Abstract
Electronic state and the Verwey transition in magnetite (Fe 3 O 4 ) are studied using a spinless three-band Hubbard model for 3 d electrons on the B sites with the Hartree–Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., \((1/\sqrt{2})[|zx\rangle+\mathrm{i}|yz\rangle]\), ordered (COO) states having noncollinear orbital moments ∼0.4 µ B on the B 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- d molecular orbitals in the Fe 4 tetrahedral units of the B sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic P m c a and P m c 2 1 structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell...
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