Band-gap trend of corundum oxides $\alpha \text{−}{M}_2{\mathrm{O}}_3$ ($M=\mathrm{Co}$, Rh, Ir): An ab initio study

In recent years, $d^6$ transition-metal corundum oxides $\alpha \text{−}{M}_2{\mathrm{O}}_3$ ($M=\mathrm{Co}$, Rh, Ir) have garnered significant interest due to their notable $p$-type conductivity; however, their electronic properties remain controversial. In this study, we employ first-principles calculations within different functional levels to systematically investigate the geometry and electronic structure of $\alpha \text{−}{M}_2{\mathrm{O}}_3$. Our findings reveal that these oxides have a relatively small difference between the indirect and direct band gap, contradicting previous studies. Additionally, we demonstrate that the band gaps of these oxides are closely associated with the ligand field splitting of the cation M d orbitals and the experimentally observed nonmonotonic trend of the direct band-gap variation can be explained by the orbital-dependent Coulomb and exchange interactions. This study enhances our understanding of how the involvement of $d$ orbitals impacts the band gap of transition-metal oxides.

Figure 1

(a) Primitive and (b) hexagonal cell of corundum $\alpha \text{−}{M}_2{\mathrm{O}}_3$ ($M=\mathrm{Co}$, Rh, Ir). Dark blue-colored spheres denote cation $M$, and tawny ones denote O. (c) Energy-level splitting for M d orbitals in distorted octahedral field with $C_3$ symmetry.

Figure 2

Electronic band structure, partial density of states, and optical absorption coefficient for (a) ${\mathrm{Co}}_2{\mathrm{O}}_3$, (b) ${\mathrm{Rh}}_2{\mathrm{O}}_3$, and (c) ${\mathrm{Ir}}_2{\mathrm{O}}_3$ calculated using $\mathrm{PBEsol}+\mathrm{\Delta }$. Valence-band maximum is set at zero.

Figure 3

Calculated Г-Г direct band gaps of $M_2{\mathrm{O}}_3$ as a function of HSE mixing parameter $\alpha$. Upward and downward arrows stand for increasing and decreasing trends of fundamental band gap with increasing cation $M$ atomic number ($\mathrm{Co}\to \mathrm{Rh}\to \mathrm{Ir}$), respectively. Experimental optical band gaps are indicated by colored spheres.