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We find, through first-principles calculations, that hole doping induces aferromagnetic phase transition in monolayer GaSe. Upon increasing hole density,the average spin magnetic moment per carrier increases and reaches a plateaunear 1.0 $\mu_{\rm{B}}$/carrier in a range of $3\times10^{13}$/cm$^{2}$-$1\times 10^{14}$/cm$^{2}$ with the system in a half-metalstate before the moment starts to descend abruptly. The predicted magnetismoriginates from an exchange splitting of electronic states at the top of thevalence band where the density of states exhibits a sharp van Hove singularityin this quasi-two-dimensional system.

Tunable Magnetism and Half-Metallicity in Hole-doped Monolayer GaSe