Electrostatically driven charge-ordering in magnetite below the Verwey temperature

This work describes the stability of different charge models for magnetite, Fe3O4, below the Verwey temperature (TV). Thirty-seven configurations allowed by the Anderson condition are analysed by means of Madelung calculations, including models proposed by Verwey, Mizoguchi and Zuo. A new approach based on summation over cubic cells is applied that ensured rapid convergence of lattice sums. The lowest Madelung energy has been found for the model in which coupled chains of Fe2+ and Fe3+ ions form structures parallel to the c-axis. These structures are similar to double helices having a period of twice the cubic lattice constant. Thus it has been shown, contrary to previous studies, that the Coulomb energy alone is sufficient to stabilize the charge order involving doubling of the c-axis.