Current-induced spin polarization in Janus WSSe monolayer

Janus engineering of transition metal dichalcogenide monolayers breaks the vertical mirror symmetry and induces huge built-in polarization and large Rashba spin-orbit coupling. By performing first-principles calculations, we find that the Rashba spin-orbit coupling induces sizable current-induced spin polarization in both the conduction and valence bands in the Janus WSSe monolayer, which is comparable to that in perovskite oxide interfaces. By constructing the low-energy $\mathbf{k}·\mathbf{p}$ Hamiltonian from the invariant theory, we find a sign change of the current-spin conductivity at chemical potential $\mu \approx -0.73$ eV, which indicates the flip of spin polarization and is attributed to the competition between the intrinsic Rashba spin-orbit coupling and the hexagonal warping of the valence bands. Our numerical and analytic results suggest that the current-induced spin polarization in the Janus WSSe monolayer is insensitive to temperature and impurity concentration but can be effectively tuned by external biaxial or uniaxial strain. The Janus WSSe monolayer could be a promising candidate to realize flexible two-dimensional spintronics devices.

Figure 1

(a) Schematics of the CISP effect and the experimental setup. The left panels show typical Rashba splitting bands and longitudinal spin polarization induced by transversal charge current, because of the shift of the Fermi surface. In the right panel, the transversal charge current is applied between brown contacts and along the $x$ direction. The bottom gate $V_G$ is used to adjust the chemical potential of the Janus WSSe monolayer. (b) Top and side views of the Janus WSSe monolayer. The hexagonal primitive cell (defined by ${\mathit{a}}_1$ and ${\mathit{a}}_2$) is indicated by the dashed lines, and the tungsten atoms, sulfur atoms, and selenium atoms are illustrated with blue, orange, and pink spheres, respectively. (c) The first Brillouin zone of the hexagonal primitive cell (defined by ${\mathit{b}}_1$ and ${\mathit{b}}_2$); the high-symmetry points are labeled with red dots.

Figure 2

(a) The band structures of the Janus WSSe monolayer. The $d$ orbitals of W atoms are decomposed into $d_{z^2},d_{x^2-y^2}+d_{xy}$ and $d_{xz}+d_{yz}$ components and are indicated by red-, blue-, and cyan-colored dots, respectively. (b) The decomposed density of states (DOS) of $p$ orbitals of S and Se atoms as well as $d$ orbitals of W atoms of the Janus WSSe monolayer.

Figure 3

(a) The C-S response $D_{yx}$ of the Janus WSSe monolayer in the vicinity of the conduction band minimum and at the temperature $T=10$ K. (b), (c), and (d) show the spin textures at chemical potentials of $\mu ={\mu }_b^v, {\mu }_c^v$, and ${\mu }_d^v$, respectively. The chemical potentials are indicated with green dashed horizontal lines in (a), accordingly. (e), (f), and (g), The zoomed-in spin textures of areas in the gray dashed boxes in (b), (c), and (d), respectively. The two spin textures locate at the $Q$ and $K$ points as shown in Fig. 1. The magnitudes of the out-of-plane spin component $s_z$ agree with the color bar on the right.

Figure 4

(a) The C-S response $D_{yx}$ of the Janus WSSe monolayer in the vicinity of the valence band maximum in the clean limit and at the temperature $T=10$ K. (b), (d), and (e) show the spin textures at chemical potentials of $\mu ={\mu }_b^v, {\mu }_d^v$, and ${\mu }_e^v$, respectively. The chemical potentials are indicated with green dashed horizontal lines in (a), accordingly. (c) Spatial spin orientation of points near the $K$ point [as indicated by the gray arrow in (b)]; the major component is aligned to the $s_z$. (f) and (g) are zoomed-in spin textures of areas in the gray dashed boxes in (d) and (e) at the $\mathrm{\Gamma }$ point, respectively. The magnitudes of the out-of-plane spin component $s_z$ agree with the color bar on the right.

Figure 5

(a) The band structures of the Janus WSSe monolayer in the vicinity of the $\mathrm{\Gamma }$ point obtained by the $\mathbf{k}·\mathbf{p}$ Hamiltonian (red solid lines) and first-principles calculations (blue open circles). (b) The spin textures at the chemical potential $\mu ={\mu }_e^v$ in Fig. 4 obtained by the $\mathbf{k}·\mathbf{p}$ Hamiltonian. (c) The C-S response $D_{yx}$ of the Janus WSSe monolayer obtained by the $\mathbf{k}·\mathbf{p}$ Hamiltonian (red solid line) and first-principles calculations (blue solid line) in the clean limit and at the temperature $T=10$ K. $D_{yx}\left({\mathbf{P}}_1\right)$ and $D_{yx}\left({\mathbf{P}}_2\right)$ are the integrations of ${\mathbf{P}}_1$ and ${\mathbf{P}}_2$, respectively. (d) Comparison of the C-S response $D_{yx}$ of the Janus WSSe monolayer obtained by the $\mathbf{k}·\mathbf{p}$ Hamiltonian (red solid line) and the same Hamiltonian but with $\alpha =0$ (green solid line), $\gamma =0$ (blue dotted line), and $\alpha =\gamma =0$ (black dashed line).

Figure 6

Comparison of the C-S response $D_{yx}$ of the Janus WSSe monolayer obtained by (a) first-principles calculations and (b) the $\mathbf{k}·\mathbf{p}$ Hamiltonian in the clean limit with different temperatures $T=10$ K (blue lines), $T=100$ K (red lines), and $T=300$ K (green lines), respectively.

Figure 7

(a) Comparison of the C-S conductivity ${\sigma }_{yx}^{\text{C-S}}$ of Janus WSSe monolayer obtained by (a) first-principles calculations and (b) the $\mathbf{k}·\mathbf{p}$ Hamiltonian with different disorder strengths $n_i{V}_0^2=0.8\times {10}^{-3}$ (${\mathrm{eV}\AA )}^2$ (blue lines), $n_i{V}_0^2=1.2\times {10}^{-3}$ (${\mathrm{eV}\AA )}^2$ (red lines), and $n_i{V}_0^2=1.6\times {10}^{-3}$ (${\mathrm{eV}\AA )}^2$ (green lines).

Figure 8

The upper panels show band structures of the Janus WSSe monolayer under (a) external biaxial tensile strain, (b) external uniaxial tensile strain along the zigzag direction, and (c) external uniaxial tensile strain along the armchair direction. The deformed crystal structures are illustrated as corresponding inset panels, and the deformation is determined as 6% larger with respect to the equilibrium lattice constant. The lower panels show C-S conductivity curves of the Janus WSSe monolayer under various (d) external biaxial tensile strains, (e) external uniaxial tensile strains along the zigzag direction, and (f) external uniaxial tensile strains along the armchair direction. The strengths of the strains are indicated with solid lines of different colors.