Global versus local ferromagnetism in a model for diluted magnetic semiconductors studied with Monte Carlo techniques

A model recently introduced for diluted magnetic semiconductors by Berciu and Bhatt [Phys. Rev. Lett. 87, 107203 (2001)] is studied with a Monte Carlo technique, and the results are compared with Hartree-Fock calculations. For doping rates close to the experimentally observed metal-insulator transition, a picture dominated by ferromagnetic droplets formed below a $T^{*}$ scale emerges. The moments of these droplets align as the temperature is lowered below a critical value $T_C<T^{*}.$ Our Monte Carlo investigations provide critical temperatures considerably smaller than Hartree-Fock predictions. Disorder does not seem to enhance ferromagnetism substantially. The inhomogeneous droplet state should be strongly susceptible to changes in doping and external fields.