Multiple polarization phases and strong magnetoelectric coupling in the layered transition metal phosphorus chalcogenides TMP2X6(T=Cu,

Magnetoelectric multiferroic materials are the potential candidates for the high-density nonvolatile data storage devices. However, up to now, multiferroic materials with strong magnetoelectric coupling are still rare. Here, based on the first-principles calculations and theoretical model, we predict a different class of single phase multiferroic materials, transition metal phosphorus chalcogenides $TM{\mathrm{P}}_{2}{X}_{6}(T=\mathrm{Cu},\phantom{\rule{0.16em}{0ex}}\mathrm{Ag};\phantom{\rule{0.16em}{0ex}}M=\mathrm{Cr},\phantom{\rule{0.16em}{0ex}}\mathrm{V};\phantom{\rule{0.16em}{0ex}}X=\mathrm{S},\phantom{\rule{0.16em}{0ex}}\mathrm{Se})$ with multiple polarization phases and strong magnetoelectric coupling. The ferroelectric polarization originates from the movement of Cu/Ag atoms breaking the symmetry of spatial inversion and the magnetism arises from partially filled $d$ orbitals of the V/Cr atoms. It is predicted that the different ferroelectric phases of $TM{\mathrm{P}}_{2}{X}_{6}$ bulk have different band gaps, providing a way to control electronic and transport properties by the external electric field. Most prominently, for $\mathrm{CuV}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ bilayer and few layers, one of the ferroelectric phases has ferromagnetic ground state and the other has antiferromagnetic states, realizing the electric-field control of magnetism. We reveal that the physical mechanism of the strong magnetoelectric coupling is from the reduced dimension and symmetry by constructing a theoretical model including the crystal field splitting, electric polarization effect, and exchange interaction. This work not only predicts a different class of magnetoelectric multiferroic materials, but also proposes a strategy to design them by controlling the interlayer interaction in van der Waals layered materials.