Theory of ferromagnetism driven by superexchange in dilute magnetic semiconductors

TL;DR

This paper presents a theoretical study of ferromagnetism in Ga$_{1-x}$Mn$_x$N, showing that superexchange interactions between Mn spins lead to ferromagnetism consistent with experimental Curie temperatures.

Contribution

It demonstrates that superexchange, rather than itinerant carriers, drives ferromagnetism in GaMnN, with quantitative agreement between theory and experiment for Curie temperatures.

Findings

Superexchange mediates ferromagnetism in GaMnN.

Theoretical Curie temperatures match experimental data.

No itinerant carriers are involved in magnetic coupling.

Abstract

Magnetic properties of Ga$_{1-x}$Mn$_x$N are studied theoretically by employing a tight binding approach to determine exchange integrals $J_{ij}$ characterizing the coupling between Mn spin pairs located at distances $R_{ij}$ up to the 16th cation coordination sphere in zinc-blende GaN. It is shown that for a set of experimentally determined input parameters there are no itinerant carriers and the coupling between localized Mn$^{3+}$ spins in GaN proceeds via superexchange that is ferromagnetic for all explored $R_{ij}$ values. Extensive Monte Carlo simulations serve to evaluate the magnitudes of Curie temperature $T_\mathrm{C}$ by the cumulant crossing method. The theoretical values of $T_\mathrm{C}(x)$ are in quantitative agreement with the experimental data that are available for Ga$_{1-x}$Mn$_x$N with randomly distributed Mn$^{3+}$ ions with the concentrations $0.01 \leq x \leq 0.1$.