Theory of Magnetic Polaron
  The concept of magnetic polaron is analysed and developed to elucidate the nature of itinerant charge carrier states in magnetic semiconductors and similar complex magnetic materials. By contrasting the scattering and bound states of carriers within the $s-d$ exchange model, the nature of bound states at finite temperatures is clarified. The free magnetic polaron at certain conditions is realized as a bound state of the carrier (electron or hole) with the spin wave. Quite generally, a self-consistent theory of a magnetic polaron is formulated within a nonperturbative many-body approach, the Irreducible Green Functions (IGF) method which is used to describe the quasiparticle many-body dynamics at finite temperatures. Within the above many-body approach we elaborate a self-consistent picture of dynamic behavior of two interacting subsystems, the localized spins and the itinerant charge carriers. In particular, we show that the relevant generalized mean fields emerges naturally within our formalism. At the same time, the correct separation of elastic scattering corrections permits one to consider the damping effects (inelastic scattering corrections) in the unified and coherent fashion. The damping of magnetic polaron state, which is quite different from the damping of the scattering states, finds a natural interpretation within the present self-consistent scheme. 
A. L. Kuzemsky