Complex-Orbital Order in Fe_3O_4 and Mechanism of the Verwey Transition

TL;DR

This paper investigates the electronic and orbital ordering in Fe_3O_4, revealing a complex orbital order that explains the Verwey transition and associated structural distortions.

Contribution

It introduces a novel complex orbital ordered state in Fe_3O_4 and elucidates its role in the Verwey transition mechanism.

Findings

Identification of complex orbital order with noncollinear moments

Connection of orbital order to structural distortions

Explanation of the Verwey transition via orbital and lattice coupling

Abstract

Electronic state and the Verwey transition in magnetite (Fe_3O_4) are studied using a spinless three-band Hubbard model for 3d electrons on the B sites with the Hartree-Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., 1/sqrt(2)[|zx> + i |yz>], ordered (COO) states having noncollinear orbital moments ~ 0.4 mu_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 Pmca and Pmc2_1 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.