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 (PRL 87, 107203 (2001)) is studied with a Monte Carlo technique, and the results are compared to 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 Tc<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.