Theoretical study of the electronic states of hollandite vanadateK2V8O16

Abstract

We consider electronic properties of hollandite vanadate ${\mathrm{K}}_{2}{\mathrm{V}}_{8}{\mathrm{O}}_{16}$, a one-dimensional zigzag-chain system of ${t}_{2g}$ orbitals in a mixed valent state. We first calculate the Madelung energy and obtain the relative stability of several charge-ordering patterns to determine the most stable one that is consistent with the observed superlattice structure. We then develop the strong-coupling perturbation theory to derive the effective spin-orbit Hamiltonian, starting from the triply degenerate ${t}_{2g}$ orbitals in the $\mathrm{V}{\mathrm{O}}_{6}$ octahedral structure. We apply an exact-diagonalization technique on small clusters of this Hamiltonian and obtain the orbital-ordering pattern and spin structures in the ground state. We thereby discuss the electronic and magnetic properties of ${\mathrm{K}}_{2}{\mathrm{V}}_{8}{\mathrm{O}}_{16}$, including predictions on the outcome of future experimental studies.