Influence of non-local exchange on RKKY interactions in III-V diluted   magnetic semiconductors
  The RKKY interaction between substitutional Mn local moments in GaAs is both spin-direction-dependent and spatially anisotropic. In this Letter we address the strength of these anisotropies using a semi-phenomenological tight-binding model which treats the hybridization between Mn d-orbitals and As p-orbitals perturbatively and accounts realistically for the non-local exchange interaction between their spins. We show that exchange non-locality, valence-band spin-orbit coupling, and band-structure anisotropy all play a role in determining the strength of both effects. We use these results to estimate the degree of ground-state magnetization suppression due to frustrating interactions between randomly located Mn ions. 
C. Timm and A.H. MacDonald