Point defects as a test ground for the local density approximation +U theory: Mn, Fe, and V(Ga) in GaN

Electronic structure of the Mn and Fe ions and of the gallium vacancy V(Ga) in GaN was analysed within the GGA + U approach. First, the +U term was treated as a free parameter, and applied to p(N), d(Mn), and d(Fe). The band gap of GaN is reproduced for U(N) ≈ 4 eV. The electronic structure of defect states was found to be more sensitive to the value of U than that of the bulk states. Both the magnitude and the sign of the U-induced energy shifts of levels depend on occupancies, and thus on the defect charge state. The energy shifts also depend on the hybridization between defect and host states, and thus are different for different level symmetries. In the case of V(Ga), these effects lead to stabilization of spin polarization and the "negative-U(eff)" behavior. The values of Us were also calculated using the linear response approach, which gives U(Fe) ≈ U(Mn) ≈ 4 eV. This reproduces well the results of previous hybrid functionals calculations. However, the best agreement with the experimental data is obtained for vanishing or even negative U(Fe) and U(Mn).