Based on the first-principles prediction, we report the magnetoelectric coupling effect in the 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 ferromagnetic state with opposite magnetic moment between two antiferromagnetically ordered layers. We found that ferroelectricity and antiferromagnetism can be coupled together by ferrovalley in bilayer VS${}_2$ to realize electronic control of magnetism. Remarkably 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${}_2$.

中文翻译：

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多铁双层VS2中的磁电耦合

基于第一性原理的预测，我们报道了二维多层多层铁VS中的磁电耦合效应${}_2$。基态3R型堆叠破坏了空间反转对称性，因此引入了垂直于层平面的自发极化。我们进一步揭示了双层VS的面外铁电极化${}_2$当面内平移的层间滑动时，可以逆转。每个VS${}_2$层具有铁磁状态，两个反铁磁有序层之间的磁矩相反。我们发现铁电和反铁磁可以通过双层VS中的ferrovalley耦合在一起${}_2$实现磁力的电子控制。通过减小层间距离可显着产生净磁矩，并且电场能够在双层VS中实现线性和二阶非线性磁电耦合${}_2$。