  Low-dimensional multiferroicity, though highly scarce in nature, has
attracted great attention due to both fundamental and technological interests.
Using first-principles density functional theory, we show that ferromagnetism
and ferroelectricity can coexist in monolayer transition metal phosphorus
chalcogenides (TMPCs) - CuMP$_2$X$_6$ (M=Cr, V; X=S, Se). These van der Waals
layered materials represent a class of 2D multiferroic semiconductors that
simultaneously possess ferroelectric and ferromagnetic orders. In these
monolayer materials, Cu atoms spontaneously move away from the center atomic
plane, giving rise to nontrivial electric dipole moment along the plane normal.
In addition, their ferromagnetism originates from indirect exchange interaction
between Cr/V atoms, while their out-of-plane ferroelectricity suggests the
possibility of controlling electric polarization by external vertical electric
field. Monolayer semiconducting TMPCs thus provide a solid-state 2D materials
platform for realizing 2D nanoscale switches and memory devices patterned with
top and bottom electrodes.
