Ferromagnetic spin-polaron on complex lattices

We present a simpler derivation of the exact solution of a spin-polaron in a ferromagnet and generalize it to complex lattices and/or longer range exchange interactions. As a specific example, we analyze a two-dimensional MnO$_2$-like lattice (as in the ferromagnetic layers in LaMnO$_3$) and discuss the properties of the resulting spin-polaron in various regimes. At strong couplings the solution is reminiscent of the Zhang-Rice singlet, however the electronic wavefunction involved in the singlet is dependent on the momentum of the singlet, and multiple bands may appear.