Based on the first-principles prediction, we report the magnetoelectric coupling effect in two-dimensional multiferroic bilayer ${\mathrm{VS}}_2$. 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 ${\mathrm{VS}}_2$ can be reversed upon interlayer sliding of an in-plane translation. Each ${\mathrm{VS}}_2$ 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 ${\mathrm{VS}}_2$ 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 ${\mathrm{VS}}_2$.

• Received 3 November 2019
• Revised 23 April 2020
• Accepted 28 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.247601