  We propose the lead sulphide (PbS) monolayer as a 2D semiconductor with a
large Rashba-like spin-orbit effect controlled by the out-of-plane buckling.
The buckled PbS conduction band is found to possess Rashba-like dispersion and
spin texture at the $M$ and $\Gamma$ points, with large effective Rashba
parameters of $\lambda\sim5~$eV$\AA~$ and $\lambda\sim1~$eV$~\AA$,
respectively. Using a tight-binding formalism, we show that the Rashba effect
originates from the very large spin-orbit interaction and the hopping term that
mixes the in-plane and out-of-plane $p$ orbitals of Pb and S atoms. The latter,
which depends on the buckling angle, can be controlled by applying strain to
vary the spin texture as well as the Rashba parameter at $\Gamma$ and $M$. Our
density functional theory results together with tight-binding formalism provide
a unifying framework for designing Rashba monolayers and for manipulating their
spin properties.
