In multiferroic materials, microscopic magnetic and electric textures are correlated with each other via magnetoelectric (ME) coupling. Thus, a ferroelectric (FE) dipolar skyrmionic crystal (or lattice so as to be abbreviated as SL for convenience) is expected to be induced once a ferromagnetic (FM) SL is stabilized in these materials. Using a quantum computational method, we find in simulations that the two sorts of topological crystals can indeed be generated simultaneously in a two-dimensional multiferroic monolayer; each FE skyrmion is a ferroelectric dipolar complex formed around one FM skyrmion; the topological charges of these FE skyrmions are quantized to be integers, half integers and multiples of certain fractional values; the topological charge density of every FE SL also forms periodic pattern; and a perpendicularly applied electric field is able to alter the wavelengths of the FM and FE SLs, elevate their formation temperatures, and destroy them below the original critical temperatures.

在多铁性材料，微观磁和电纹理通过磁电（ME）耦合相互关联。因此，一旦铁磁（FM）SL在这些材料中稳定，预计将诱导铁电（FE）偶极skyrmionic晶体（或晶格以便为方便起见缩写为SL）。使用量子计算方法，我们在模拟中发现两种拓扑晶体确实可以在二维多铁单层中同时生成；每个 FE skyrmion 都是围绕一个 FM skyrmion 形成的铁电偶极复合物；这些 FE skyrmions 的拓扑电荷被量化为整数、半整数和某些小数值的倍数；每个FE SL的拓扑电荷密度也形成周期性图案；