Strain-driven control of spin-splitting parameters in the persistent spin helix state of monolayer X O 2 Y 2 ( X = W , Mo; Y = Cl , Br, I)

The realization of spin field-effect transistors requires robust spin-orbit splitting and coherent spin precession in the presence of ferroelectric polarization, which can be observed in two-dimensional noncentrosymmetric systems. To control the spin-orbit coupling (SOC) parameters, we adopted strain engineering. Within the framework of the density functional theory, we investigated the electronic structure, spontaneous electric polarization, and spin texture of $X{\mathrm{O}}₂{Y}₂$ ($X=\mathrm{W}$, Mo; $Y=\mathrm{Cl}$, Br, I) monolayer under uniaxial strain from $\ensuremath{-}1$% to 5%. We obtained tunable spin splitting in the conduction band minimum of all the monolayers. Among them, ${\mathrm{WO}}₂{\mathrm{Cl}}₂$ monolayer shows considerable SOC strength reaching up to 2.16 $\mathrm{eV}$ \AA{}, allowing the device to function at room temperature. We also found that the spontaneous electric polarization is substantially influenced by the applied strain, which is increased from 156.2 pC/m to 255.3 pC/m. Additionally, we highlight the emergence of a reversible persistent spin helix (PSH) across all the compounds, maintained across strained variants. For practical applications, we confirm the fully reversed PSH under external electric $\ensuremath{-}0.8$ V/nm. The highly tunable spontaneous electric polarization and the SOC strength as well as the emergence and reversibility of the PSH state in $X{\mathrm{O}}₂{Y}₂$ ($X=\mathrm{W}$, Mo; $Y=\mathrm{Cl}$, Br, I) monolayer underscore the potential for the application to the spin diffusion channel in spin-field effect transistors.