Hybrid density functional theory study of vanadium monoxide

Abstract

First-principles calculations of nondefective VO in the $\mathrm{Fm}3\ifmmode\bar\else\textasciimacron\fi{}m$ structure based on a range of single-particle Hamiltonians containing varying amounts of exact exchange indicate that the ground electronic state is that of a ${d}^{3}$ high spin, antiferromagnetic (AF), Mott-Hubbard insulator with an ${\mathrm{AF}}_{1}$ spin alignment of the local cation moments. This description remains essentially unchanged down to 10% exact exchange, and only for the pure density functional theory (DFT) potential is the ${\mathrm{AF}}_{1}$ phase found to be metallic. Strong spin-lattice interaction is predicted with differences in lattice constant of up to 1.6% between ${\mathrm{AF}}_{1}$ and FM (ferromagnetic) order. The ${\mathrm{AF}}_{1}$ lattice constant is predicted to be $\ensuremath{\sim}4.37\AA{},$ which is roughly 7% greater than the reported lattice constants for the defective material. The bulk modulus is comparable to those of CaO, MnO, and NiO. A mapping of total energies onto an Ising spin Hamiltonian containing both direct and superexchange interactions reveals the dominant magnetic interaction to be the direct coupling of antiferromagnetically aligned nearest-neighbor cation spins, which leads to the stability of the ${\mathrm{AF}}_{1}$ phase. Direct coupling energies are found in the range $\ensuremath{-}11.1$ to $\ensuremath{-}44.3\mathrm{meV}$ as the proportion of exact exchange is reduced, leading to an estimated critical disorder temperature in the range 300--450 K. However, the limitations of such mapping are exposed by a consideration of the relative stabilities of the ${\mathrm{AF}}_{1}$ and ${\mathrm{AF}}_{3}$ alignments. Orbital projected densities of states reveal filled to unfilled gaps which depend strongly on the proportion of exact exchange and for the B3LYP potential (20% exact exchange) are $\ensuremath{\sim}2.5\mathrm{eV}$ for the spin-forbidden $xy(\ensuremath{\uparrow})\ensuremath{\rightarrow}xy(\ensuremath{\downarrow})$ excitation, $\ensuremath{\sim}3.0\mathrm{eV}$ for $xy(\ensuremath{\uparrow})\ensuremath{\rightarrow}{z}^{2}(\ensuremath{\uparrow}),$ and $\ensuremath{\sim}3.5\mathrm{eV}$ for $\stackrel{\ensuremath{\rightarrow}}{V}\mathrm{O}$ charge transfer. Variationally stable, highly local crystal-field excited states ranging in energy from $\ensuremath{\sim}0.6$ to $\ensuremath{\sim}2.7\mathrm{eV}$ are predicted for exchange-correlation potentials down to 30% exact exchange and from comparisons with the corresponding band excitation estimates of $\ensuremath{\sim}1$ to $\ensuremath{\sim}2\mathrm{eV}$ are obtained for the localization energy of Frenkel excitons. From a mapping of the excited crystal-field energies onto a Kanamori Hamiltonian, values are obtained for the lattice Racah B and C parameters and the $d$-orbital averaged exchange and crystal-field energies. A comparison of mapped and directly calculated energies of the two-electron excitation $(xz,yz)\ensuremath{\rightarrow}{(z}^{2}{,x}^{2}\ensuremath{-}{y}^{2})$ confirms the validity of Kanamori mapping, notably in the limit of exact exchange.