Exploring Hopfion Stability and Dynamics in Ring-Like Structures

Using numerical simulations, we explore the static and dynamic response of hopfions to an external magnetic field in cylindrical and toroidal nanorings. Results evidence that the nucleation and stability of hopfions are intricately linked to geometry. When including an external field, due to the Dzyaloshinskii–Moriya interaction and the field direction-dependent annihilation mechanism, the hopfion displays distinct behavior under magnetic fields pointing along opposite directions. We have also obtained the spin wave resonance modes of the magnetization patterns nucleated in both nanorings and show the impact of geometry on the suppression of some of them. The interplay between curvature, topology, and magnetization dynamics opens new possibilities toward hopfion-based spin torque oscillator fabrication. © 2024 The Authors