Effective Hamiltonian for Ga_{1-x}Mn_xAs in the Dilute Limit

Abstract

We derive an effective Hamiltonian for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ in the dilute limit, where ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ can be described in terms of spin $F=3/2$ polarons hopping between the {\rm Mn} sites and coupled to the local {\rm Mn} spins. We determine the parameters of our model from microscopic calculations. Our approach treats the large Coulomb interaction in a non-perturbative way, captures the effects of spin-orbit coupling and disorder, and is appropriate for other p-doped magnetic semiconductors. Our model applies to uncompensated {\rm Mn} concentrations up to $x\sim 0.03$.

4 pages, 4 figures, Version to appear in Phys. Rev. Lett