Many-body effects and non-local charge fluctuations in the double perovskite Sr2FeMoO6

We studied the electronic structure of Sr2FeMoO6 using core level and valence band photoemission. The spectra were obtained using high energy X-rays of 1840 eV, which provide bulk sensitive information on the electronic structure. The experimental data were analyzed using the spectral weight from cluster model calculations. The ground state reveals a large Fe–O and Mo–O hybridization, as well as the importance of non-local Fe–O–Mo charge fluctuations. The latter is crucial to explain the half-metallic character attributed to the Sr2FeMoO6 compound. The core level and valence band photoemission spectra show charge transfer satellites. These satellites are related to many-body effects and are larger for the Fe levels than for the Mo states.


Introduction
The Sr 2 FeMoO 6 (SFMO) double perovskite presents very interesting physical properties. 1,2 The crystal structure of this compound is tetragonal with a ¼ 5.557Å and c ¼ 7.887Å. This material is a half-metallic ferrimagnet with an ordering temperature of T C ¼ 420 K. The magnetic moment, up to m ¼ 3.7 m B , depends on the degree of Fe/Mo cationic disorder. 3 The SFMO oxide exhibits a considerable magneto-resistance (MR) at room temperature. The accepted MR mechanism involves tunneling across grain boundaries. For these reasons, this compound is being considered for applications in spintronic devices. More details on the SFMO double perovskite can be found in recent reviews. [4][5][6] The electronic structure of SFMO was studied using a variety of spectroscopic techniques, which aimed at understanding the microscopic origin of its physical properties. 7 The optical conductivity conrmed the half-metallic character of the SFMO compound. 2 The core-level X-ray photoelectron spectra (XPS) determined the chemical shis of the Fe/Mo ions. 8,9 The valence band X-ray photoemission spectra (PES) elucidated the electronic states at the Fermi level. [10][11][12] The X-ray absorption spectra (XAS) was utilized to investigate the Fe/Mo valencies. 9,11,13 The X-ray emission spectra (XES) provided site selected information on the electronic structure. 14 Finally, the magnetic circular dichroism spectra (MCD) was used to study the Fe/Mo magnetic moments. 13,15 In an ionic approximation, the electronic structure of SFMO can be viewed as a combination of Fe 3+ (3d 5 ) and Mo 5+ (4d 1 ). 1,2 However, the Fe 3d and Mo 4d electrons present a covalent hybridization with the O 2p states. 12 Further, the majority Fe 3+ (3d 5 ) electrons are localized, whereas the minority Mo 5+ (4d 1 ) electron is itinerant, which is consistent with both the halfmetallic conductivity and the ferrimagnetic ordering of SFMO. The valence band spectra of SFMO were compared to diverse density functional theory (DFT) methods. The agreement with the experiment improves if one includes in the calculation the Mott-Hubbard U. 10,11 The values of U used in the LDA + U approach at the Fe sites are relatively large, about U ¼ 2-4 eV. Based on these values, Kuepper et al. concluded that the electronic structure of SFMO was highly correlated. 14 In particular, the valence band spectra of this oxide might present distinct many-body effects beyond the DFT description.
We studied the electronic structure of SFMO using a cluster model approach, [16][17][18][19] which consists of two FeO 6 and MoO 6 octahedra which are either connected (double cluster model) or not (single cluster model) by one corner O atom. This method includes both the Fe 3d-O 2p and Mo 4d-O 2p hybridization, as well as the Mo-O-Fe charge uctuations in the FeO 6 -MoO 6 double cluster. The electronic structure is calculated using the conguration interaction approach, 17 which includes many relevant correlation effects within the double cluster. The calculations are compared to the core level and valence band spectra of SFMO. Finally, the experimental spectra were obtained using bulk sensitive high-energy X-rays.

