  The field of magnonics, which aims at using spin waves as carriers in data
processing devices, has attracted increasing interest in recent years. We
present and study micromagnetically a nonlinear nanoscale magnonic ring
resonator device for enabling implementations of magnonic logic gates and
neuromorphic magnonic circuits. In the linear regime, this device efficiently
suppresses spin-wave transmission using the phenomenon of critical resonant
coupling, thus exhibiting the behavior of a notch filter. By increasing the
spin-wave input power, the resonance frequency is shifted leading to
transmission curves, depending on the frequency, reminiscent of the activation
functions of neurons or showing the characteristics of a power limiter. An
analytical theory is developed to describe the transmission curve of magnonic
ring resonators in the linear and nonlinear regimes and validated by a
comprehensive micromagnetic study. The proposed magnonic ring resonator
provides a multi-functional nonlinear building block for unconventional
magnonic circuits.
