First-principles study of the mixed oxide $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$

We have investigated the electronic and magnetic properties of the mixed oxide $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$ and compared it to the parent oxides $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ and $\alpha \text{−}{\mathrm{Cr}}_2{\mathrm{O}}_3$. Density functional theory B3LYP calculations with the nonlocal Hartree-Fock exchange contribution reduced from 20% to 10% were found to reproduce the band gaps of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ and $\alpha \text{−}{\mathrm{Cr}}_2{\mathrm{O}}_3$ remarkably well. Optimized cell constants also agreed very well with experimental values. Thus, this method was used to study $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$. $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$ is predicted to be a charge-transfer insulator with $\mathrm{O}\left(2p\right)$ and $\mathrm{Cr}\left(3d\right)$ predominating in the upper edge of the valence band and $\mathrm{Fe}\left(3d\right)$ in the lower edge of the conduction band. The direct band gap of $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$ is predicted to be close in value to that of $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$. For ordered $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$, the lowest energy is found for chromium ions occupying the sites related by the $c$ glide plane. The antiferromagnetic ground state of this oxide is found to be that with magnetic ordering as in $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$.

Figure 1

Primitive unit cell for corundum-type oxides, $\alpha \text{−}{\mathrm{M}}_2{\mathrm{O}}_3$, showing the labeling of the cation sites used in this paper; large sphere oxide ions and smaller sphere metal ions.

Figure 2

Total density of states and projection of $M3d$ and $\mathrm{O}2p$ on the density of states for the most stable antiferromagnetic configurations of (a) $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ and (b) $\alpha \text{−}{\mathrm{Cr}}_2{\mathrm{O}}_3$ from calculations using B3LYP, with the Hartree-Fock exchange contribution reduced to 10%. Continuous line refers to “spin-up” electrons and dotted line to “spin-down” electrons.

Figure 3

Total density of states and projection of $M3d$ and $\mathrm{O}2p$ on the density of states for the most stable antiferromagnetic configurations of $\alpha \text{−}\mathrm{Fe}\mathrm{Cr}{\mathrm{O}}_3$ with (a) cation ordering FeCrFeCr, (b) cation ordering CrFeFeCr, and (c) cation ordering FeFeCrCr from calculations using B3LYP, with the Hartree-Fock exchange contribution reduced to 10%. Continuous line refers to spin-up electrons and dotted line to spin-down electrons.