Magnetic skyrmions embedded in a vortex

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 $\mathit{\text{n}}$-skyrmion vortex, which represents a skyrmion-embedded vortex state. These composite states possess quantized topological charges $Q$ that follow the relation $Q_{\text{total}}=Q_{\text{vortex}}+n{Q}_{\text{skyrmion}}$, where $n$ denotes the number of embedded skyrmions. Similar to vortices, these states exhibit independent chirality and polarity and are energetically degenerate.