Theory of magnetic and transport properties of double perovskites*

We map out the finite temperature phase diagram of the generalized double exchange model for double perovskites $A_2BB^\prime O_6$ by self consistently solving the tight-binding Hamiltonian of the ``fast'' electrons moving in a background of ``slowly'' fluctuating classical spins. We investigate the stability of ferromagnetic and various antiferromagnetic phases as a function of electron density, the $B$-$B^\prime$ charge transfer energy, the direct $B^\prime$-$B^\prime$ hopping and various exchange interactions. We compute the temperature and doping dependence of the $B$-site magnetization and conduction electron polarization. We also investigate the effects of antisite ($B/B^\prime$) disorder on magnetism and transport. We thus gain insight into material trends in the properties of $A_2 Fe B^\prime O_6$ and $A_2 Cr B^\prime O_6$ families, with $B^\prime =Mo, W$ and $A=La, Ca, Sr$.