The third pre-edge feature, centered at 7115.9 eV labeled Peak 3, is compatible with a mixture of quadrupolar and a dipolar transition that involve a neighboring Mo site. 41 In transition metal oxides, dipolar contributions in the preedge can also arise from transitions to neighboring d states that are mediated via bridging oxygen through intersite Fe (4p)−O (2p)−Mo (4d) 25,41,45 hybridized states. Similar nonlocal features have also been identified in manganites 46 and cobaltites. 35 We support this interpretation by analyzing the calculated partial density of states (PDOS) that are separated into spin-up and spin-down contributions as shown in Figures 4c and 4d. The Fe d PDOS, shown in Figure 4d, shows a sizable intensity in the unoccupied region of the spin-down channel around 1 eV above the E F that defines the local quadrupolar 1s → 3d transitions. The PDOS of Fe p orbitals furthermore shows structures for both spin directions at about 4.5 eV above the Fermi level, which could correspond to the absorption feature shown around 7120 eV. Similar structures are also observed in the PDOS of Mo d states at the same position of energy axis, implying hybridization between Mo d orbitals and Fe p orbitals. Moreover, the spin-down Fe d PDOS shows a relatively small intensity around 2 eV above E F that most likely correspond to the "Peak 3" intrasite transition for SFMO with oxygen mediated intersite mixing between Fe p state and adjacent neighbor Mo d state. In fact, concomitant Fe p and Mo d (spin-down) DOS are present at the same energy. The small Fe PDOS character explains the relative enhanced absorption feature intensity.
Recent studies using hard X-ray photoemission have shown features in core-level spectra of transition metals oxides which are consistently explained in terms of well-screened peaks. 50,51 With its increased probe depth, HAXPES measurements show true bulk electronic structure and reveal satellite features and screening effects due to the large probing depth otherwise not straightforward from soft X-rays. The inclusion of additional nonlocal screening channels has been shown to be useful for understanding the 2p photoelectron spectra of NiO, 52 cuprates, 53 ruthenates, 54 and manganites. 55 Although there are several reports on the Fe 2p core levels for SFMO, 56,57 measurements at high X-ray photon energies have yet to be reported to the best of our knowledge, particularly for the description of local and nonlocal features. Figure 5a shows the Fe 2p hard X-ray photoemission spectra along with reference Fe oxides. The Fe 3+ reference α-Fe 2 O 3 , LaFeO 3 , and Ca 2 FeReO 6 compounds show two main-line peaks that are due to spin−orbit split Fe 2p core levels. For each spin−orbit component, there are also high binding energy (E B ) satellite features denoted as S1 and S2 in Figure 5a. These features have been previously assigned to charge-transfer (CT) structures that are dominated by c3d 5 and c3d 6 L final states configurations, 58,59 where c and L denote a core hole and L a hole in the nearest ligand.
The SFMO Fe 2p HAXPES is characterized by broader main lines including a low binding energy contribution that are indicated by dashed arrows in Figure 5a. Low-E B features in correlated oxides have varying explanations including a holedoped bound state interaction like those in NiO, 52 a coherent metallic band formation in vanadates, 60 and magnetic transitions. 61 We exclude the broadening of the Fe 2p main line due to hole doping at the Fe site, 62,63 but rather due to the formation of a nonlocal metallic band with Mo 4d and O 2p character. This conclusion is supported from the hybridization function presented in Figure 5b, which shows very little contribution from Fe d states close to E F . This observation is further corroborated by considering the asymmetric broadening of the O 1s photoemission line shape (see Figure S1b), which are common to systems with metallic screening. 64 The HAXPES binding energy position for SFMO O 1s is 529.1 eV, exactly matching the absorption threshold in the O 1s XAS spectrum of 529.0 eV, reflecting the empty oxygen 2p states at E F . We therefore suggest that this line-shape change is due to delocalized states with considerable O 2p−Mo 4d hybridization. We exclude the lower binding energy features due to contributions from a lower valence such as Fe 2+ or Fe 0 , since the existence of such species would be detected with appreciable shifts from the measured Fe K absorption and emission spectra. Consequently, we attribute these low binding energy features at approximately 706 and 708 eV (indicated by The Journal of Physical Chemistry C pubs.acs.org/JPCC Article arrows in Figure 5a) to screening from hybridized Fe 3d−O 2p−Mo 4d valence states that screen the photoexcited Fe. From previously reported double cluster calculations on SFMO, 20 the ground state was reported to be described by a mixed character of ionic 3d 5 as well as locally screened 3d 6 L and nonlocal 3d 6 v configurations, where v represent a hole in the valence band. The nonlocal screening involves an oxygen mediated Fe 3d−O 2p−Mo 4d hybridization. This configuration interaction picture has merit due to the strong nonlocal character of the ground state of SFMO. Nonlocal screening has been successfully discussed in terms of the energy-dependent hybridization function in correlated systems. 51,65 The hybridization function encodes orbital and spin interactions and is composed of distance-shell contributions. 65,66 The larger the magnitude of hybridization function, the larger the overlap of that orbital with all other orbitals. The spin-resolved hybridization function is shown in Figure 5b. The intensities from 2 to −2 eV for Mo d corresponds to hybridized delocalized Mo 4d bands. The intensity is rather strong for Mo minority d states close to the E F , largely attributable to the stronger amplitude of an indirect Fe−O− Mo hopping term, i.e., the conducting minority spin channel. This gives merit to a ground-state configuration with a hole in the valence band (3d 6 v) that tracks its origin to the spin-down Mo d band validating nonlocal effects in SFMO. We note that the hybridization function of Mo d majority states does not show any strong feature close to the Fermi level. The hybridization strength at E F that are prominent for Mo d bands shown in Figure 5b are responsible for the width and shape of the Fe 2p low-E B features. The hybridization function being the main indicator of itinerancy and localization, our results illustrate the significance of analyzing spin-resolved character of the Mo d bands for understanding the nonlocal effects in SFMO.

■ CONCLUSIONS
We have investigated the electronic structure properties of SFMO through several hard X-ray core-level spectroscopies. Our study provides direct support for nonlocal effects in SFMO. From Fe K-edge absorption and emission, we find that SFMO exhibits a high-spin 3d 5 configuration with a nominal spin density of S = 2.5, similar to its trivalent Fe 3+ analogues. Fe K-edge HERFD-XANES in SFMO shows a broad pre-edge structure that is a convolution of quadrupolar and dipolar peaks, one of which can be linked to an excitation in an intersite Fe 4p−O 2p−Mo 4d band. The spin-selective HERFD-XANES spectra show pre-edge features that are characteristics of spin-polarized properties of SFMO. Hard X-ray photoemission for the Fe 2p core-level show several structures in the low-E B region that are highly probable of a nonlocal screening channel from an electron near the Fermi level. This nonlocal screening can effectively be tied to the strong hybridization density from the Mo 4d band, a consequence of optimal near-collinear Fe−O−Mo lattice geometry in SFMO. Our results point to a strong relationship between localized and nonlocalized character in SFMO that leads to its large T C and high spin polarization. These results highlight the significance of nonlocal charge interactions in mediating a large exchange coupling strength (J) between Fe and Mo, where T C is maximized. This combined approach of hard X-ray core-level spectroscopy techniques with theoretical simulations that include intersite effects is very useful to gain insights into double perovskite oxides and correlated systems in general. We hope our results advances the fundamental understanding of intersite physics in magnetic oxides that can lead to new directions in spintronic applications.