  Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle
behaviors which arise from their topological protection, including
well-defined, three-dimensional dynamic modes that occur at microwave
frequencies. During dynamic excitation, spin waves are ejected into the
interstitial regions between skyrmions, creating the magnetic equivalent of a
turbulent sea. However, since the spin waves in these systems have a
well-defined length scale, and the skyrmions are on an ordered lattice, ordered
structures from spin wave interference can precipitate from the chaos. This
work uses small angle neutron scattering (SANS) to capture the dynamics in
hybrid skyrmions and investigate the spin wave structure. Performing
simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a
large increase in low-angle scattering intensity which is present only in the
resonance condition. This scattering pattern is best fit using a mass fractal
model, which suggests the spin waves form a long-range fractal network. The
fractal structure is constructed of fundamental units with a size that encodes
the spin wave emissions and are constrained by the skyrmion lattice. These
results offer critical insights into the nanoscale dynamics of skyrmions,
identify a new dynamic spin wave fractal structure, and demonstrates SANS as a
unique tool to probe high-speed dynamics.
