  Two-dimensional (2D) ferromagnetic semiconductors show great interest due to
their potential applications for the nanoscale electronic devices. In this
work, the Janus 2$H$-Gd$XY$ ($X$, $Y$=Cl, Br, I, $X$$\neq$$Y$) monolayers with
rare-earth element Gd (4$f^{7}$+5$d^{1}$) are predicted by the first-principles
calculations. Small exfoliation energy of less than 0.25 J/m$^{2}$ and
excellent dynamical/thermal stabilities can be confirmed for the Janus
2$H$-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, the in-plane magnetic
anisotropy can be observed in the 2$H$-GdICl and 2$H$-GdIBr monolayers. On the
contrary, the 2$H$-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 2$H$-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
2$H$-Gd$XY$ monolayers induces a giant valley splitting of 60-120 meV, which is
also robust against various external biaxial strains. Tunable valley degree of
freedom in the Janus 2$H$-Gd$XY$ systems is very necessary for encoding and
processing information.
