Complex-Orbital Order in Fe<SUB>3</SUB>O<SUB>4</SUB> and Mechanism of the Verwey Transition
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Electronic state and the Verwey transition in magnetite (Fe<SUB>3</SUB>O<SUB>4</SUB>) are studied using a spinless three-band Hubbard model for 3<I>d</I> electrons on the <I>B</I> sites with the Hartree–Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., (1⁄\\sqrt2)[|<I>zx</I>›+<I>i</I>|<I>yz</I>›], ordered (COO) states having noncollinear orbital moments ∼0.4 μ<SUB>B</SUB> on the <I>B</I> sites are obtained with the cubic lattice structure of the high-temperature phase. The COO state is a novel form of magnetic ordering within the orbital degree of freedom. It arises from the formation of Hund’s second rule states of spinless pseudo-<I>d</I> molecular orbitals in the Fe<SUB>4</SUB> tetrahedral units of the <I>B</I> sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic <I>Pmca</I> and <I>Pmc</I>2<SUB>1</SUB> structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell deformation and Jahn–Teller like distortion. From these findings, we consider that at the Verwey transition temperature, the COO state remaining to be short-range order impeded by dynamical lattice distortion in high temperature is developed into that with long-range order coupled with the monoclinic lattice distortion.
- Journal of the Physical Society of Japan
Journal of the Physical Society of Japan 77(7), 074711-074711, 2008
THE PHYSICAL SOCIETY OF JAPAN