Crystal field model simulations of magnetic response of pairs, triplets and quartets of Mn3+ ions in GaN

A ferromagnetic coupling between localized Mn spins was predicted in a series of ab initio and tight binding calculations and experimentally verified for the dilute magnetic semiconductor Ga1−x Mn x N. In the limit of small Mn concentrations, x ≲ 0.01, the paramagnetic properties of this material were successfully described using a single ion crystal field model approach. In order to obtain the description of magnetization in (Ga,Mn)N in the presence of interacting magnetic centers, we extend the previous model of a single substitutional Mn3+ ion in GaN by considering pairs, triplets and quartets of Mn3+ ions coupled by a ferromagnetic superexchange interaction. Using this approach we investigate how the magnetic properties, particularly the magnitude of the uniaxial anisotropy field, change as the number of magnetic Mn3+ ions in a given cluster increases from 1 to 4. Our simulations are then exploited in explaining experimental magnetic properties of Ga1−x Mn x N with x ≅ 0.03, where the presence of small magnetic clusters gains in significance. As a result the approximate lower and upper limits for the values of exchange couplings between Mn3+ ions in GaN, being in nearest neighbors (nns) J nn and next nns J nnn positions, respectively, are established.