Electronic structure and exchange coupling inα′−NaV2O5

Abstract

Band-structure calculations of the electronic structure of ${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{-}{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}$ were performed using the linear muffin-tin orbital method within the local-density approximation (LDA). The results of the calculations were used to determine the parameters of an extended tight-binding model which describes the dispersion of the bands formed by V ${d}_{\mathrm{xy}}$ orbitals and includes explicitly V ${d}_{\mathrm{xy}}--\mathrm{O}{p}_{x,y}$ hopping terms. It has been found that the effective hopping between ${d}_{\mathrm{xy}}$ orbitals of V atoms placed at the opposite ends of consecutive rungs of a ladder is comparable to the hopping along the leg of the ladder, which suppresses the dispersion of the upper pair of V ${d}_{\mathrm{xy}}$ bands. The electronic structure of different models for the charge-ordered low-temperature phase of ${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{-}{\mathrm{NaV}}_{2}{\mathrm{O}}_{5}$ was studied using the $\mathrm{LDA}+U$ approach. The $\mathrm{LDA}+U$ ground-state energy was calculated and compared for in-line and zigzag charge order in different magnetic configurations. The set of effective exchange constants between ${\mathrm{V}}^{4+}$ magnetic moments was calculated by mapping to the ground-state energy of a localized Heisenberg model.