Spin Frustration and Orbital Order in Vanadium Spinels

TL;DR

This paper investigates how geometrical frustration and spin-orbital interactions influence magnetic ordering in vanadium spinels, revealing that orbital order reduces frustration and promotes a three-dimensional antiferromagnetic transition.

Contribution

The study introduces a spin-orbital-lattice model and a reduced spin Hamiltonian to explain the stabilization of antiferromagnetic order in vanadium spinels, highlighting the role of orbital order.

Findings

Orbital order reduces spin frustration via spatial anisotropy.

The reduced spin model resembles weakly-coupled 1D antiferromagnetic chains.

Magnetic transition follows the 3D Heisenberg universality class.

Abstract

We present the results of our theoretical study on the effects of geometrical frustration and the interplay between spin and orbital degrees of freedom in vanadium spinel oxides $A$V$_2$O$_4$ ($A$ = Zn, Mg or Cd). Introducing an effective spin-orbital-lattice coupled model in the strong correlation limit and performing Monte Carlo simulation for the model, we propose a reduced spin Hamiltonian in the orbital ordered phase to capture the stabilization mechanism of the antiferromagnetic order. Orbital order drastically reduces spin frustration by introducing spatial anisotropy in the spin exchange interactions, and the reduced spin model can be regarded as weakly-coupled one-dimensional antiferromagnetic chains. The critical exponent estimated by finite-size scaling analysis shows that the magnetic transition belongs to the three-dimensional Heisenberg universality class. Frustration remaining in the mean-field level is reduced by thermal fluctuations to stabilize a collinear ordering.