The ground state phases of orbitally degenerate spinel oxides

I review the microscopic spin-orbital Hamiltonian and ground state properties of spin one-half spinel oxides with threefold t2g orbital degeneracy. It is shown that for any orbital configuration a ground state of corresponding spin only Hamiltonian is infinitely degenerate in the classical limit. The extensive classical degeneracy is lifted by the quantum nature of the spins, an effect similar to order-out-of-disorder phenomenon by quantum fluctuations. This drives the system to a non-magnetic spin-singlet dimer manifold with a residual degeneracy due to relative orientation of dimers. The magneto-elastic mechanism of lifting the “orientational” degeneracy is also briefly reviewed.