Orbital order and electron itinerancy in CoV2O4 and Mn0.5Co0.5V2O4 from first principles

In view of the recent experimental predictions of a weak structural transition in CoV2O4 we explore the possible orbital order states in its low temperature tetragonal phases from first principles density functional theory calculations. We observe that the tetragonal phase with I41/amd symmetry is associated with an orbital order involving complex orbitals with a reasonably large orbital moment at vanadium sites while in the phase with I41/a symmetry, the real orbitals with quenched orbital moment constitute the orbital order. Further, to study the competition between orbital order and electron itinerancy we considered Mn0.5Co0.5V2O4 as one of the parent compounds, CoV2O4, lies near itinerant limit while the other, MnV2O4, lies deep inside the orbitally ordered insulating regime. Orbital order and electron transport have been investigated using first principles density functional theory and Boltzmann transport theory in CoV2O4, MnV2O4 and Mn0.5Co0.5V2O4. Our results show that as we go from MnV2O4 to CoV2O4 there is enhancement in the electron's itinerancy while the nature of orbital order remains unchanged.