Vanadium spinels (ZnV_2O_4, MgV_2O_4, and CdV_2O_4) exhibit a sequence of structural and magnetic phase transitions, reflecting the interplay of lattice, orbital, and spin degrees of freedom. We offer a theoretical model taking into account the relativistic spin-orbit interaction, collective Jahn-Teller effect, and spin frustration. Below the structural transition, vanadium ions exhibit ferroorbital order and the magnet is best viewed as two sets of antiferromagnetic chains with a single-ion Ising anisotropy. Magnetic order, parametrized by two Ising variables, appears at a tetracritical point.
@article{arxiv.cond-mat/0401203,
title = {Structural, orbital, and magnetic order in vanadium spinels},
author = {O. Tchernyshyov},
journal= {arXiv preprint arXiv:cond-mat/0401203},
year = {2007}
}