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Onset of Ferromagnetism in Low-Doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Ga</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>โ</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Mn</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mi>As</mml:mi></mml:math>
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 โฆ