Aspects of the Verwey transition in magnetite

A mechanism of the Verwey transition in magnetite (Fe₃O₄), which has been argued to be a charge ordering transition so far, is proposed. Based on mean-field calculations for a three-band model of spinless fermions appropriate for d electrons of Fe ions in B sites, it is indicated that the phase transition should be a bond dimerization due to the cooperative effects of strong electronic correlation and electron-phonon interaction. The results show that the ferro-orbital ordered state is stabilized in a wide temperature range due to the strong on-site Coulomb interaction between different t2g orbitals, resulting in an effectively one-dimensional electronic state, which leads the system toward an insulating state through a Peierls lattice distortion with a period of two Fe(B) ions, i.e., bond dimerization. Furthermore, it is found that the interplay between such lattice distortions in Fe(B) ions, and the lattice elastic energy of Fe(B)-O as well as Fe(A)-O bonds, gives rise to a competition between two different three-dimensional patterns for the bond dimerization, and can stabilize a complicated one with a large unit-cell size. The results are compared with the known experimental facts.