Reversible spin textures with giant spin splitting in two-dimensional Ga<i>XY</i> (X = Se, Te; <i>Y</i> = 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 (k)over-right-arrow . (p)over-right-arrow analysis, we report the emergence of the reversible spin textures in the two-dimensional (2D) GaXY (X = Se, Te; Y = 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.