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I review the microscopic spin-orbital Hamiltonian and ground state properties of spin one-half spinel oxides with threefold $t_{2g}$ 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.
Ultrasound velocity measurements of the orbitally-frustrated GeCo$_2$O$_4$ reveal unusual elastic instabilities due to the phonon-spin coupling within the antiferromagnetic phase. Shear moduli exhibit anomalies arising from the coupling to short-rang
We investigate the magnetic instabilities of the two-dimensional model of interacting e_g electrons for hole doping away from two electrons per site in the mean-field approximation. In particular, we address the occurrence of orbitally polarized stat
Controlling phase transitions in transition metal oxides remains a central feature of both technological and fundamental scientific relevance. A well-known example is the metal-insulator transition which has been shown to be highly controllable while
Capturing the non-collinear magnetic ground state of the spinel vanadates AV$_2$O$_4$ (A= Mn, Fe and Co) remains an outstanding challenge for state-of-the-art ab-initio methods. We demonstrate that both the non-collinear spin texture, as well as the
We report on the emergent magnetic state of (111)-oriented CoCr2O4 ultrathin films sandwiched by Al2O3 in the quantum confined geometry. At the two-dimensional crossover, polarized neutron reflectometry reveals an anomalous enhancement of the total m