Spin-wave fractals in a quasi-one-dimensional magnonic crystal

Fractals are a ubiquitous phenomenon in nonlinear physics and a key facet of natural systems, from the lungs in our bodies to attractors underlying the weather. Spin-wave fractals have previously been observed in a Y$_{\mathrm{3}}$Fe$_{\mathrm{5}}$O$_{\mathrm{12}}$ (YIG) thin film-based active feedback ring, where the periodic amplification ensures the strong nonlinearity of the spin waves, while the periodic feedback was used as a time-dependent potential to create regions of large dispersion in the spin-wave spectrum. Strong nonlinearity and high dispersion are two essential ingredients needed for fractal development. This presentation reports for the first time that it is also possible to use a position-dependent potential to create the large dispersion necessary for fractal formation. As the power ($P_{\mathrm{in}})$ delivered to the magnonic crystal increases, one observes that a frequency comb forms around the input microwave frequency ($f_{\mathrm{0}})$, where the strongest peak sits at $f_{\mathrm{0}}$. As $P_{\mathrm{in}}$ is increased further, each peak in the comb evolves into its own, finer frequency comb. If $P_{\mathrm{in}}$ is increased even further, one can observe yet another set of finer frequency combs.