  The recently synthesized two-dimensional electride Gd$_2$C was proposed to be
a ferromagnetic metal that possesses multiple pairs of Weyl points and may
display a large anomalous Hall conductivity [Liu \textit{et al.}, Phys. Rev.
Lett. \textbf{125}, 187203 (2020)]. In view of its layered structure, here we
carry out first-principles studies on the magnetic and electronic properties of
Gd$_2$C in the ultrathin monolayer limit. We find that monolayer Gd$_2$C
remains ferromagnetic like the bulk form and the hydrogenation can effectively
tune its magnetism and electronic structure. With one-sided coverage of
hydrogen atoms, monolayer Gd$_2$C becomes a half-metal with one spin channel
around the Fermi level. For two-sided hydrogenation, monolayer Gd$_2$C
transforms to an antiferromagnetic insulator with a band gap of 0.8 eV. Our
studies show that monolayer electride Gd$_2$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.
