Onset of spin wave time-domain fractals in a dynamic artificial crystal

We report on the first observation of an exact fractal pattern in the time-domain arising spontaneously from a dynamic artificial crystal (DAC). The all-magnon process occurs in a passive, unlithographed magnetic waveguide. The DAC was created by a standing spin wave of frequency $f_{\mathrm{DAC}}$ in a region of nonlinear waveguide, resulting in a spatio-temporally periodic potential. The interaction of travelling spin waves of frequency $f'$ with the DAC resulted in a series of new modes appearing in a comb with intervals $\Delta f^{(0)} = \mid f_{\mathrm{DAC}}-f'\mid$. As $H$ was increased a 1st pre-fractal pattern was observed with frequency interval $\Delta f^{(1)} =\Delta f^{(0)}/2$. Finally, the onset of a 2nd pre-fractal was observed with frequency interval $\Delta f^{(2)} =\Delta f^{(1)}/2 = \Delta f^{(0)}/4$. The magnetic field dependence of the nonlinear signals effect matched that of the DAC. The fractal-like behavior was demonstrated for different values of $f'$.