New aspects of Verway transition in magnetite

A new mechanism of the Verway transition in magnetite (Fe3O4), which has been argued to be a charge ordering transition so far, is proposed. Based on the mean field calculations for the three band model of spinless fermions appropriate for the d electrons of the Fe ions on the B sites, it is indicated that the phase transition should be the 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 by the Peierls lattice distortion with the period of two Fe(B) ions, i.e., bond dimerization. Furthermore, it is found that the interplay between such lattice distortion in the Fe(B) ions and the lattice elastic energy of the Fe(B)-O as well as the 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. PACS: 71.10.Fd,71.30.+h,71.10.Hf,75.50.Gg