Orbital order in vanadium spinels

TL;DR

This paper investigates the orbital symmetry of vanadium spinel oxides using a theoretical model, revealing complex orbital ground states and predicting experimental signatures for detection.

Contribution

It introduces a comprehensive theoretical framework combining superexchange and spin-orbit coupling to clarify the orbital order in vanadium spinels.

Findings

Confirmed the complex orbital nature of the ground state.

Predicted tetragonal flattening of oxygen octahedra.

Proposed detection method via resonant x-ray scattering.

Abstract

Motivated by recent theoretical and experimental controversy, we present a theoretical study to clarify the orbital symmetry of the ground state of vanadium spinel oxides AV$_2$O$_4$ (A=Zn, Mg, Cd). The study is based on an effective Hamiltonian with spin-orbital superexchange interaction and a local spin-orbit coupling term. We construct a classical phase-diagram and prove the complex orbital nature of the ground state. Remarkably, with our new analysis we predict correctly also the coherent tetragonal flattening of oxygen octahedra. Finally, through analytical considerations as well as numerical ab-initio simulations, we propose how to detect the predicted complex orbital ordering through vanadium K edge resonant x-ray scattering.