Onset of ferromagnetism in low-doped Ga1-xMnxAs

We develop a quantitatively predictive theory for impurity-band ferromagnetism in the low-doping regime of Ga1-xMnxAs. We compare it with measurements of a series of samples whose compositions span the transition from paramagnetic insulating to ferromagnetic conducting behavior. The theoretical Curie temperatures depend sensitively on the local fluctuations in the Mn-hole binding energy, which originate from Mn disorder and As antisite defects. The experimentally determined hopping energy is an excellent predictor of the Curie temperature, in agreement with the theory.