A hierarchy of multi-moment skyrmion phases in twisted magnetic bilayers.

The recent discovery of two-dimensional (2D) Van der Waals (VdW) magnets is a crucial turning point in the quantum magnet research field, since quantum fluctuations and experimental difficulties often elude stable magnetic orders in 2D. This opens new doors to delve for novel quantum and topological spin configurations, which may or may not have direct analogs in bulk counterparts. Here we study a twisted bilayer geometry of 2D magnets in which long-range spin-spin interactions naturally commence along the inter-layer Heisenberg ($J_{\perp}$) and dipole-dipole ($J_{\rm D}$) channels. The $J_{\perp}-J_{\rm D}$ parameter space unveils a hierarchy of distinct skyrmions phases, ranging from point-, rod-, and ring-shaped topological charge distributions. Furthermore, we predict a novel topological antiferroelectric phase, where oppositely-charged antiskyrmion pairs are formed, and the corresponding topological dipole moments become ordered in a N\'eel-like state $-$ hence dubbed topological antiferroelectric state. The results indicate that twisted magnetic layer provides a new setting to engineer and tune a plethora of novel and exotic skyrmion phases and their dynamics.