Two-dimensional rare-earth Janus 2H−GdXY (X,Y=Cl,Br,I;

Two-dimensional (2D) ferromagnetic semiconductors hold great interest due to their potential applications for nanoscale electronic devices. In this paper, the Janus $2H\text{\ensuremath{-}}\mathrm{Gd}XY$ $(X, Y=\mathrm{Cl},\mathrm{Br},\mathrm{I},X\ensuremath{\ne}Y)$ monolayers with rare-earth element Gd ($4{f}^{7}+5{d}^{1}$) are predicted by first-principles calculations. Small exfoliation energy of less than $0.25 \mathrm{J}/{\mathrm{m}}^{2}$ and excellent dynamical/thermal stabilities can be confirmed for the Janus $2H\text{\ensuremath{-}}\mathrm{Gd}XY$ monolayers, which exhibit the bipolar magnetic semiconductor character with high Curie temperatures above 260 K and large spin-orbit coupling effect, and can be further transformed into the half-semiconductor phase under proper tensile strains (5--6%). In addition, in-plane magnetic anisotropy can be observed in the $2H$-GdICl and $2H$-GdIBr monolayers. On the contrary, the $2H$-GdBrCl monolayer exhibits perpendicular magnetic anisotropy character, which originates from the competition between Gd-$p/d$ and halogen atom-$p$ orbitals. Calculated valley optical actions of the Janus $2H\text{\ensuremath{-}}\mathrm{Gd}XY$ monolayers exhibit distinguished valley-selective circular dichroisms, which is expected to realize the special valley excitation by polarized light. Spontaneously, valley-Zeeman effect in the valance band for the Janus $2H\text{\ensuremath{-}}\mathrm{Gd}XY$ monolayers induces a giant valley splitting of 60--120 meV, which is also robust against various external biaxial strains. A tunable valley degree of freedom in Janus $2H\text{\ensuremath{-}}\mathrm{Gd}XY$ systems is very necessary for encoding and processing information.