Orbital disorder induced by charge fluctuations in vanadium spinels
  Motivated by recent experiments on vanadium spinels, $A$V$_2$O$_4$, that show an increasing degree of electronic delocalization for smaller cation sizes, we study the evolution of orbital ordering (OO) between the strong and intermediate-coupling regimes of a multi-orbital Hubbard Hamiltonian. The underlying magnetic ordering of the Mott insulating state leads to a rapid suppression of OO due to enhanced charge fluctuations along ferromagnetic bonds. Orbital double-occupancy is rather low at the transition point indicating that the system is in the crossover region between strong and intermediate-coupling regimes when the orbital degrees of freedom become disordered. 
Yasuyuki Kato, Gia-Wei Chern, K. A. Al-Hassanieh, Natalia B. Perkins,   C. D. Batista
cond-mat.str-el cond-mat.stat-mech