Magnetoelectric Coupling in Multiferroic Bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>VS</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Xingen Liu, A. P. Pyatakov, Wei Ren
Abstract
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}.