Orbital Order in (LaMnO$_3$)$_m$(SrMnO$_3$)$_n$ Superlattice

A realistic model for (LaMnO$_3$)$_m$ (SrMnO$_3$)$_n$ is constructed and solved by the semiclassical approximation. The model includes electron-electron, electron-lattice, and lattice-lattice interactions. Technically, we generalize the semiclassical approximation to the multi-orbital system and include the cooperative Jahn-Teller effect in the impurity problem. Within this framework, we present the orbital order in the superlattice.