Orbital structures in spinel vanadates AV₂O₄ (A = Fe, Mn)

Spinel FeV₂O₄ exhibits successive structural phase transitions, reflecting the interplay between the Fe2⁺ (3d6) and V3⁺ (3d2) ions, both of which have orbital and spin degrees of freedom. The temperature-dependent orbital shapes of Fe2⁺ and V3 ⁺ were investigated by means of single-crystal structure analysis, and were compared with those in MnV₂O₄, where only the V3⁺ ions are Jahn-Teller active. The highest-temperature transition from the cubic to the high-temperature tetragonal phase was driven by a ferroic Fe2⁺ 3z2-r2 orbital order (OO). At 110 K, where the ferrimagnetic transition takes place, the magnetic order modified the orbital shape through intratomic spin-orbit coupling, causing an orthorhombic distortion. The V3 ⁺ orbital order (V-OO) contributed to the lowest temperature transition from the orthorhombic to the low-temperature tetragonal phase. The V-OO in FeV₂O₄ was qualitatively different from that in MnV₂O₄. We propose that ferro-OO contains a complex orbital in FeV₂O₄ in contrast to the V-OO of real orbitals observed in MnV₂O₄.