Sigmoidal curve behavior of 0 and $\pi$ state probability in a magnon parametron, using yttrium iron garnet (${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$) thin disk, is systematically investigated. We demonstrate that the probability distribution can be tuned by bias and pump microwave power. Our numerical calculation that considers increasing damping due to four-magnon scattering processes reproduces the results well.

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• Magnetization dynamics
• Magnons
• Spin optoelectronics
• Spin waves
• Artificial neural networks
• Nonlinear waves
• Fokker–Planck equation
• Microwave techniques