Theoretical study of the electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$

TL;DR

This paper provides a theoretical analysis of the electronic and magnetic properties of hollandite vanadate K$_2$V$_8$O$_{16}$, focusing on charge ordering, orbital, and spin structures using computational models.

Contribution

It introduces a comprehensive theoretical framework combining charge stability analysis, strong-coupling perturbation theory, and exact diagonalization to understand the material's electronic states.

Findings

Identified the most stable charge-ordering pattern consistent with experiments.

Derived the effective spin-orbit Hamiltonian for the system.

Predicted specific orbital and spin configurations in the ground state.

Abstract

We consider electronic properties of hollandite vanadate K$_2$V$_8$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 VO$_6$ 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 K$_2$V$_8$O$_{16}$ including predictions on the outcome of future experimental studies.