High-Topological-Number Skyrmion and Topologically Protected Dissipative Structure

Magnetic skyrmion with topological number of unity ($Q=1$) is a nanometric swirling spin structure, where the helicity is fixed to be either N\'eel or Bloch type depending on the interfacial or bulk Dzyaloshinskii-Moriya interaction. Here, we show that a skyrmion with topological number of two ($Q=2$) can be created and stabilized by applying vertical spin-polarized current. It is intrinsically a nonequilibrium dynamic object, subsisting on a balance between the energy input from the current and the energy dissipation by the Gilbert damping. Nevertheless, once it is created, it is a topologically protected object as far as the current is injected. We may call it a topologically protected dissipative structure. The high-topological-number skyrmion is contrasted with the ordinary skyrmion, as its helicity always evolves, interpolating the N\'eel and Bloch types.