Field-driven resonances of magnetic Hopfions

Here, we report on micromagnetic simulations of fast dynamics in three dimensional spin textures. We focus on the resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 66 mT coinciding with a transition from Hopfions to torons. The modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space, and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. Most remarkably, we have identified pronounced differences in spin wave spectra between Hopfions, torons and target skyrmions that can serve as fingerprints in future experimental validation studies of these novel 3d topological spin textures.