Orbital Order and Structural Phase Transitions in Vanadium Spinel FeV₂O₄

Orbital degrees of freedom plays an important role in condensed matter physics because it is strongly related with phase transitions and induces the fascinating physical properties. A spinel oxide FeV₂O₄ is one of the peculiar examples because this compound has double orbital degrees of freedom at both Fe²⁺ and V³⁺ ions. Furthermore, this material represents exotic physical properties [1,2], i.e.; multiferroic, large magnetostriction, and successive structural transitions with decreasing temperature: cubic - tetragonal (c < a: tetraHT, 138K) - orthorhombic (orthoHT, 108 K) - tetragonal (c > a: tetraLT, 68 K). However, the origin of structural transitions and physical properties is controversial until now. In order to clarify the origin, we have performed synchrotron x-ray diffraction experiments at low temperatures at beamline BL02B2 (for the powder samples) in SPring-8 and BL-4C (for the single crystal) of the Photon Factory, KEK. Furthermore, we have carried out the magnetization and the specific heat measurements using polycrystalline samples and single crystal of FeV₂O₄. We have firstly found another orthorhombic phase (orthoLT) below 30 K in the polycrystalline sample of FeV₂O₄, shown in figure 1. The Rietveld analysis was performed, and the overall qualities of fittings were fairly good. In order to investigate the details of the orbital state of Fe²⁺ and V³⁺ in FeV₂O₄, we have performed the normal mode analysis, which is based on static displacements of the tetrahedron of FeO₄ and octahedron of VO₆. In the orthoLT phase, we found the orbital order of Fe²⁺ ions, which is mixture of 3z²-r² and y²-z² orbitals, without change of orbital order of V³⁺ ions. This result indicates that the origin of the orthoLT phase is derived from the competition between cooperative Jahn-Teller effect and relativistic spin-orbit coupling of Fe²⁺ ions. We also discuss the origins of the other phase transitions considering the orbital state of V³⁺ and Fe²⁺ ions, and then the orbital dilution effect, where the structural and magnetic properties are investigated by using powder samples substituted for Fe²⁺ and V³⁺ ions by other ions (Mn²⁺ and Fe³⁺) with no orbital degrees of freedom.