Magnetic behavior and clustering effects in Mn-doped boron nitride sheets

Ab initio calculations are performed in the framework of density functional theory on Mn-doped boron nitride sheets, which are candidates for two-dimensional diluted magnetic semiconductors (DMSs). Each type of substitution reveals a qualitatively different magnetic behavior encompassing ferromagnetic, anti-ferromagnetic and spin glass ordering. The ability of formation of these defects is also discussed. We analyze the dependence of the exchange couplings on the distance between impurities and the typical range and distribution are extracted. Multiple-impurity configurations are considered and the results are mapped on an Ising-type Hamiltonian with higher order exchange interactions, revealing deviations from the standard two-spin models. The percolation of interacting magnetic moments is discussed and the critical concentration is determined for the underlying transition from a ferromagnetic to a super-paramagnetic state. We conclude our study by providing the optimal conditions for doping in order to obtain a ferromagnetic DMS.