Magnetic model for the ordered double perovskites

We construct an effective spin model from the coupled spin-fermion problem appropriate to double perovskites of the form A(2)BB(')O(6). The magnetic model that emerges is reminiscent of double exchange and we illustrate this "reduction" in detail for the case of perfect B-B(') structural order, i.e., no antisite disorder. We estimate the effective exchange between the magnetic B ions in terms of the electronic parameters, study the "classical" magnetic model using Monte Carlo techniques and compare this approach to a full numerical solution of the spin-fermion problem. The agreement is surprisingly good and promises a quick estimate of magnetic properties when coupled with ab initio electronic structure. The scheme generalizes to the presence of antisite disorder.