Magnetism in semiconductors: A dynamical mean field study of ferromagnetism in Ga₁₋ₓMnₓAs

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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=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 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 in which the spin-orbit coupling is switched off, we conclude that the spin-orbit coupling in Ga₁₋ₓMnₓAs gives rise to frustration in the ferromagnetic order, strengthening recent findings by Zarand and Janko (Phys. Rev. Lett. 89, 047201 (2002)).