Magnetoelectric Coupling in Multiferroic Bilayer VS_{2}

Based on the first-principles prediction, we report the magnetoelectric coupling effect in two-dimensional multiferroic bilayer VS_{2}. The ground-state 3R-type stacking breaks space inversion symmetry, therefore introducing a spontaneous polarization perpendicular to the layer plane. We further reveal that the out-of-plane ferroelectric polarization of bilayer VS_{2} can be reversed upon interlayer sliding of an in-plane translation. Each VS_{2} layer has a ferromagnetic state with an opposite magnetic moment between two antiferromagnetically ordered layers. We found that ferroelectricity and antiferromagnetism can be coupled together by a ferrovalley in bilayer VS_{2} to realize electronic control of magnetism. Remarkably, a net magnetic moment is generated by reducing the interlayer distance, and an electric field is able to achieve linear and second-order nonlinear magnetoelectric coupling in bilayer VS_{2}.