Possibility of combining ferroelectricity and Rashba-like spin splitting in monolayers of the1T-type transition-metal dichalcogenidesMX2(M=

First-principles calculations were carried out to explore the possible coupling between spin-polarized electronic states and ferroelectric polarization in monolayers of transition-metal dichalcogenides $M{X}_{2}$ ($M=\mathrm{Mo},\mathrm{W};X=\mathrm{S},\mathrm{Se},\mathrm{Te})$ with distorted octahedrally coordinated $1T$ structures. For ${d}^{2}$ metal ions, two competing metal clustering effects can take place, where metal ions are arranged in trimers or zigzag chains. Among these, the former structural distortion comes along with an improper ferroelectric phase which persists in the monolayer limit. Switchable Rashba-like spin-polarization features are predicted in the trimerized polytype, which can be permanently tuned by acting on its ferroelectric properties. The polar trimerized structure is found to be stable for $1T\ensuremath{-}{\mathrm{MoS}}_{2}$ only, while the nonpolar polytype with zigzag metal clustering is predicted to stabilize for other transition-metal dichalcogenides with ${d}^{2}$ metal ions.