The results of augmented-plane-wave (APW) energy-band calculations for the $3d$ transition-series monoxides CaO, TiO, VO, MnO, FeO, CoO, and NiO are interpreted in terms of the electrical and optical data for these compounds. A detailed analysis of the effects of a crystalline field on the nonmagnetic $d$ bands in the rocksalt structure shows that these bands are not split into nonoverlapping $e_g$ and $t_{2g}$ bands by a cubic field. Instead, these effects broaden the $d$ bands in such a way that each of these compounds with partially filled $d$ bands should exhibit metallic behavior. This model is consistent with the insulating properties of CaO and the metallic behavior of TiO and VO. However, the observed electrical and optical properties of MnO, FeO, CoO, and NiO suggest that these materials are Mott insulators, despite the fact that the present calculations predict $3d$ bandwidths $W\approx 3$ eV. Assuming that the $3d$ electrons in these materials are in localized Wannier rather than itinerant Bloch states, the APW energy bands are used to calculate the crystal-field parameters $\Delta$ for these insulating compounds, where $\Delta$ is the difference in the average energies of the $e_g$ and $t_{2g}$ bands. This leads to calculated values for $\Delta$ which are consistently 30% smaller than the experimental values. One interpretation of this discrepancy suggests that the true $3d$ bandwidths $W$ are closer to 4 eV rather than 3 eV for these insulating compounds. Hubbard's simplified model calculations show that a Mott transition occurs when $W\approx U$, the Coulomb interaction energy between two electrons on the same atom. The fact that MnO to NiO are Mott insulators implies that $U>\mathrm{}4\mathrm{}$ eV in these compounds.

• Received 5 August 1971

DOI:https://doi.org/10.1103/PhysRevB.5.306