Off-plane polarization orderings in metal chalcogen-diphosphates from bulk to monolayer*

Vertically (off-plane) ferroelectric ordering in ultra-thin films has been pursued for decades. We report the existence of intrinsic vertical polarization orderings in CuInP₂Se₆, a member of layered metal chalcogen-diphosphates (MCDs). Using first-principles calculations and the electrostatic-energy model, we find that the ground state of bulk CuInP₂Se₆ is ferroelectric (FE) while that of monolayer is antiferroelectric (AFE), and the critical thickness for this FE/AFE transition is around 6 layers. On the other hand, because of the small energy difference but the large barrier between FE and AFE orderings, the FE state can be practically realized in monolayer, giving rise to two-dimensional ferroelectrics. Applying Monte Carlo simulations, we further predict the corresponding ferroelectric Curie temperature (T_c) and electric hysteresis. Our results not only help understand recent contradictory measurements of MCDs but also shed light on realizing and tuning vertical 2D polarization.