Theory of successive transitions in vanadium spinels and order of orbitals and spins

We have theoretically studied successive transitions in vanadium spinel oxides with (t_2g)^2 electron configuration. These compounds show a structural transition at ~ 50K and an antiferromagnetic transition at ~ 40K. Since threefold t_2g orbitals of vanadium cations are occupied partially and vanadiums constitute a geometrically-frustrated pyrochlore lattice, the system provides a particular example to investigate the interplay among spin, orbital and lattice degrees of freedom on frustrated lattice. We examine the models with the Jahn-Teller coupling and/or the spin-orbital superexchange interaction, and conclude that keen competition between these two contributions explains the thermodynamics of vanadium spinels. Effects of quantum fluctuations as well as relativistic spin-orbit coupling are also discussed.