Experimental details
The ceramic Sr 2 FeMoO 6 sample was prepared using the solidstate reaction method. The corresponding reagents were mixed and calcined in air at 950 C for 24 h. The resulting powder was pulverized, mixed and red again several times. The reduction of the powder was carried out in a owing mixture of 1% H 2 -Ar gas at 1050 C for 1 h. Finally, the substance was ground, pressed into pellets, and sintered in a vacuum for 12 h at 1200 C. The powder XRD analysis conrmed that the sample was a single-phase material. The Rietveld renement showed a tetragonal I4/mmm structure with the aforementioned parameters. The relative intensity of the (101) reection indicated a highly ordered sample with less than 3% cationic disorder. 3 The photoemission measurements were performed at the SXS beamline at the Laboratório Nacional de Luz Síncrotron (LNLS) in Campinas (Brazil). 20 The photon energy scale of the monochromator was calibrated using the Si K absorption edges. The photoemission spectra was taken using a SPECS Phoibos 150 electron energy analyzer; the energy scale of the analyzer was calibrated using a clean gold foil. All the spectra presented here were taken at room temperature with a photon energy of 1840 eV. The base pressure in the UHV experimental chamber was in the low 10 À9 mbar range. The pellets were thoroughly scraped with a diamond le to remove the surface contamination. The core level Fe 2p and Mo 3p spectra presented here are new, whereas the valence band spectrum was already presented in a previous study. 21

Calculation details
The electronic structure of Sr 2 FeMoO 6 was calculated using a double cluster model, composed by an FeO 6 and a MoO 6 octahedra sharing a corner O atom. The double octahedra considered here is represented schematically in the top panel of Fig. 1. The double cluster model was solved using a symmetryadapted conguration interaction method. 16,18 The Fe 3d and Mo 4d orbitals are split by crystal eld effects into t 2g and e g symmetries. The symmetry-adapted combination of orbitals with a local t 2g and e g character are depicted in the bottom panel of Fig. 1. The t 2g combination is crucial to describe the minority Fe-O-Mo delocalized electron, which is related to both the halfmetallic and ferrimagnetic character of Sr 2 FeMoO 6 .
In a rst ionic approximation, the transition metals ions in Sr 2 FeMoO 6 are in a 3d 5 4d 1 state. 22 The ground state is expanded in terms of 3d 5+n L n+m 4d 1+m covalently mixed congurations, where L denotes a symmetry-adapted O 2p ligand hole. All the possible charge transfer congurations are included explicitly in the ground state expansion. Non-local charge uctuations such as 3d 5 4d 1 / 3d 4 4d 2 and 3d 5 4d 1 / 3d 6 4d 0 are also contemplated. They can be achieved by an indirect secondorder process via the O 2p orbitals, for instance: 3d 5 4d 1 / 3d 6 L4d 1 / 3d 6 4d 0 .
There are two complete sets of model parameters for each transition metal octahedron: the Coulomb repulsion U, the p-d charge transfer energy D, the core-hole potential Q (Q ¼ U/0.83), and the pds charge transfer integral T s (T p ¼ ÀT s /2). 17 These parameters are given with respect to the average of the multiplet of each conguration. The multiplet splittings of each 3d 5+n L n+m 4d 1+m charge transfer conguration are given in terms of the crystal eld parameter 10Dq, the set of Kanamori parameters u, u 0 , and j, as well as the p-p hybridization ppsppp. 17 The main model parameters and the multiplet parameters for the FeO 6 and MoO 6 octahedra are given in Table 1. These parameters follow the expected chemical trend, 17,18 and are consistent with those in related compounds. [22][23][24] The calculation of the different spectral weights is performed in three steps. First, the Hamiltonian matrixĤ is diagonalized to obtain the ground state |j 0 i. Then, the corresponding Green function G(u) is calculated using the following expression: whereÔ is the appropriate operator for each experimental technique. For the valence band photoemission spectrum,Ô annihilates the Fe 3d, Mo 4d and O 2p valence electrons. For the core level photoemission spectra,Ô annihilates Fe 2p and Mo  3p core electrons. Finally, the corresponding spectral weight function A(u) is obtained using the standard formula: The entire calculation procedure is implemented using the built in facilities of the Quanty package. [25][26][27] The single cluster model calculations of the FeO 6 and MoO 6 octahedra were performed in the same way and using the same set of parameters.

