Hopfion based magnonic crystal

We conduct a numerical analysis to explore the magnonic band structure of spin waves (SWs) within a unique magnonic crystal. The latter is composed of a waveguide hosting a linear array of hopfions, evenly spaced along its center, generated through micromagnetic simulations. The computed dispersion relationship of spin waves (SWs) in the envisioned hopfions magnonic crystal, illustrating the frequency versus wave vector, demonstrates a periodic attribute, a hallmark of conventional magnonic crystal band structures. Likewise, the computed magnonic spectra reveal both permitted frequency bands and restricted frequency bandgaps. These results may inspire additional exploration into the diverse functionalities offered by magnonic crystals built on periodic Hopfion lattices.