Theory of the self-trapped paramagnetic spin polaron

The self-trapped spin polaron is studied for a purely paramagnetic crystal in the limit of an extremely dilute system of carriers. A Zubarev-Green-function decoupling scheme is used. Owing to spin-flip processes the trapping potential for the spin polaron is shown to vanish as the width of the conduction band,E _b, becomes small compared with thes?f ors?d exchange constant,I. ForE _b?I our results agree with those of Kasuyaet al. In the opposite limit of a degenerate system of carriers the term that leads to trapping in the dilute case is shown to become the RKKY indirect-exchange interaction.