Disorder and the effective Mn-Mn exchange interaction in Ga$_{1-x}$Mn$_x$As diluted magnetic semiconductors

TL;DR

This study uses ab initio calculations to analyze how disorder affects Mn-Mn exchange interactions in GaMnAs diluted magnetic semiconductors, revealing concentration dependence and the significance of disorder in magnetic properties.

Contribution

It provides the first detailed ab initio analysis of disorder effects on Mn-Mn exchange interactions across multiple neighbor shells in GaMnAs.

Findings

Mn-Mn exchange interactions depend on Mn concentration.

Disorder and clustering cause large variations in exchange interactions.

Proper disorder modeling is crucial for understanding magnetic behavior.

Abstract

We perform a theoretical study, using {\it ab initio} total energy density-functional calculations, of the effects of disorder on the $Mn-Mn$ exchange interactions for $Ga_{1-x}Mn_xAs$ diluted semiconductors. For a 128 atoms supercell, we consider a variety of configurations with 2, 3 and 4 Mn atoms, which correspond to concentrations of 3.1%, 4.7%, and 6.3%, respectively. In this way, the disorder is intrinsically considered in the calculations. Using a Heisenberg Hamiltonian to map the magnetic excitations, and {\it ab initio} total energy calculations, we obtain the effective $\JMn$, from first ($n=1$) all the way up to sixth ($n=6$) neighbors. Calculated results show a clear dependence in the magnitudes of the $\JMn$ with the Mn concentration $x$. Also, configurational disorder and/or clustering effects lead to large dispersions in the Mn-Mn exchange interactions, in the case of fixed Mn concentration. Moreover, theoretical results for the ground-state total energies for several configurations indicate the importance of a proper consideration of disorder in treating temperature and annealing effects.