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The foldover effect of nonlinear eigenmodes in feedback ring systems was observed for the first time. Experiments made use of a system that consisted of a magnetic thin film strip, which supported the propagation of spin waves, and a microwave amplifier, which amplified the signal from the output of the magnetic strip and then fed it back to the input of the magnetic strip. The signal amplitude vs. frequency response in this ring system showed resonant peaks which resulted from ring eigenmodes. With an increase in the resonance amplitude, those resonant peaks evolved from symmetric peaks to asymmetric ones and then folded over to higher frequencies. The experimental observations were reproduced by theoretical calculations that took into account the nonlinearity‐produced frequency shift of the traveling spin waves. Active feedback ring systems consisting of a closed loop of a dissipative transmission line and an active element to compensate for the dissipation constitute an excellent testbed for exploring nonlinear dynamics in driven damped systems. Example systems include electromagnetic transmission line ring oscillators [1 ,2 ,3 ,4 ], optical fiber rings [5 ,6 ,7 ,8 ,9 ], and magnetic thin film‐based feedback rings [10,11,12,13,14]. Such systems not only sustain the self‐generation of envelope solitons, both bright [1,6,7,11] and dark [15], but have also enabled the observation of symmetry‐breaking nonlinear modes [11], chaotic solitons [2,7,8,13,14], and soliton fractals [12] and have also allowed for the study of the excitation of chaotic dynamics via different nonlinear processes [2,5,7,9,10,16,17]. This letter reports that active feedback rings also support another fascinating nonlinear effect ‐ the foldover effect. The nonlinear foldover effect originates from the nonlinearity in which the oscillation frequency varies with the amplitude, and manifests itself as the bending of the resonant peak in an oscillation amplitude vs. frequency plot. It occurs in nonlinear systems as diverse as driven pendula [18], spring‐based mechanical oscillators [19], electrical RLC resonant circuits [20], and precessional magnetic moments in both insulating and metallic magnets [21,22,23]. The effect, however, has never been observed in ring systems so far. The experiments made use of an active feedback ring that consists of a magnetic thin film strip serving as a spin‐wave transmission line and a microwave amplifier which amplifies the output signal from the magnetic strip and then feeds it back to the input of the magnetic strip. This ring system has a sequence of resonant eigenmodes for which the phase per round trip satisfies constructive interference conditions [24]. Thanks to these eigenmodes the amplitude vs. frequency response of the ring signal shows resonant peaks at certain frequencies, and these peaks fold over to higher frequencies when the peak amplitude is large. This foldover effect is intrinsic and originates from the nonlinearity‐caused frequency shift of the traveling spin wave. It is not associated with either high‐power heating or four‐wave interactions, as evident from the experimental data. To better understand the physical origin of the observed foldover effect, theoretical calculations were carried out that took into account the nonlinearity of the spin waves. The theoretical results not only confirmed the experimental observations, but also showed the rolling over of the top part of the resonant peaks which cannot be measured experimentally.

Foldover of nonlinear eigenmodes in magnetic thin film based feedback rings