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

TL;DR

This paper calculates effective Heisenberg exchange integrals in diluted magnetic semiconductors using realistic multi-band tight-binding models, revealing how impurity scattering influences magnetic ordering.

Contribution

It introduces a detailed tight-binding approach to compute exchange interactions in DMS, highlighting the impact of impurity potential on magnetic behavior.

Findings

Long-range RKKY-like interactions without impurity scattering

Short-range, predominantly positive exchange with realistic impurity potential

Agreement with ab-initio results on exchange interactions

Abstract

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 {\DH} 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.