Ground state properties
The occupancy of the different conguration in the ground state of Sr 2 FeMoO 6 are listed in Table 2. The dominant contribution is given by the charge transfer congurations 3d 5 L4d 2 and 3d 6 L4d 1 , which are followed by the base ionic conguration 3d 5 4d 1 . The relatively large occupancy of the charge transfer congurations indicates a great degree of covalent bonding. The calculated occupation of the Fe 3d orbitals in the ground state is 5.5 electrons, whereas the calculated occupation of the Mo 4d levels is 1.6 electrons. These occupations are larger than the expected Fe 3+ (3d 5 ) and Mo 5+ (4d 1 ) ionic values, which signals the importance of the Fe 3d-O 2p and Mo 4d-O 2p hybridization. The relevance of hybridization is also revealed by the relatively large occupancy of the double charge transfer conguration 3d 6 L 2 4d 2 .
The relatively large percentage of the 3d 6 4d 0 conguration indicates the importance of non-local Mo-O-Fe charge uctuations. This conguration is not achieved by the direct 3d 5 4d 1 / 3d 6 4d 0 process, but rather by the indirect 3d 5 4d 1 / 3d 6 L4d 1 / 3d 6 4d 0 process. On the other hand, the opposite non-local Fe-O-Mo charge transfer 3d 4 d 2 conguration shows a relatively small occupation. This charge uctuation is strongly suppressed due to the relatively large exchange stabilization of the Fe 3d 5 electrons. It is worth noting that the relatively strong 3d 5 4d 1 / 3d 6 4d 0 process corresponds to the minority Mo 4d 1 electron, whereas the 3d 5 4d 1 / 3d 4 4d 2 transition involves the majority Fe 3d 5 electrons and is greatly diminished. The opposite behavior of the minority vs. majority charge uctuations is in agreement with the half-metallic character of Sr 2 FeMoO 6 . Fig. 2 shows the experimental Fe 2p core level photoemission spectrum of Sr 2 FeMoO 6 (dots). The Fe 2p peak is split by spinorbit interaction into the Fe 2p 3/2 and Fe 2p 1/2 contributions about 711 and 724 eV, respectively. In turn, these peaks are followed by broad charge transfer satellites at around 718 eV and 731 eV.   1 19.6% 3d 6 L 2 4d 2 15.2% 3d 5 L 2 4d 3 7.7% 3d 6 4d 0 7.3% 3d 6 L 3 4d 3 4.8% 3d 5 L 3 4d 4 1.3% 3d 7 L 2 4d 1 1.2% 3d 7 L 3 4d 2 0.7% 3d 6 L 4 4d 4 0.7% 3d 7 L4d 0 0.5% 3d 4 4d 2 0.1% core hole lifetime. Finally, an integral background was added to the calculated curve to take into account inelastic processes. The calculated spectral weight of the double cluster model reproduces satisfactorily the experimental data. The main peaks are due to the well screened Fe 2p 5 3d 6 L states, whereas the satellite structures are composed of Fe 2p 5 3d 7 L 2 states. These charge transfer satellites in the core level spectrum represent a many-body effect, which reects the highly correlated nature of the Fe 3+ (3d 5 ) ion in Sr 2 FeMoO 6 (U > T s ). The energy position and relative intensity of the satellites are sensitive to the U, D and T s parameters. On the other hand, the single cluster calculation overestimates the intensity of the charge transfer satellites, mainly because it does not include the non-local screening contribution which comes from the MoO 6 octahedra. Fig. 3 shows the experimental Mo 3p core level photoemission spectrum of Sr 2 FeMoO 6 (dots). The Mo 3p peaks are split by spin-orbit interaction into the Mo 3p 3/2 and Mo 3p 1/2 contributions around 398 and 416 eV, respectively. In this case, the core level spectrum does not exhibit a prominent satellite structure. Finally, the experimental data presents an accidental superposition with the Sr LMM Auger electron decay around 430 eV. Fig. 3 also compares the experimental data to the calculated core-level spectral weight (solid line) of the double and single cluster models. Likewise, the discrete contributions were also broadened to account for the experimental resolution and the core hole lifetime. In the same way, the integral background was calculated and added to the nal calculated curve.

