Hole magnetic polarons in zinc-blende semimagnetic semiconductors

A theory of hole magnetic polarons in diluted magnetic semiconductors of zinc-blende structure is presented, following the method introduced by Baldereschi and Lipari to solve the neutral acceptor problem. An expression for the nonlinear magnetic potential is determined in the mean-field approximation. An efficient numerical method is used to solve the system of two coupled differential equations. Results are presented for quantum dots, neutral accepters and free magnetic polarons. The present theory predicts a substantial increase of the magnetic polaron energy in all cases. An excellent parameter-free fit of acceptor magnetic polaron energy versus temperature is obtained for diluted systems. Simplified models based on a single parabolic band with two adjustable parameters, the hole mass and the exchange integral, are shown to be inadequate, in particular in the case of quantum dots.