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Nonlinear interaction theory for parametrically-excited spin-wave modes in confined micromagnetic systems

We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise across many areas of physics and engineering. The ferromagnetic sample is driven by parallel pumping with an external applied magnetic field having two tones at different frequencies, which are able to trigger parametric instability of two resonant modes. The two excited spin-wave modes interact in a strongly nonlinear fashion giving rise to quasiperiodicity, hysteresis and non-commutativity of steady-state oscillation regimes. To disentangle such a complex variety of dynamics, we develop a reduced-order model based on magnetization normal modes that is amenable of appropriate analytical treatment, leading to quantitative description of parametric instability thresholds, post-instability steady-state amplitude saturation and complete determination of phase diagrams for steady-state oscillation regimes. We have performed validation of the theory using numerical simulations. The phase diagrams allow to predict and explain all the features of the nonlinear interaction between the parametrically-excited spin-wave modes and can be directly compared with experimental results.