Ferromagnetic to ferrimagnetic crossover in Cr-doped GaN nanohole arrays

Using spin-polarized density-functional theory with exchange and correlation potential, approximated by both the generalized gradient approximation (GGA) and the GGA+U methods, we show that the coupling between a pair of Cr atoms substituted in GaN nanoholes is ferromagnetic. The interaction between the two Cr atoms, each carrying an average magnetic moment of around 2.5 mu(B), is short ranged and mediated by the neighboring N atom. As the concentration of Cr increases, clustering ensues and the coupling changes from ferromagnetic to ferrimagnetic resulting in a significant reduction in the average magnetic moment per Cr atom.