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 $0.01 \leq x \leq 0.1$.
Categories: cond-mat.mtrl-sci cond-mat.mes-hall