Ferromagnetic-antiferromagnetic transition in double perovskites

We study the ordered double perovskite of the type Sr₂FeMO₆ using a tight-binding model with the renormalized perturbation expansion technique. In the ferromagnetic phase (F), we determine the behavior of the critical temperature as a function of the band filling and the Fe-M charge transfer energy. In the antiferromagnetic phase (AF) as in Sr₂FeWO₆ the bands reduce to three one-dimensional bands. The electronic energy remains larger than in the F state but the difference decreases with increasing charge transfer energy. Therefore, with increasing Fe-M charge transfer energy, the transition to the AF state can be easily driven by the superexchange interaction. We find that the transition occurs for values of the charge transfer energy such that the Fe and M valences obtained are compatible with the values 2 + and 6 + usually considered for Sr₂FeWO₆. Our approach thus provides a sensible scheme for the transition. We also discuss the F-AF transition in Sr₂ FeMo_x W_{1 - x} O₆ as a function of doping.