Theory of Manganese-Manganese interaction in GaMnAs

TL;DR

This paper studies the anisotropic interaction between Mn ions in GaMnAs, revealing how it varies with distance and concentration, and confirms the validity of an effective Hamiltonian in dilute regimes.

Contribution

It provides a detailed analysis of Mn-Mn interactions in GaMnAs using a six-band model and derives parameters for an effective Hamiltonian in dilute conditions.

Findings

Interaction is strongly anisotropic at low concentrations

Interaction becomes nearly isotropic at short distances

Effective Hamiltonian parameters are extracted for dilute limit

Abstract

We investigate the interaction of two Mn ions in the dilute magnetic semiconductor GaMnAs using the variational envelope wave function approach within the framework of six band model of the valence band. We find that the effective interaction between the Mn core spins at a typical separation d is strongly anisotropic for active Mn concentrations less than x = 1.3%, but it is almost isotropic for shorter distances (d < 13A). As a result, in unannealed and strongly compensated samples strong frustration effects must be present. We also verify that an effective Hamiltonian description can be used in the dilute limit, x < 1.3%, and extract the parameters of this effective Hamiltonian.