  By means of density functional theory calculations, we predict that several
two dimensional AB binary monolayers, where A and B atoms belong to group IV or
III-V, are ferroelectric. Dipoles arise from the buckled structure, where the A
and B ions are located on the sites of a bipartite corrugated honeycomb lattice
with trigonal symmetry. We discuss the emerging valley-dependent properties and
the coupling of spin and valley physics, which arise from the loss of inversion
symmetry, and explore the interplay between ferroelectricity and Rashba
spin-spitting phenomena. We show that valley-related properties originate
mainly from the binary nature of AB monolayers, while the Rashba spin-texture
developing around valleys is fully controllable and switchable by reversing the
ferroelectric polarization.
