Theory of the magnetic polaron

We construct exact Green's functions for a single electron in a ferromagnetic semiconductor, including both spin-conserving and spin-flip processes at $T=0$. We contrast two cases: ferromagnetic and antiferromagnetic coupling of the electron's spin to the lattice. In the former case, a small-k electron will have its spin totally polarized in the predominant direction, whereas in the latter, deviation from saturation polarization is to be expected. Crucial differences between bound- and scattering-state contributions to the electron's spectral weight are highlighted.