Henrique P. Martins*a,
Eduardo B. Guedesa,
Rodrigo J. O. Mossaneka,
Fernando D. Pradob,
Alberto Caneiroc and
Miguel Abbatea
aDepartamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990 Curitiba, PR, Brazil. E-mail: hpmartins@gmail.com
bDepartamento de Física, Universidad Nacional del Sur, Av. Leandro N. Alem 1253, 8000 Bahía Blanca, Argentina
cCentro Atómico Bariloche, Comisión Nacional de Energía Atómica, Av. Ezequiel Bustillo 9500, 8400 Bariloche, Argentina
First published on 22nd January 2018
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.
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 confirmed the half-metallic character of the SFMO compound.2 The core-level X-ray photoelectron spectra (XPS) determined the chemical shifts of the Fe/Mo ions.8,9 The valence band X-ray photoemission spectra (PES) elucidated the electronic states at the Fermi level.10–12 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 Fe3+ (3d5) and Mo5+ (4d1).1,2 However, the Fe 3d and Mo 4d electrons present a covalent hybridization with the O 2p states.12 Further, the majority Fe3+ (3d5) electrons are localized, whereas the minority Mo5+ (4d1) electron is itinerant, which is consistent with both the half-metallic conductivity and the ferrimagnetic ordering of SFMO. In fact, the conducting electron is delocalized along Mo–O–Fe–O–Mo chains in this material, indicating the importance of the Fe 3d–O 2p and Mo 4d–O 2p covalent mixing, as well as the non-local Mo–O–Fe charge fluctuations.
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 = 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,16–19 which consists of two FeO6 and MoO6 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 fluctuations in the FeO6–MoO6 double cluster. The electronic structure is calculated using the configuration 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.
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 10−9 mbar range. The pellets were thoroughly scraped with a diamond file 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
In a first ionic approximation, the transition metals ions in Sr2FeMoO6 are in a 3d54d1 state.22 The ground state is expanded in terms of 3d5+nn+m4d1+m covalently mixed configurations, where
denotes a symmetry-adapted O 2p ligand hole. All the possible charge transfer configurations are included explicitly in the ground state expansion. Non-local charge fluctuations such as 3d54d1 → 3d44d2 and 3d54d1 → 3d64d0 are also contemplated. They can be achieved by an indirect second-order process via the O 2p orbitals, for instance: 3d54d1 → 3d6
4d1 → 3d64d0.
There are two complete sets of model parameters for each transition metal octahedron: the Coulomb repulsion U, the p–d charge transfer energy Δ, the core-hole potential Q (Q = U/0.83), and the pdσ charge transfer integral Tσ (Tπ = −Tσ/2).17 These parameters are given with respect to the average of the multiplet of each configuration. The multiplet splittings of each 3d5+nn+m4d1+m charge transfer configuration are given in terms of the crystal field parameter 10Dq, the set of Kanamori parameters u, u′, and j, as well as the p–p hybridization ppσ–ppπ.17 The main model parameters and the multiplet parameters for the FeO6 and MoO6 octahedra are given in Table 1. These parameters follow the expected chemical trend,17,18 and are consistent with those in related compounds.22–24
Parameter | Fe3+ | Mo5+ |
---|---|---|
U | 7.5 | 2.6 |
Δ | 3.0 | 6.1 |
Tσ | 2.1 | 3.9 |
10Dq | 1.3 | 3.3 |
j | 0.8 | 0.6 |
ppσ–ppπ | 1.0 | 1.0 |
The calculation of the different spectral weights is performed in three steps. First, the Hamiltonian matrix Ĥ is diagonalized to obtain the ground state |ψ0〉. Then, the corresponding Green function G(ω) is calculated using the following expression:
The entire calculation procedure is implemented using the built in facilities of the Quanty package.25–27 The single cluster model calculations of the FeO6 and MoO6 octahedra were performed in the same way and using the same set of parameters.
