标题： 扭曲双层NiI2中的莫尔诱导磁电性 显示英文标题

标题： Moiré-Induced Magnetoelectricity in Twisted Bilayer NiI2

摘要： 扭曲磁性范德华（vdW）材料为多铁工程提供了有前途的途径，但建模大规模莫尔超晶格仍然具有挑战性。 利用一种新开发的SpinGNN++框架，该框架能有效处理自旋-晶格耦合系统，我们开发了一个全面的原子间机器学习（ML）势，并将其应用于扭曲双层NiI2（TBN）。 结构弛豫引入了莫尔周期性的“凸起”，使层间间距调制约0.55~\AA{}，面内离子位移高达0.48~\AA{}。 同时，我们的ML势能准确捕捉所有关键自旋相互作用，产生了可靠的磁配置；结合广义KNB机制，它产生了精确的自旋驱动极化。 对于扭转角度1.89^{\circ } \leq \theta \leq 2.45^{\circ }，这两种机制都变得显著，产生丰富的极化纹理，将离子面外偶极子与纯电子面内区域相结合。 在刚性（未弛豫）双层中，没有斯kyrmions；晶格弛豫对于生成极化-磁拓扑结构是必不可少的。 与之相反，在{\theta } \approx 60^{\circ }附近，堆叠依赖的铁电位移占主导地位，导致极性涡旋-反涡旋网络的形成。 这些结果揭示了TBN中的协同离子和自旋驱动的铁电性，将扭曲的vdW磁体定位为可调节多铁器件的适应性平台。 显示英文摘要

摘要： Twisted magnetic van der Waals (vdW) materials offer a promising route for multiferroic engineering, yet modeling large-scale moir\'e superlattices remains challenging. Leveraging a newly developed SpinGNN++ framework that effectively handles spin-lattice coupled systems, we develop a comprehensive interatomic machine learning (ML) potential and apply it to twisted bilayer NiI2 (TBN). Structural relaxation introduces moir\'e-periodic "bumps" that modulate the interlayer spacing by about 0.55~\AA{} and in-plane ionic shifts up to 0.48~\AA{}. Concurrently, our ML potential, which faithfully captures all key spin interactions, produces reliable magnetic configurations; combined with the generalized KNB mechanism, it yields accurate spin-driven polarization. For twist angles 1.89^{\circ} \leq \theta \leq 2.45^{\circ}, both mechanisms become prominent, yielding rich polarization textures that combine ionic out-of-plane dipoles with purely electronic in-plane domains. In the rigid (unrelaxed) bilayer, skyrmions are absent; lattice relaxation is essential for generating polar-magnetic topologies. In contrast, near {\theta} \approx 60^{\circ}, stacking-dependent ferroelectric displacements dominate, giving rise to polar meron-antimeron networks. These results reveal cooperative ionic and spin-driven ferroelectricity in TBN, positioning twisted vdW magnets as adaptable platforms for tunable multiferroic devices.