The RKKY interaction between substitutional Mn local moments in GaAs is both spin-direction dependent and spatially anisotropic. In this paper we address the strength of these anisotropies using a semiphenomenological tight-binding model that treats the hybridization between Mn $d$-orbitals and As $p$-orbitals perturbatively and accounts realistically for its nonlocality. We show that valence-band spin-orbit coupling, exchange nonlocality, and band-structure anisotropy all play a role in determining the strength of these effects. We use the results to estimate the degree of ground-state magnetization suppression due to frustrating interactions between randomly located Mn ions and to comment on the relationships between different models of III-V diluted magnetic semiconductor ferromagnetism.

• Received 5 January 2005

DOI:https://doi.org/10.1103/PhysRevB.71.155206