  The coexistence of ferroelectricity and spin-orbit coupling (SOC) in
noncentrosymmetric systems may allow for a nonvolatile control of spin degrees
of freedom by switching the ferroelectric polarization through the well-known
ferroelectric Rashba effect (FRE). Although the FER has been widely observed
for bulk ferroelectric systems, its existence in two-dimensional (2D)
ferroelectric systems is still very rarely discovered. Based on
first-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-plane
ferroelectricity. Due to the large in-plane ferroelectric polarization, a giant
out-of-plane Rashba effect is observed in the topmost valence band, producing
unidirectional out-of-plane spin textures in the momentum space. 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. Thus, our findings can
open avenues for interplay between the unidirectional out-of-plane Rashba
effect and the in-plane ferroelectricity in 2D materials, which is useful for
efficient and non-volatile spintronic devices.
