  Ferroelectric Rashba semiconductors (FERSC) have recently emerged as a
promising class of spintronics materials. The peculiar coupling between spin
and polar degrees of freedom responsible for several exceptional properties,
including ferroelectric switching of Rashba spin texture, suggests that the
electron's spin could be controlled by using only electric fields. In this
regard, recent experimental studies revealing charge-to-spin interconversion
phenomena in two prototypical FERSC, GeTe and SnTe, appear extremely relevant.
Here, by employing density functional theory calculations, we investigate spin
Hall effect (SHE) in these materials and show that it can be large either in
ferroelectric or paraelectric structure. We further explore the compatibility
between doping required for the practical realization of SHE in semiconductors
and polar distortions which determine Rashba-related phenomena in FERSC, but
which could be suppressed by free charge carriers. Based on the analysis of the
lone pairs which drive ferroelectricity in these materials, we have found that
the polar displacements in GeTe can be sustained up to a critical hole
concentration of over $\sim 10^{21}$/cm$^{3}$, while the tiny distortions in
SnTe vanish at a minimal level of doping. Finally, we have estimated spin Hall
angles for doped structures and demonstrated that the spin Hall effect could be
indeed achieved in a polar phase. We believe that the confirmation of spin Hall
effect, Rashba spin textures and ferroelectricity coexisting in one material
will be helpful for design of novel multifunctional spintronics devices
operating without magnetic fields.
