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Magnetisms in $p$-type monolayer GaX (X=S,Se) is investigated by performingdensity-functional calculations. Due to the large density of states near thevalence band edge, these monolayer semiconductors are ferromagnetic within asmall range of hole doping. The intrinsic Ga vacancies can promote localmagnetic moment while Se vacancies cannot. Magnetic coupling betweenvacancy-induced local moments is ferromagnetic and surprisingly long-range. Theresults indicate that magnetization can be induced by hole doping and can betuned by controlled defect generation.

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