  Two-dimensional ferroelectrics (FEs) are promising in the miniaturization of
memory devices with ultra-high-density data storage and low power consumption.
However, many thiophosphate monolayers, i.e., analogs of CuInP$_2$S$_6$ and
referred to as ABP$_2$X$_6$, lose ferroelectricity and instead exhibit an
antiferroelectric (AFE) or paraelectric ordering. We propose to tune the AFE
ABP$_2$X$_6$ monolayers into the FE ordering through interface engineering. The
mechanism is that there are couplings between the charge polarizations of the
ABP$_2$X$_6$ monolayers and the local dipoles as well as the induced electronic
polarizations in the substrate which have a tendency to stabilize the FE
ordering. We further perform first-principles calculations for CuInP$_2$Se$_6$
and CuCrP$_2$S$_6$ monolayers and their van der Waals heterostructures. We find
that an AFE CuInP$_2$Se$_6$ monolayer becomes FE as interfaced with graphene,
MoS$_2$, and h-BN monolayers. In contrast, the CuCrP$_2$S$_6$ monolayer remains
AFE since there is a large energy difference between the AFE and FE phases.
Interfacing it with a MoTe$_2$ monolayer induces a metal-insulator transition
for the heterostructure, whereas interfacing with a polar surface MgO(111) can
drive it into FE. The interfacing effect can also be used to manipulate the FE
properties of ABP$_2$X$_6$ multilayers. We further find that the AFE-to-FE
transition is electrically switchable in these systems. In particular, it is
accompanied by an indirect-direct band-gap transition for the CuInP$_2$Se$_6$
monolayer. Our study offers an effective approach to tune the FE and electronic
properties of ABP$_2$X$_6$ thin films for applications in electronics and
optoelectronics.
