Band Effects on Charge Ordering in Fe 3 O 4

The stability of the electronic long‐range order in Fe 3 O 4 with respect to the band term is investigated using a spinless fermion model with Coulomb interactions between nearest ( U 1 ) and next nearest neighbours ( U 2 ), where U 1 > t > U 2 ( t overlap integral) is assumed. This model is treated by perturbation theory up to third order in t and an effective spin Hamiltonian is constructed. From an approximate solution the long‐range order condition at T = 0 is found to be \documentclass{article}\pagestyle{empty}\begin{document}$ t< 0,85\sqrt[3]{{U_1^2 U_2 }} $\end{document} and thedependence of the Verwey transition temperature T V on t is calculated. The experimentally observed pressure dependence of T V is explained.