Magnetic transition and orbital degrees of freedom in vanadium spinels

TL;DR

This paper presents a model explaining the two phase transitions in vanadium spinels, linking orbital order and spin order to lattice distortions and frustration release, consistent with experimental observations.

Contribution

It introduces an effective spin-orbital model on the pyrochlore lattice to explain the sequential orbital and spin ordering in vanadium spinels.

Findings

Orbital order occurs at ~50 K due to Jahn-Teller distortion.

Spin order emerges at ~40 K after frustration is partially released.

The model's predictions align with experimental data.

Abstract

We propose a scenario for the two phase transitions in $A$V$_2$O$_4$ ($A$=Zn, Mg, Cd), based on an effective spin-orbital model on the pyrochlore lattice. At high temperatures, spin correlations are strongly frustrated due to the lattice structure, and the transition at $\sim$50 [K] is an orbital order, supported by Jahn-Teller lattice distortion. This orbital order introduces spatial modulation of spin exchange couplings depending on the bond direction. This partially releases the frustration, and leads to a spin order at $\sim$40 [K]. We also study the stable spin configuration by taking account of third-neighbor exchange couplings and quantum fluctuations. The result is consistent with the experimental results.