  The anisotropic Rashba effect allows for the manipulation of electron spins
in a more precise and tunable manner since the magnitude of the Rashba
splitting and orientation of the spin textures can be simply controlled by
tuning the direction of the externally applied electric field. Herein, we
predict the emergence of the anisotropic Rashba effect in the two-dimensional
(2D) Janus $XA_{2}Y$ constructed from the group IV ($A$= Si, Sn, Ge) and group
V ($X,Y$ = Sb, Bi) elements having trigonal prismatic structures but lacking
in-plane mirror symmetry. Due to the lowering point group symmetry of the
crystal, the Rashba spin splitting is enforced to becomes anisotropic around
certain high symmetry points in the Brillouin zone and preserves the
out-of-plane spin textures. We illustrate this behavior using density
functional theory calculations supplemented with $\vec{k}\cdot\vec{p}$ analysis
on the Janus SbSi$_{2}$Bi monolayer as a representative example. Specifically,
we observed large and anisotropic Rashba splitting with prominence contribution
of the out-of-plane spin textures in the conduction band minimum around the $M$
point and valence band maximum around the $\Gamma$ point. More importantly, the
anisotropic spin splitting and out-of-plane spin polarization are sensitively
affected by surface imperfections, depending on the concentration and
configuration of the $X$ and $Y$ elements in the 2D Janus $XA_{2}Y$ surface.
Our study offer the possibility to realize the present systems for spintronics
applications.
