Double Exchange via Degenerate Orbitals

We consider the double exchange for systems in which doped electrons occupy degenerate orbitals, treating the realistic situation with double degenerate $e_g$ orbitals. We show that the orbital degeneracy leads in general to the formation of anisotropic magnetic structures and that, in particular, depending on the doping concentration, the layered magnetic structures of the $A$-type and the chainlike structures of the $C$-type are stabilized. The phase diagram that we obtain provides an explanation for the experimentally observed magnetic structures of some overdoped (electron-doped) manganites of the type ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$, ${\mathrm{Pr}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$, and ${\mathrm{Sm}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$, with $x>\mathrm{}0.5\mathrm{}$.