Ferromagnetism in GaN:Gd: A Density Functional Theory Study

First-principle calculations of the electronic structure and magnetic interaction of GaN:Gd have been performed within the generalized gradient approximation (GGA) of the density functional theory with the on-site Coulomb energy $U$ taken into account (also referred to as $\mathrm{GGA}+U$). The ferromagnetic $p\mathrm{\text{−}}d$ coupling is found to be over 2 orders of magnitude larger than the $s\mathrm{\text{−}}d$ exchange coupling. The experimental colossal magnetic moments and room-temperature ferromagnetism in GaN:Gd reported recently are explained by the interaction of Gd $4f$ spins via $p\mathrm{\text{−}}d$ coupling involving holes introduced by intrinsic defects such as Ga vacancies.

Figure 1

${\mathrm{GdGa}}_7{\mathrm{N}}_8$ supercells of Gd-doped GaN with the (a) zinc blende and (b) wurtzite structures. The blue balls represent N atoms, the mauve balls represent Ga atoms while the turquoise balls represent Gd atoms.

Figure 2

Calculated band structures [(a) and (b)] and $d$ orbital DOS (c) of the ${\mathrm{GdGa}}_7{\mathrm{N}}_8$ supercell in the FM configuration. The circle size of each state in the band structures has been chosen to be proportional to the strength of the Gd $4f$ orbitals (said to be band-character plotted in some literature). The energy of the VBM is taken to be zero.

Figure 3

Calculated band structure [(a) and (b)] and $d$ orbital DOS (c) of ${\mathrm{GdGa}}_7{\mathrm{N}}_7$ supercell in the FM configuration. The Gd $d$ orbitals are now band-character plotted in the band structures while the Fermi level is now taken to be zero.

Figure 4

Calculated band structures [(a) and (b)] and $d$ orbital DOS (c) of ${\mathrm{GdGa}}_6{\mathrm{N}}_8$ in the FM configuration. The Gd $d$ orbitals are again band-character plotted in the band structures. The Fermi level is again taken to be zero.