Verwey transition in magnetite: Finite-temperature mean-field solution of the Cullen-Callen model

Verwey transition in magnetite is studied by solving the Cullen-Callen spinless one-band model at finite temperature, extending the work of Cullen and Callen from the T=0 to T{≠}0 regime. A complete phase diagram of the model in the (U/t,T) plane is presented here, which exhibits three phases---a disordered phase and two ordered phases, one multiply ordered and one singly ordered. It is also explicitly shown that the transitions from the disordered phase to the ordered phases are of the first-order type, and they are entropy driven. I also find that for the transition temperature near the experimental value of 120 K, the transition is from the disordered state to the multiply ordered state, and not to the singly ordered state.