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The coexistence of ferroelectricity and spin-orbit coupling (SOC) innoncentrosymmetric systems may allow for a nonvolatile control of spin degreesof freedom by switching the ferroelectric polarization through the well-knownferroelectric Rashba effect (FRE). Although the FER has been widely observedfor bulk ferroelectric systems, its existence in two-dimensional (2D)ferroelectric systems is still very rarely discovered. Based onfirst-principles calculations, supplemented with $\vec{k}\cdot\vec{p}$analysis, we report the emergence of the FRE in the Ga$XY$ ($X$= Se, Te; $Y$=Cl, Br, I) monolayer compounds, a new class of 2D materials having in-planeferroelectricity. Due to the large in-plane ferroelectric polarization, a giantout-of-plane Rashba effect is observed in the topmost valence band, producingunidirectional out-of-plane spin textures in the momentum space. Importantly,such out-of-plane spin textures, which can host a long-lived helical spin modeknown as a persistent spin helix, can be fully reversed by switching thedirection of the in-plane ferroelectric polarization. Thus, our findings canopen avenues for interplay between the unidirectional out-of-plane Rashbaeffect and the in-plane ferroelectricity in 2D materials, which is useful forefficient and non-volatile spintronic devices.

Reversible giant out-of-plane Rashba effect in two-dimensional Ga$XY$ ($X$= Se, Te; $Y$= Cl, Br, I) compounds for persistent spin helix