Stability and dynamics of free magnetic polarons

The stability and dynamics of a free magnetic polaron are studied by Monte Carlo simulation of a classical two-dimensional Heisenberg model coupled to a single electron. We compare our results to the earlier mean-field analysis of the stability of the polaron, finding qualitative similarity but quantitative differences. The dynamical simulations give estimates of the temperature dependence of the polaron diffusion, as well as a crossover to a tunnelling regime.