Configuration | Occupancy |
---|---|
3d5![]() |
20.9% |
3d6![]() |
20.0% |
3d54d1 | 19.6% |
3d6![]() |
15.2% |
3d5![]() |
7.7% |
3d64d0 | 7.3% |
3d6![]() |
4.8% |
3d5![]() |
1.3% |
3d7![]() |
1.2% |
3d7![]() |
0.7% |
3d6![]() |
0.7% |
3d7![]() |
0.5% |
3d44d2 | 0.1% |
The relatively large percentage of the 3d64d0 configuration indicates the importance of non-local Mo–O–Fe charge fluctuations. This configuration is not achieved by the direct 3d54d1 → 3d64d0 process, but rather by the indirect 3d54d1 → 3d64d1 → 3d64d0 process. On the other hand, the opposite non-local Fe–O–Mo charge transfer 3d4d2 configuration shows a relatively small occupation. This charge fluctuation is strongly suppressed due to the relatively large exchange stabilization of the Fe 3d5 electrons. It is worth noting that the relatively strong 3d54d1 → 3d64d0 process corresponds to the minority Mo 4d1 electron, whereas the 3d54d1 → 3d44d2 transition involves the majority Fe 3d5 electrons and is greatly diminished. The opposite behavior of the minority vs. majority charge fluctuations is in agreement with the half-metallic character of Sr2FeMoO6.
Fig. 2 also compares the experimental result to the calculated core level spectral weight (solid line). The top panel displays the results of the double cluster calculation, whereas the bottom panel compares to the single cluster model results. The discrete contributions were broadened with Gaussian and Lorentzian broadenings to account for the experimental resolution and the 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 2p53d6 states, whereas the satellite structures are composed of Fe 2p53d7
2 states. These charge transfer satellites in the core level spectrum represent a many-body effect, which reflects the highly correlated nature of the Fe3+ (3d5) ion in Sr2FeMoO6 (U > Tσ). The energy position and relative intensity of the satellites are sensitive to the U, Δ and Tσ 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 MoO6 octahedra.
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 final calculated curve.
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 3p54d2 and 3p54d1 final states, while the smaller contribution at 400 eV has mainly Mo 3p54d1 character. The smaller satellite structure, in this case, is attributed to the less correlated character of the Mo5+ (4d1) ion in Sr2FeMoO6 (U < Tσ). 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.
Fig. 4 also compares the experimental data to the calculated spectral weight (solid line) using double and single cluster model calculations. The individual contributions of the Fe 3d, Mo 4d and O 2p states are presented below. The intensity of the peaks were weighted with the appropriate photoelectron cross-sections for a photon energy of 1840 eV. The discrete peaks were convoluted with a Gaussian function to account for the experimental resolution. Finally, an integral background was added to take into account inelastic scattering effects. The single cluster result was calculated using a linear combination of the FeO6 and MoO6 single clusters.
The calculated spectral weight of the double cluster model is in good agreement with the experimental valence band photoemission data. The first feature around 1.0 eV is attributed to Fe 3d–O 2p–Mo 4d mixed states; these are related to the non-local charge fluctuations which give rise to the conducting behavior of Sr2FeMoO6. The Fe 3d states are split by crystal field effects into the Fe t2g and Fe eg contributions, and appear about 5.5 and 4.0 eV, respectively. The non-bonding O 2p band corresponds to O 2p states which are not hybridized with Fe 3d and Mo 4d states, and shows up between 4.0 and 8.0 eV (purple line). On the other hand, the bonding O 2p band corresponds to O 2p states which are hybridized with Fe 3d and Mo 4d states, and arises from 6.0 and 10.0 eV (blue line). Finally, the charge 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.
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 L3 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 3d5 and Mo 4d1 magnetic moments, which is in agreement with the observed ferrimagnetic ordering in Sr2FeMoO6, 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 fluctuations, 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 fluctuations and gives rise to an insulating state.
The non-local charge fluctuations are reflected not only in the composition of the ground state, but also contribute to the individual transitions in the experimental spectra. In fact, the first 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 Sr2FeMoO6, but also the character of the spectral features present in the valence band spectrum.
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