Reversible spin textures with giant spin splitting in two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Ga</mml:mi><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>Se</mml:mi></mml:mrow></mml:math> , Te; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mi>Cl</mml:mi></mml:…

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