Physical realization of complex dynamical pattern formation in magnetic spinwave active feedback rings

We report the clean experimental realization of cubic-quintic complex Ginzburg-Landau physics in a single driven, damped system. Five numerically predicted categories of complex dynamical behavior and pattern formation are identified for bright and dark solitary waves propagating around an active magnetic thin film feedback ring: (1) periodic breathing; (2) recurrence; (3) spontaneous spatial shifting; (4) intermittency; and (5) interactions of multiple solitary waves. These non-transient, long lifetime behaviors are observed in microwave spinwave envelopes circulating within a dispersive, nonlinear Yttrium-Iron-Garnet wave guide operating in a ring geometry where net losses are directly compensated for via linear amplification on each round trip (~100 ns). The behaviors exhibit periods ranging from 10s to 1000s of round trip times (~ 1 ms) and are stable for 1000s of periods (~1 s). We find these dynamical behaviors span the experimentally accessible ranges of attractive cubic nonlinearity, dispersion, and external field strength that support the self-generation of backward volume spinwaves in a four-wave mixing regime.