We derive an effective Hamiltonian for ${ \rm Ga}_{ 1-x}{ \rm Mn}_x { \rm As}$ in the dilute limit, where ${ \rm Ga}_{ 1-x}{ \rm Mn}_x { \rm As}$ 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 $x \sim 0.03$.
Categories: cond-mat.mtrl-sci cond-mat.mes-hall