Effective three-band model for double perovskites

We start from a six-band model describing the transition-metal ${t}_{2g}$ orbitals of half metallic double perovskite systems, such as ${\mathrm{Sr}}_{2}{\mathrm{FeMoO}}_{6},$ in which only one of the transition-metal ions (Fe) contains important intratomic repulsion ${U}_{\mathrm{Fe}}.$ By eliminating the Mo orbitals using a low-energy reduction similar to that used in the cuprates, we construct a Hamiltonian which contains only effective ${t}_{2g}$ Fe orbitals. This allows us to treat exactly ${U}_{\mathrm{Fe}}$ and most of the Fe-Mo hopping. As an application, we treat the effective Hamiltonian in the slave-boson mean-field approximation and calculate the position of the metal-insulator transition and other quantities as a function of pressure or on-site energy difference.