Two-dimensional multiferroic semiconductors with coexisting ferroelectricity and ferromagnetism

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.