Orbital order and electron itinerancy in CoV₂O₄ and Mn_0.5Co_0.5V₂O₄ 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 Mn_0.5Co_0.5V₂O₄ 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 Mn_0.5Co_0.5V₂O₄. 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.