Theoretical Analysis of Electronic and Magnetic Properties of NaV$_2$O$_4$: Crucial Role of the Orbital Degrees of Freedom

TL;DR

This paper provides a theoretical analysis showing that the orbital ordering, rather than geometry, explains the anisotropic electronic and magnetic properties of NaV$_2$O$_4$, highlighting the role of orbital degrees of freedom.

Contribution

It introduces a realistic low-energy model demonstrating the crucial influence of orbital ordering on NaV$_2$O$_4$'s properties, advancing understanding of its quasi-one-dimensional behavior.

Findings

Orbital ordering divides $t_{2g}$ states into localized and delocalized types.

Symmetric orbitals form the metallic band, explaining anisotropic electrical resistivity.

NaV$_2$O$_4$ classified as a double exchange system.

Abstract

Using realistic low-energy model with parameters derived from the first-principles electronic structure calculation, we address the origin of the quasi-one-dimensional behavior in orthorhombic NaV$_2$O$_4$, consisting of the double chains of edge-sharing VO$_6$ octahedra. We argue that the geometrical aspect alone does not explain the experimentally observed anisotropy of electronic and magnetic properties of NaV$_2$O$_4$. Instead, we attribute the unique behavior of NaV$_2$O$_4$ to one particular type of the orbital ordering, which respects the orthorhombic $Pnma$ symmetry. This orbital ordering acts to divide all $t_{2g}$ states into two types: the `localized' ones, which are antisymmetric with respect to the mirror reflection $y \rightarrow -$$y$, and the symmetric `delocalized' ones. Thus, NaV$_2$O$_4$ can be classified as the double exchange system. The directional orientation of symmetric orbitals, which form the metallic band, appears to be sufficient to explain both quasi-one-dimensional character of interatomic magnetic interactions and the anisotropy of electrical resistivity.