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We employ the dynamical mean-field approximation to perform a systematic study of magnetism in Ga1-xMnxAs. Our model incorporates the effects of the strong spin-orbit coupling on the J=32 GaAs valence bands and of the exchange interaction between the randomly distributed magnetic ions and the itinerant holes. The ferromagnetic phase transition temperature Tc is obtained for different values of the impurity-hole coupling Jc and of the hole concentration nh at the Mn doping of x=0.05. We also investigate the temperature dependence of the local magnetization and spin polarization of the holes. By comparing our results with those for a single band Hamiltonian, we conclude that the spin-orbit coupling in Ga1-xMnxAs gives rise to frustration in the ferromagnetic order, strengthening recent findings by Zaránd and Jankó [Phys. Rev. Lett. 89, 047201 (2002)]. © 2005 The American Physical Society.

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Physical Review B - Condensed Matter and Materials Physics