The recently synthesized two-dimensional electride ${\mathrm{Gd}}_{2}\mathrm{C}$ was proposed to be a ferromagnetic metal that possesses multiple pairs of Weyl points and may display a large anomalous Hall conductivity [Liu et al., Phys. Rev. Lett. 125, 187203 (2020)]. In view of its layered structure, here we carry out first-principles studies on the magnetic and electronic properties of ${\mathrm{Gd}}_{2}\mathrm{C}$ in the ultrathin monolayer limit. We find that monolayer ${\mathrm{Gd}}_{2}\mathrm{C}$ remains ferromagnetic like the bulk form and the hydrogenation can effectively tune its magnetism and electronic structure. With one-sided full coverage of hydrogen atoms, monolayer ${\mathrm{Gd}}_{2}\mathrm{C}$ becomes a half-metal with one spin channel around the Fermi level. For two-sided full hydrogenation, monolayer ${\mathrm{Gd}}_{2}\mathrm{C}$ transforms to an antiferromagnetic insulator with a band gap of 0.8 eV. Our studies show that monolayer electride ${\mathrm{Gd}}_{2}\mathrm{C}$ can perform multiple magnetic and electronic transitions with different levels of hydrogenation and may be also adopted to construct a planar heterojunction with selective area adsorption of hydrogen atoms, which has promising applications in future electronic and spintronic devices.
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