Effective Heisenberg exchange integrals of diluted magnetic semiconductors determined within realistic multi-band tight-binding models

Diluted magnetic semiconductors (DMS) like Ga 1− x Mn x As are described by a realistic tight-binding model (TBM) for the (valence) bands of GaAs, by a Zener ( J -)term modeling the coupling of the localized Mn-spins to the spins of the valence band electrons, and by an additional potential scattering ( V -) term due to the Mn-impurities. We calculate the effective (Heisenberg) exchange interaction between two Mn-moments mediated by the valence electrons. The influence of the number of bands taken into account (6-band or 8-band TBM) and of the potential (impurity) scattering V -term is investigated. We find that for realistic values of the parameters the indirect exchange integrals show a long-range, oscillating (RKKY-like) behavior, if the V -term is neglected, probably leading to spin-glass behavior rather than magnetic order. But by including a V -term of a realistic magnitude the exchange couplings become short ranged and mainly positive allowing for the possibility of ferromagnetic order. Our results are in good agreement with available results of ab initio treatments.