Magnetisms in $p$-type monolayer gallium chalcogenides (GaSe, GaS)

Magnetisms in $p$-type monolayer GaX (X=S,Se) is investigated by performing density-functional calculations. Due to the large density of states near the valence band edge, these monolayer semiconductors are ferromagnetic within a small range of hole doping. The intrinsic Ga vacancies can promote local magnetic moment while Se vacancies cannot. Magnetic coupling between vacancy-induced local moments is ferromagnetic and surprisingly long-range. The results indicate that magnetization can be induced by hole doping and can be tuned by controlled defect generation.