It has been predicted that for a series of two-dimensional (2D) materials, their van der Waals bilayers may possess sliding ferroelectricity with vertical polarizations switchable via interlayer sliding. Such intriguing ferroelectricity has been recently experimentally confirmed in a series of nonmagnetic bilayer systems like BN, MoS₂, etc., while magnetic bilayers remain unexplored in those reports. In this paper we show first-principles evidence that three most prevalent 2D ferromagnetic materials, CrI₃, Cr₂Ge₂Te₆ and Fe₃GeTe₂, can all be entailed with sliding ferroelectricity (FE) with vertical polarizations over 0.1 pC/m in their bilayers and are thus multiferroic. In particular, Fe₃GeTe₂ bilayer may exhibit magnetoelectric coupling effect with a net magnetization moment of 0.01 μ_B per unit cell switchable upon ferroelectric switching. Moreover, it is shown to be both piezoelectric and piezomagnetic as both its vertical electric polarization and the net magnetic moment can be approximately doubled when the interlayer distance is compressed by 10%, giving rise to unprecedented “piezo-multiferroic” effect where the magnetoelectric coupling effect is intensified with reduced interlayer distance.

据预测，对于一系列二维 (2D) 材料，它们的范德瓦尔斯双层可能具有滑动铁电性，垂直极化可通过层间滑动切换。这种有趣的铁电性最近已在一系列非磁性双层系统（如 BN、MoS ₂等）中得到实验证实，而磁性双层在这些报告中仍未得到探索。_{在本文中，我们展示了三种最普遍的二维铁磁材料 CrI 3}、Cr ₂ Ge ₂ Te ₆和 Fe ₃ GeTe ₂的第一性原理证据，都可以在其双层中具有超过 0.1 pC / m 的垂直极化的滑动铁电性（FE），因此是多铁性的。具体而言，Fe ₃ GeTe ₂双层可表现出磁电耦合效应，每单位晶胞的净磁化矩为 0.01 μ _B，可在铁电切换时切换。此外，它被证明是压电和压磁的，因为当层间距离压缩 10% 时，它的垂直电极化和净磁矩都可以大约加倍，从而产生前所未有的“压电多铁”效应，其中磁电耦合效果随着层间距离的减小而增强。