Magnetism in semiconductors: A dynamical mean field study of ferromagnetism in Ga_(1-x)Mn_xAs

We employ the dynamical mean field approximation to perform a systematic study of magnetism in Ga_{1-x}Mn_xAs. Our model incorporates the effects of the strong spin-orbit coupling on the J=3/2 GaAs valence bands and of the exchange interaction between the randomly distributed magnetic ions and the itinerant holes. The ferromagnetic phase transition temperature T_c is obtained for different values of the impurity-hole coupling J_c and of the hole concentration n_h 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 in which the spin-orbit coupling is switched off, we conclude that the spin-orbit coupling in Ga_{1-x}Mn_xAs gives rise to frustration in the ferromagnetic order, strengthening recent findings by Zarand and Janko (Phys. Rev. Lett. 89, 047201 (2002)).