Eur. Phys. J. B (2013) 86: 11
https://doi.org/10.1140/epjb/e2012-30795-4

Regular Article

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

¹ Institute for Theoretical Physics, University of Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
² Institut Néel, 25 avenue des Martyrs, B.P. 166, 38042 Grenoble Cedex 09, France
³ School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany

^a e-mail: sbarthel@itp.uni-bremen.de

Received: 31 August 2012
Received in final form: 31 October 2012
Published online: 14 January 2013

Abstract

Diluted magnetic semiconductors (DMS) like Ga_1−xMn_xAs 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.