Polaron Percolation in Diluted Magnetic Semiconductors

We theoretically study the development of spontaneous magnetization in diluted magnetic semiconductors as arising from a percolation of bound magnetic polarons. Within the framework of a generalized percolation theory we derive analytic expressions for the Curie temperature and the magnetization in the limit of low carrier density, obtaining excellent quantitative agreement with Monte Carlo simulation results and good qualitative agreement with experimental results.