  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.
