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The magnetic properties of the diluted magnetic semiconductor Ga1-xMnxAs are studied within the dynamical cluster approximation. We use the k•p Hamiltonian to describe the electronic structure of GaAs with spin-orbit coupling and strain effects. We show that nonlocal effects are essential for explaining the experimentally observed transition temperature and saturation magnetization. We also demonstrate that the cluster anisotropy is very strong and induces rotational frustration and a cube-edge direction magnetic anisotropy at low temperature. With this, we explain the temperature-driven spin reorientation in this system. © 2010 The American Physical Society.

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Physical Review Letters