Phase transitions associated with the orbitals of electrons are one of our main topics of our group. These phase transitions are expected in d- and f-electron systems with strong correlations (because they have orbital degrees of freedom).
In vanadium spinel oxides, AV2O4(A=Zn, Mg, Cd), we explored the possibilities of complex ordered states including the spin and the orbitals. The experimental results show that there are a structural phase transition at around 50 K and magnetic one around 40 K.
We constructed the effective theory including orbital degrees of freedom. By analyzing this effective model, we showed that the orbital ordered state is stable and pointed out that the structural phase transition inferred by the experiments is indeed the orbital order. Furthermore, we found that the formation of orbital order affects the interactions between the spins and this enabled us to explain the magnetic pattern in low temperatures.