Local and collective magnetism of gallium vacancies in GaN studied by GGA+U approach

Magnetic properties of Ga vacancies VGa and vacancy pairs in GaN are analyzed by employing the Generalized Gradient Approximation with the +U corrections. Strong spin polarization stabilizes high spin configurations of VGa, and leads to its negative-Ueff character. Both features are reflected in the magnetic properties of vacancies pairs. Because of electron transfer between two vacancies induced by negative-Ueff, both vacancies can be in different charge and spin states, and thus the spin ground states of a pair can be ferrimagnetic rather than ferro- or antiferromagnetic. Magnetic coupling of VGa-VGa pairs as a function of separation between the defects, their relative orientation, and of the charge state, was calculated. The strength of magnetic coupling is reduced by the U-induced localization of the wave functions. The obtained results show that gallium vacancies can lead to the observed ferromagnetism in irradiated GaN samples.