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Double perovskites like Sr$_2$FeMoO$_6$ are materials with half-metallicground states and ferrimagnetic T$_{\rm{c}}$'s well above room temperature.This paper is the second of our comprehensive theory for half metallic doubleperovskites. Here we derive an effective Hamiltonian for the Fe core spins by"integrating out" the itinerant Mo electrons and obtain an unusual doublesquare-root form of the spin-spin interaction. We validate the classical spinHamiltonian by comparing its results with those of the full quantum treatmentpresented in the companion paper "Theory of Half-Metallic Double Perovskites I:Double Exchange Mechanism". We then use the effective Hamiltonian to computemagnetic properties as a function of temperature and disorder and discuss theeffect of excess Mo, excess Fe, and anti-site disorder on the magnetization andT$_{\rm{c}}$. We conclude with a proposal to increase T$_{\rm{c}}$ withoutsacrificing carrier polarization.

Theory of Half-Metallic Double Perovskites II: Effective Spin Hamiltonian and Disorder Effects