Orbital degeneracy and Mott transition in Mo pyrochlore oxides

We present our theoretical results on an effective two-band double-exchange model on a pyrochlore lattice for understanding intricate phase competition in Mo pyrochlore oxides. The model includes the twofold degeneracy of $e_g'$ orbitals under trigonal field splitting, the interorbital Coulomb repulsion, the Hund's-rule coupling between itinerant $e_g'$ electrons and localized $a_{1g}$ spins, and the superexchange antiferromagnetic interaction between the $a_{1g}$ spins. By Monte Carlo simulation with treating the Coulomb repulsion at an unrestricted-type mean-field level, we obtain the low-temperature phase diagram as functions of the Coulomb repulsion and the superexchange interaction. The results include four dominant phases with characteristic spin and orbital orders and the metal-insulator transitions among them. The insulating region is characterized by a `ferro'-type orbital ordering of the $e_g'$ orbitals along the local $<111>$ axis, irrespective of the spin ordering.