Orbital ordering in FeV2O4: Spinel with two orbitally active sites

By employing first-principles electronic structure calculations, we investigate orbital ordering in FeV2O4, a spinel with orbital degrees of freedom both at Fe and V sites that exhibits two tetragonal phases, one compressed at high temperature and another elongated at low temperature. Our first-principles study shows the ferro-orbital ordering of d(x2-y2) and d(3z2-r2) types at Fe sites at the high-and low-temperature phases, respectively. The orbital ordering at V sites is found to consist of orbital chains running along different directions with orbitals rotated alternatively within each chain, similar to that found for MnV2O4 [S. Sarkar et al., Phys. Rev. Lett. 102, 216405 (2009)]. Further, we find that the single-ion anisotropy effect with hard and easy c axis favors the compressed and elongated tetrahedral shapes. This gives rise to magnetocrystalline anisotropy-dependent shapes, similar to that reported in the context of rare-earth-based magnetic shape memory alloys.