Charge ordering in the spinels AlV$_2$O$_4$ and LiV$_2$O$_4$

TL;DR

This paper presents a microscopic theory for charge ordering in spinels AlV$_2$O$_4$ and LiV$_2$O$_4$, explaining their phase transitions and electronic properties through lattice coupling and an extended Hubbard model.

Contribution

It introduces a novel microscopic model incorporating lattice deformation effects to accurately describe charge ordering in these spinels.

Findings

Charge ordering is driven by lattice deformations favoring inequivalent V sites.

AlV$_2$O$_4$ remains metallic due to band filling, while LiV$_2$O$_4$ becomes a semiconductor under pressure.

The model correctly predicts the first-order nature of the charge transition.

Abstract

We develop a microscopic theory for the charge ordering (CO) transitions in the spinels AlV$_2$O$_4$ and LiV$_2$O$_4$ (under pressure). The high degeneracy of CO states is lifted by a coupling to the rhombohedral lattice deformations which favors transition to a CO state with inequivalent V(1) and V(2) sites forming Kagom\'e and trigonal planes respectively. We construct an extended Hubbard type model including a deformation potential which is treated in unrestricted Hartree Fock approximation and describes correctly the observed first-order CO transition. We also discuss the influence of associated orbital order. Furthermore we suggest that due to different band fillings AlV$_2$O$_4$ should remain metallic while LiV$_2$O$_4$ under pressure should become a semiconductor when charge disproportionation sets in.