  Exact fractals of nonlinear waves that rely on strong dispersion and
nonlinearity and arise spontaneously out of magnetic media were observed for
the first time. The experiments make use of a microwave to excite a spin wave
in a quasi-one-dimensional magnonic crystal. When the power of the input
microwave (Pin) is low, the output signal has a power-frequency spectrum that
consists of a single peak. When Pin is increased to a certain level, the new
side modes are generated through modulational instability (MI), resulting in a
comb-like frequency spectrum. With a further increase in Pin, each peak in the
frequency comb can evolve into its own, finer comb through the MI. As Pin is
increased further, one can observe yet another set of finer frequency combs.
Such a frequency-domain fractal manifests itself as multiple layers of
amplitude modulation in the time-domain signal.
