Dynamical mean field study of ferromagnetism in Ga1-xMnxAs

We study magnetism in magnetically doped semiconductors with the specific example of Ga1-xMnxAs. Amongst a number of interesting models proposed so far, the model employed by G. Zar'and and B. Jank'o is of specific attention as it incorporates both the strong spin-orbit coupling effect in the band structure of the pure GaAs and the carriers (in this case holes) interaction with magnetic impurity atoms. The dispersion part of the Hamiltonian for this model is a simplification of a more general Hamiltonian first introduced by Kohn and Luttinger. The spin-orbit coupling part of this simplified Hamiltonian can be diagonalized by the quantization of carriers spins along their momentum directions that maps the Hamiltonian onto a chiral basis. Based upon a perturbation theory approach, (RKKY) Zar'and and Jank'o conclude that due to the chirality of this Hamiltonian, Ga1-xMnxAs is a frustrated ferromagnet exhibiting features similar to spin glasses and spin ice compounds. We develop a systematic dynamical mean field based approach and invoke it in order to more precisely address the effect of chirality in Zar'and and Jank'o Hamiltonian. We calculate the impurity atom magnetization, ferromagnetic phase transition temperature Tc and carrier spin polarization for a variety of physically relevant parameters. Our findings support the conclusion by Zar'and and Jank'o that chirality leads to frustration in the Ga1-xMnxAs system. In addition, a number of other formerly observed physical features are also inspected and verified in this work. There is also illustrated a comparison between the static mean field and the DMFA in both the presence and absence of chirality. It turns out that for large values of impurity-carrier (holes) coupling Jc, the static mean field and DMFA to some extent differ.