Successive orbital ordering transitions in FeV2O4 from first-principles calculation

The interactions among spin, orbital, and lattice are essential to reveal the complicated phase transitions in FeV2O4, a spinel with spin and orbital degrees of freedom both at Fe and V sites. By employing first-principle calculations, we investigate these interactions to propose the orbital ordering of Fe2+ and V3+ ions. At the Fe sites, orbital states transform from d z 2 to d x 2 − z 2, to d x 2 − y 2, and to d y 2 − z 2 accompanying structural phase transitions. At the V sites, one electron occupies the dxy, dxz, dxy, and dyz orbitals. The second electron occupies the d x z ± d y z, d x y ± d y z, d x z ± d y z, and d x y ± d x z orbitals, which alternate in the corresponding ab, ac, ab, and bc planes along the c, b, c, and a axes, respectively. The effect of spin-orbital coupling on the orbital ordering of Fe2+ and V3+ ions is not significant. The orbital orderings are driven by the combination of the Jahn-Teller distortions and the electron correlation effect.The interactions among spin, orbital, and lattice are essential to reveal the complicated phase transitions in FeV2O4, a spinel with spin and orbital degrees of freedom both at Fe and V sites. By employing first-principle calculations, we investigate these interactions to propose the orbital ordering of Fe2+ and V3+ ions. At the Fe sites, orbital states transform from d z 2 to d x 2 − z 2, to d x 2 − y 2, and to d y 2 − z 2 accompanying structural phase transitions. At the V sites, one electron occupies the dxy, dxz, dxy, and dyz orbitals. The second electron occupies the d x z ± d y z, d x y ± d y z, d x z ± d y z, and d x y ± d x z orbitals, which alternate in the corresponding ab, ac, ab, and bc planes along the c, b, c, and a axes, respectively. The effect of spin-orbital coupling on the orbital ordering of Fe2+ and V3+ ions is not significant. The orbital orderings are driven by the combination of the Jahn-Teller distortions and the electron correlation ...