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.Comment: 4 pages RevTeX, 2 figures included, v2: replacement because of font
proble