Optical and energy-loss spectra of the antiferromagnetic transition metal oxides MnO, FeO, CoO, and NiO including quasiparticle and excitonic effects

Claudia Rödl and Friedhelm Bechstedt

Phys. Rev. B 86, 235122 – Published 17 December 2012

Abstract

We calculate the frequency-dependent dielectric function for the series of antiferromagnetic transition metal oxides (TMOs) from MnO to NiO using many-body perturbation theory. Quasiparticle, excitonic, and local-field effects are taken into account by solving the Bethe-Salpeter equation in the framework of collinear spin polarization. The optical spectra are based on electronic structures which have been obtained using density-functional theory with a hybrid functional containing screened exchange (HSE03) and a subsequent quasiparticle calculation in the $G W$ approximation to describe exchange and correlation effects adequately. These sophisticated quasiparticle band structures are mapped to electronic structures resulting from the computationally less expensive $GGA + U + Δ$ scheme that includes an on-site interaction $U$ and a scissors shift $Δ$ and allows us to calculate the large number of electronic states that is necessary to construct the Bethe-Salpeter Hamiltonian. For an accurate description of the optical spectra, an appropriate treatment of the strong electron-hole attraction is mandatory to obtain agreement with the experimentally observed absorption-peak positions. The itinerant $s$ and $p$ states as well as the localized transition metal $3 d$ states have to be considered on an equal footing. We find that a purely atomic picture is not suitable to understand the optical absorption spectra of the TMOs. Reflectivity spectra, absorption coefficients, and loss functions at vanishing momentum transfer are computed in a wide spectral range and discussed in light of the available experimental data.

Received 12 October 2012

DOI:https://doi.org/10.1103/PhysRevB.86.235122

Authors & Affiliations

Claudia Rödl and Friedhelm Bechstedt

Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität and European Theoretical Spectroscopy Facility (ETSF), Max-Wien-Platz 1, 07743 Jena, Germany

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Vol. 86, Iss. 23 — 15 December 2012

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Figure 1
Quasiparticle band structures for MnO, FeO, CoO, and NiO. The solid lines represent the $GGA + U + Δ$ bands, whereas the red dots denote the HSE03 $+ G_{0} W_{0}$ reference band structures from Ref. 20. The valence-band maximum is set to zero. The high-symmetry points of the Brillouin zone are labeled as in Ref. 49.Reuse & Permissions
Figure 2
Real and imaginary parts of the frequency-dependent macroscopic dielectric function $ɛ (ω)$ for MnO, FeO, CoO, and NiO calculated in the independent-quasiparticle approximation (IQPA) and solving the Bethe-Salpeter equation (BSE). Experimental spectra that are derived from reflectivity (Messick et al.,[22] Ksendzov et al.,[23] Hiraoka et al.,[50] and Powell and Spicer[24]) or ellipsometry (Kang et al.[51] and Goldhahn and Schley[52]) measurements are shown for comparison. The spectrum of FeO from Hiraoka et al. is biased by strong defect absorption at low frequencies due to the nonstoichiometry of the sample.[50]Reuse & Permissions
Figure 3
Analysis of the transitions that contribute to the main absorption peaks of MnO (a) and NiO (b). In the left panels, the imaginary parts of the dielectric functions in IQPA (all bands) are shown together with the contributions of the $e_{g} \to s$ and $e_{g} \to t_{2 g}$ (MnO) or $t_{2 g} \to e_{g}$ transitions (NiO). In the right panels, the corresponding states in the band structures are highlighted. The black solid lines indicate the valence-band $e_{g}$ (MnO) or $t_{2 g}$ states (NiO). The final states of the respective optical transitions are shown in the same colors as the partial optical spectra in the left panels. Furthermore, the right panels depict the optical transition matrix elements ${| p |}^{2}$ for the interband transitions (dotted curves) along the Brillouin-zone path. It is clearly visible that interband transitions which are forbidden at the $Γ$ point for symmetry reasons can contribute strongly to the optical absorption in other parts of the Brillouin zone.Reuse & Permissions
Figure 4
Reflectivities for MnO, FeO, CoO, and NiO at normal incidence. The spectra have been calculated by solving the Bethe-Salpeter equation (BSE) including excitonic and local-field effects. The experimental data are taken from Ksendzov et al.,[23] Hiraoka et al.,[50] and Powell and Spicer.[24] The reflectivity spectrum of FeO from Hiraoka et al. is biased by strong defect absorption at low frequencies due to the nonstoichiometry of the sample.[50]Reuse & Permissions
Figure 5
Absorption coefficients for MnO, FeO, CoO, and NiO. The spectra have been calculated by solving the Bethe-Salpeter equation (BSE) including excitonic and local-field effects. The experimental curves from Ksendzov et al.[23] and Powell and Spicer[24] have been derived from reflectivity data.Reuse & Permissions
Figure 6
Energy-loss spectra for MnO, FeO, CoO, and NiO at vanishing momentum transfer, including excitonic and local-field effects (BSE). The experimental reference data have been derived from reflectivity measurements (Ksendzov et al.[23]), EELS (Fromme et al.,[64] Gorschlüter and Merz[65]) of the MnO and NiO (100) surfaces, and IXS of CoO and NiO along the [100] and [111] directions (Larson et al.[54]). The curves from Fromme et al. and Gorschlüter and Merz are plotted in arbitrary units.Reuse & Permissions

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