Reversible spin textures with giant spin splitting in two-dimensional GaXY ( X=Se , Te; Y=Cl , Br, I) compounds for a persistent spin helix

The coexistence of ferroelectricity and spin-orbit coupling in noncentrosymmetric systems may allow for a nonvolatile control of spin textures in the momentum space by tuning the ferroelectric polarization. Based on first-principles calculations, supplemented with $\stackrel{P\vec}{k}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{p}$ analysis, we report the emergence of the reversible spin textures in the two-dimensional (2D) $\mathrm{Ga}XY$ ($X=\mathrm{Se}$, Te; $Y=\mathrm{Cl}$, Br, I) monolayer compounds, a new class of 2D materials exhibiting in-plane ferroelectricity. We find that due to the large in-plane ferroelectric polarization, unidirectional out-of-plane spin textures are induced in the topmost valence band having giant spin splitting. Importantly, such out-of-plane spin textures, which can host a long-lived helical spin mode known as a persistent spin helix, can be fully reversed by switching the direction of the in-plane ferroelectric polarization. We show that the application of an external in-plane electric field oriented oppositely to the in-plane ferroelectric polarization direction is an effective method to flip the orientation of the out-of-plane spin textures. Thus, our findings can open avenues for interplay between the unidirectional out-of-plane spin textures and the in-plane ferroelectricity in 2D materials, which is useful for efficient and nonvolatile spintronic devices.