Nonlinear mode interactions under parametric excitation in a YIG microdisk

A pair of quantized spin-wave modes is driven by two-tone parallel pumping in a YIG microdisk. The nonlinear dynamics is experimentally investigated by probing the resulting steady state, which is found to critically depend on the chosen pair of modes, the detuning between the pump frequencies and the modes parametric resonance, as well as the temporal sequence of the two rf tones. A general theory of parametric excitation in confined structures based on magnetization normal modes is developed and quantitatively accounts for the observed dependence and non-commutative behaviors, which emerge from the interplay between the self and mutual nonlinear frequency shifts of the spin-wave modes. Owing to its high degree of external controllability and scalability to larger sets of modes, this dynamical system provides a model platform for exploring nonlinear phenomena and a promising route toward rf driven state mapping relevant to neuromorphic and unconventional computing.