Mo 3p core level spectroscopy
The calculated spectral weight of the double cluster calculation successfully reproduces the peaks in the experimental result. The leading structure at 398 eV arises from mixed Mo 3p 5 4d 2 L and 3p 5 4d 1 nal states, while the smaller contribution at 400 eV has mainly Mo 3p 5 4d 1 character. The smaller satellite structure, in this case, is attributed to the less correlated character of the Mo 5+ (4d 1 ) ion in Sr 2 FeMoO 6 (U < T s ). For this reason, the calculated results are less sensitive to the values of the model parameters. In this case, the single cluster calculation reproduces reasonably well the experimental spectrum, mainly because the charge transfer processes are less important than in the Fe 2p core level spectrum.  transfer satellites, mostly related to the Fe 3d states, emerge above 9.0 eV. We note that the Fe 3d-O 2p and Mo 4d-O 2p hybridization are crucial to describe the features in the valence band spectrum. Further, the correlation effects of the Fe 3d states is essential to explain the charge transfer satellites at high binding energies.

Valence band spectroscopy
The Mo 4d spectral weight (green line) presents a peak around 1.0 eV as well as structure about 8.0 eV. The former is related to the Fe 3d-O 2p-Mo 4d mixed states, whereas the later is attributed to Mo 4d-O 2p hybridization. The energy position and relative intensity of these Mo 4d structures are in agreement with those observed in a recent Mo L 3 resonant photoemission experiment. 21 Although the single cluster model results reproduce the overall shape of the valence band, they fail to explain the magnetic order and the electrical conductivity of the compound. The double cluster model gives an anti-parallel ordering of the Fe 3d 5 and Mo 4d 1 magnetic moments, which is in agreement with the observed ferrimagnetic ordering in Sr 2 FeMoO 6 , whereas the single cluster model produces an independent alignment of the magnetic moments yielding a paramagnetic state. Further, the double cluster model indicates the importance of the non-local Fe 3d-O 2p-Mo 4d uctuations, which are related to the half-metallic character of this oxide, whereas the single cluster model only consider the local Fe 3d-O 2p and Mo 4d-O 2p uctuations and gives rise to an insulating state.
The non-local charge uctuations are reected not only in the composition of the ground state, but also contribute to the individual transitions in the experimental spectra. In fact, the rst removal state in the valence band spectra, around 1 eV, is a non-local Fe 3d-O 2p-Mo 4d mixed state, according to the double cluster, but it is a local Mo 4d-O 2p state in the single cluster calculation. Therefore, the double cluster calculation is crucial to explain not only the physical properties of Sr 2 FeMoO 6 , but also the character of the spectral features present in the valence band spectrum.

Summary and conclusions
In summary, we studied the electronic structure of Sr 2 FeMoO 6 using bulk sensitive photoemission spectroscopy. The experimental data were analyzed using conguration interaction cluster model calculations. The charge transfer 3d 5 L4d 2 and 3d 6 L4d 1 congurations dominate the ground state; this indicates a large degree of Fe-O and Mo-O hybridization in this compound. The occupancy of the 3d 6 4d 0 conguration shows the importance of non-local Fe-O-Mo charge uctuations; this conguration is achieved through the indirect 3d 5 4d 1 / 3d 6 L4d 1 / 3d 6 4d 0 process. This non-local charge uctuation occurs in the minority spin channel, whereas the transitions in the majority spin sector are strongly suppressed; which is in accordance with the half-metallic character attributed to the Sr 2 FeMoO 6 compound. The Fe 2p core level photoemission spectrum shows rather large charge transfer satellites. These satellites are related to many-body effects caused by the highly correlated nature of the Fe 3d levels. On the other hand, these effects are smaller in the Mo 3p core level spectrum due to the less correlated character of the Mo 4d states. Charge transfer satellites are also observed in the valence band spectrum and are again associated to the Fe 3d electrons. Although the single cluster model calculations are able to reproduce the experimental spectra, they fail to explain the physical properties of the Sr 2 FeMoO 6 compound. In this context, the double cluster model calculations are crucial to explain both the ferrimagnetic ordering and the half-metallic character of this compound. To conclude, the metal-oxygen hybridization, non-local Fe-O-Mo charge uctuations, and many-body effects are all relevant topics in the electronic structure of Sr 2 FeMoO 6 .

Conflicts of interest
There are no conicts to declare.