It is demonstrated by SQUID measurements that (Ga,Mn)As films can exhibit perpendicular easy axis at low temperatures, even under compressive strain, provided that the hole concentration is sufficiently low. In such films, the easy axis assumes a standard in-plane orientation when the temperature is raised towards the Curie temperature or the hole concentration is increased by low temperature annealing. These findings are shown to corroborate quantitatively the predictions of the mean-field Zener model for ferromagnetic semiconductors. The in-plane anisotropy is also examined, and possible mechanisms accounting for its character and magnitude are discussed.
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