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 fDAC 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 Δf(0)=|fDAC-f′|. As the magnetic field H was increased a 1st pre-fractal pattern was observed with frequency interval Δf(1)=Δf(0)/2. Finally, the onset of a 2nd pre-fractal was observed with frequency interval Δf(2)=Δf(1)/2=Δf(0)/4. The magnetic field dependence of the nonlinear signals matched that of the DAC. The spin wave fractal behavior was demonstrated for different values of f′.