Effect of spin-orbit coupling on magnetic and orbital order in MgV$_2$O$_4$

TL;DR

This study investigates how spin-orbit coupling influences magnetic and orbital order in MgV$_2$O$_4$, revealing chain-dependent effects that align with experimental observations and intermediate behavior among related vanadium spinels.

Contribution

The paper provides a detailed first-principles analysis of spin-orbit effects on orbital order in MgV$_2$O$_4$, highlighting chain-specific variations and their consistency with experimental data.

Findings

Spin-orbit coupling affects orbital order differently in alternate V chains.

The effect of SO coupling in MgV$_2$O$_4$ is intermediate compared to ZnV$_2$O$_4$ and MnV$_2$O$_4$.

The study confirms the importance of SO interactions in understanding magnetic and orbital properties.

Abstract

Recent measurements on MgV$_2$O$_4$ single crystal have reignited the debate on the role of spin-orbit (SO) coupling in dictating the orbital order in Vanadium spinel systems. Density functional theory calculations were performed using the full-potential linearized augmented-plane-wave method within the local spin density approximation (LSDA), Coulomb correlated LSDA+U, and with SO interaction (LSDA+U+SO) to study the magnetic and orbital ordering in low temperature phase of MgV$_2$O$_4$. It is observed that the spin-orbit coupling in the experimentally observed antiferromagnetic phase, affects the orbital order differently in alternate V-atom chains along c-axis. This observation is found to be consistent with the experimental prediction that the effect of spin-orbit coupling is intermediate between that in case of ZnV$_2$O$_4$ and MnV$_2$O$_4$.