Neutral and charged embedded clusters of Mn in doped GaN from first principles

Based on extensive density-functional theory calculations, the spatial distribution and magnetic coupling of Mn atoms in Mn:GaN have been reinvestigated by doping up to five Mn atoms in large supercells, where the formation energies and the electronic structure for both the neutral and charged valence states are studied. The doped Mn atoms have a strong tendency to form substitutional Mn-N-Mn bonded embedded clusters with short-range magnetic interactions, where the long-range wurtzite structure is maintained. While for neutral pair doping the coupling is ferromagnetic regardless of the distance and orientation of the Mn atoms, the negatively charged states tend to weaken the parallel coupling. Significantly, for larger (than pair) cluster configurations for both neutral and all the energetically favorable charged states, states containing antiparallel coupling are always favored. Thus, we argue that the "giant cluster moment" in Mn:GaN, as proposed by Rao and Jena based on study of free clusters and calculated by Sandratskii [Phys. Rev. B 71, 045210 (2005)], is not applicable for "larger" (>2) Mn-cluster-doped GaN. The size of the supercells employed and the atomic relaxation are found crucial for an accurate description, and are partially responsible for these discrepancies. Also important is that the electrical conductivity of Mn:GaN depends sensitively on the valence states, where the negatively charged state Mn2+ (d5) exhibits highly insulating character as observed in experiments. The formation of embedded clustering leads to a strong local structural distortion and a significant spin polarization on neighboring N atoms due to hybridization of Mn 3d and N 2p orbitals. Our results highlight the intrinsically complex nature of the spatial distribution and magnetism in transition metal doped dilute magnetic semiconductors, and can rationalize some hitherto puzzling experimental observations, notably the low saturation moments, the contracted lattice constants, and the highly insulating behavior.