  We present a combined theoretical and experimental study of the ferromagnetic
semiconductor (Ga,Mn)As which explains the remarkably large changes observed on
low temperature annealing. Careful control of the annealing conditions allows
us to obtain samples with ferromagnetic transition temperatures up to 159 K. Ab
initio calculations, and resistivity measurements during annealing, show that
the observed changes are due to out-diffusion of Mn interstitials towards the
surface, governed by an energy barrier of about 0.7-0.8 eV. The Mn interstitial
is a double donor resulting in compensation of charge carriers and suppression
of ferromagnetism. Electric fields induced by high concentrations of
substitutional Mn acceptors have a significant effect on the diffusion.
