Theory of ferromagnetic double perovskites*

We derive and validate an effective classical spin model which describes the magnetic properties of double perovskites (DP) like Sr$_{2}$FeMoO$_{6}$, including the effects of disorder and carrier concentration. This model generalizes the Anderson-Hasegawa model for manganites to DP's. We validate our effective spin model by making detailed comparisons with the results obtained from a quantum Hamiltonian of itinerant electrons interacting with spins on the Fe-sites. We show that the conduction electron polarization at the chemical potential $P(T)$ tracks the temperature-dependence of the total magnetization $M(T)$. We point out the importance of Coulomb correlation $U$ on Mo-sites and of direct Mo-Mo hopping $t^\prime$ on stabilizing the ferromagnetic phase as a function of electron doping (by La substitution of Sr). We show how the small parameters $U$ and $t^\prime$ are crucial in understanding the experimental results for T$_c$ as a function of carrier concentration. We predict how the ferromagnetic $T_c$ can be raised substantially (up to 40\%), without sacrificing the polarization $P$, by a combination of excess Fe and La-doping.