Two-dimensional rare-earth Janus $2H\text{−}\mathrm{Gd}XY (X,Y=\mathrm{Cl},\mathrm{Br},\mathrm{I}; X\ne Y)$ monolayers: Bipolar ferromagnetic semiconductors with high Curie temperature and large valley polarization

Two-dimensional (2D) ferromagnetic semiconductors hold great interest due to their potential applications for nanoscale electronic devices. In this paper, the Janus $2H\text{−}\mathrm{Gd}XY$ $(X, Y=\mathrm{Cl},\mathrm{Br},\mathrm{I},X\ne Y)$ monolayers with rare-earth element Gd ($4f^7+5d^1$) 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 $2H\text{−}\mathrm{Gd}XY$ 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 $2H\text{−}\mathrm{Gd}XY$ 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 $2H\text{−}\mathrm{Gd}XY$ 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 $2H\text{−}\mathrm{Gd}XY$ systems is very necessary for encoding and processing information.

Figure 1

(a) Top/side views of the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers and the coordination environment of the Gd atom. The unit cell is marked by the red lines. The (b) FM and (c) AFM states of crystal structures; red (blue) arrow shows the direction of spin-up (spin-down). The phonon dispersion of the Janus (d) $2H$-GdBrCl, (e) $2H$-GdICl, and (f) $2H$-GdIBr monolayers.

Figure 2

The projected PBE band structures for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers (a)–(c) without and (d)–(f) with considering SOC. The Fermi level is set to zero.

Figure 3

(a) The biaxial strain dependencies on the ferromagnetic stability energy $\mathrm{\Delta }E$ for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers. The biaxial strain dependencies on $E_{\mathrm{g}}\text{−}\alpha , E_{\mathrm{g}}\text{−}\beta$, and $E_{\mathrm{g}}$ for the (b) $2H$-GdBrCl, (c) $2H$-GdICl, and (d) $2H$-GdIBr monolayers.

Figure 4

The (a) total MAE and (b)–(d) atoms-resolved MAE for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers.

Figure 5

MAE of the (a)–(c) Janus $2H\text{−}\mathrm{Gd}XY$ monolayers along $xy, xz$ and $yz$ planes and (d) over the whole space for the $2H$-GdBrCl monolayer. The contributions of (e) Br/I/Cl-$p$ orbitals and (e) Gd-$p$, -$d$, -$f$ orbitals to MAE for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers.

Figure 6

(a) The magnetic moments (${\mathrm{M}}_{\mathrm{Gd}}$) and (b) specific heat for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers as functions of temperature.

Figure 7

(a) The valley optical transitions with ${\sigma }^{+}$ (${\sigma }^{-}$) circular polarizations at the K (${\mathrm{K}}^{\prime }$) valleys. (b) The circular polarization $\eta \left(k\right)$ of optical transition for the Janus $2H$-GdBrCl monolayer over the first Brillouin zone.

Figure 8

(a)–(c) Contour map of Berry curvatures as well as (d) Berry curvatures along the high-symmetry points for the Janus $2H\text{−}\mathrm{Gd}XY$ monolayers. (e) Schematic diagram of anomalous valley Hall effects under external electric fields $E$. The red and blue arrows represent the spin-up and spin-down holes.