Magnetic skyrmions embedded in a vortex

Abstract: Magnetic vortices and skyrmions represent two fundamental classes of topological spin textures in ferromagnetic systems, distinguished by their unique stabilization mechanisms and degrees of freedom. Vortices, characterized by circular in-plane magnetization (chirality) and out-of-plane core polarization, naturally arise in confined geometries due to the interplay between exchange and dipolar interactions. In contrast, skyrmions typically require the Dzyaloshinskii-Moriya interaction for stabilization and exhibit fixed chirality-polarity relationships. Through micromagnetic simulations, we reveal that these seemingly distinct topological states can coexist, forming a novel composite state termed the \textit{n}-skyrmion vortex, which represents a skyrmion-embedded vortex state. These composite states possess quantized topological charges $Q$ that follow the relation $Q_{\text{total}} = Q_{\text{vortex}} + nQ_{\text{skyrmion}}$, where $n$ denotes the number of embedded skyrmions. Similar to vortices, these states exhibit independent chirality and polarity and are energetically degenerate.