Ferroelectric control of charge-to-spin conversion in ${\mathrm{WTe}}_2$

Ferroelectric materials hold great potential for alternative memories and computing, but several challenges need to be overcome before bringing the ideas to applications. In this context, the recently discovered link between electric polarization and spin textures in some classes of ferroelectrics expands the perspectives of the design of devices that could simultaneously benefit from ferroelectric and spintronic properties. Here, we explore the concept of nonvolatile ferroelectric control of charge-to-spin conversion in semimetallic ${\mathrm{WTe}}_2$, which may provide a way for nondestructive readout of the polar state. Based on the first-principles simulations, we show that the Rashba-Edelstein effect (REE) that converts electric currents into spin accumulation switches its sign upon the reversal of the electric polarization. The numerical values of REE, calculated for the first time for both bulk and bilayer ${\mathrm{WTe}}_2$, demonstrate that the conversion is sizable, and may remain large even at room temperature. The ferroelectric control of spin transport in nonmagnetic materials provides functionalities similar to multiferroics and allows the design of memories or logic-in-memory devices that combine ferroelectric writing of information at low power with the spin-orbit readout of state.

Figure 1

Structure of bulk ${\mathrm{WTe}}_2$ with the polarization upwards ($P_{\uparrow }$). (a) Perspective view. (b) Side view. (c) Top view. The displacements ${\delta }_1=0.23$ and ${\delta }_2=0.30$ Å describe the ferroelectric distortion of the state with $P_{\uparrow }$. The configuration $P_{\downarrow }$ (not shown) can be obtained by sliding the layer so that ${\delta }_1\to -{\delta }_2$ and ${\delta }_2\to -{\delta }_1$ [14]. Dashed lines denote the symmetries, the mirror reflection $M_x$, the glide reflection ${\overline{M}}_y$, and the two-fold screw rotation ${\overline{C}}_{2z}$.

Figure 2

Electronic properties of bulk ${\mathrm{WTe}}_2$ with polarization upwards ($P_{\uparrow }$). (a) Band structure calculated between the high-symmetry points defined in (b). (b) Fermi surface consisting of four bands (1–4) shown in separate panels. The color scheme reflects the local band velocity [29]. (c) Constant energy contours ($E=E_F$) plotted at the $k_x–k_y$ plane for $k_z=0$. The arrows correspond to ($S_x, S_y$) components of the spin texture along the Fermi contours, indicating the spin direction. The $S_z$ component of the spin texture is negligible and it is not shown. The numbers correspond to Fermi sheets displayed in (b).

Figure 3

Electronic properties of bilayer ${\mathrm{WTe}}_2$ with polarization upwards ($P_{\uparrow }$). (a) Band structure calculated along the high-symmetry lines in the BZ; the high-symmetry points are displayed in (b). (b) Fermi surface ($E=0$) consisting of four bands; the full BZ is displayed for convenience. (c) Spin texture along the contours shown in (b). The arrows represent ($S_x, S_y$) components of the spin texture. The $S_z$ component is negligible and it is not included.

Figure 4

Ferroelectric control of REE in ${\mathrm{WTe}}_2$. (a) Schematic illustration of REE in bulk/bilayer ${\mathrm{WTe}}_2$ with electric polarization $P_{\uparrow }$ and $P_{\downarrow }$ shown in upper and bottom panels, respectively. In both cases, the charge current flows along the $y$ direction and the spin accumulation is parallel or antiparallel to $x$. (b) Illustration of REE in the reciprocal space for a simple Rashba model; the upper and bottom panels represent opposite chirality of spin. When the current flows along $y$, it induces the imbalance of spins along $x$ (${\chi }_{xy}$), as marked around the shaded regions which represent the variation of electron distribution. (c) The Edelstein tensor ${\chi }_{xy}$ vs chemical potential calculated for the bulk according to the geometry shown in (a). The curves corresponding to opposite ferroelectric ground states $P_{\uparrow }$ and $P_{\downarrow }$ are represented as red and blue, respectively. The solid and dashed lines correspond to temperatures $T=0$ and $T=300$ K, respectively. (d) The same as (c) for bilayer ${\mathrm{WTe}}_2$. The volume equivalent was calculated using the effective thickness of ${\mathrm{WTe}}_2$ equal to 15 Å.