Theory of half-metallic double perovskites. II. Effective spin Hamiltonian and disorder effects

Double perovskites such as Sr₂FeMoO₆ are materials with half-metallic ground states and ferrimagnetic Tc's well above room temperature. This paper is the second of our comprehensive theory for half-metallic double perovskites. Here we derive an effective Hamiltonian for the Fe core spins by ``integrating out'' the itinerant Mo electrons and obtain an unusual double-square-root form of the spin-spin interaction. We validate the classical spin Hamiltonian by comparing its results with those of the full quantum treatment presented in a companion paper [O. N. Meetei et al., Phys. Rev. B 87, 165104 (2013)]. We then use the effective Hamiltonian to compute magnetic properties as a function of temperature and disorder and discuss the effect of excess Mo, excess Fe, and antisite disorder on the magnetization and Tc. We conclude with a proposal to increase Tc without sacrificing carrier polarization.