We develop a quantitatively predictive theory for impurity-band ferromagnetism in the low-doping regime of GaMnAs and compare with experimental 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 originates from disorder in the Mn distribution as well as the presence of As antisite defects. The experimentally-determined hopping energy at the Curie temperature is roughly constant over a series of samples whose conductivities vary more than 10^4 and whose hole concentrations vary more than 10^2. Thus in this regime the hopping energy is an excellent predictor of the Curie temperature for a sample, in agreement with the theory.
@article{arxiv.0708.1063,
title = {Onset of ferromagnetism in low-doped GaMnAs},
author = {B. L. Sheu and R. C. Myers and J. -M. Tang and N. Samarth and D. D. Awschalom and P. Schiffer and M. E. Flatté},
journal= {arXiv preprint arXiv:0708.1063},
year = {2008}
}