This Letter reports the first experimental demonstration of chaotic excitations through modulational instability for waves with a repulsive nonlinearity. The experiments were carried out for surface spin waves in a magnetic thin film strip in an active feedback ring configuration. At a low ring gain level, one observes the self-generation of one eigenmode. With an increase in the ring gain, one observes the production of additional modes and the onset and enrichment of chaotic behaviors.

The transition from stationary to chaotic spin-wave soliton trains has been observed. The experiment utilized cw excitation of envelope solitons through self-modulation instability of spin waves. By increasing the spin-wave power, the secondary self-modulation instability succeeded the primary modulation instability, resulting in after-modulation of the soliton train amplitude. Further increase of the spin-wave power led to development of the higher-order instabilities, resulting in formation of the chaotic soliton train.

A theory has been developed for the waveguiding characteristics of dual-tunable multiferroic magnonic crystals (MCs). The crystals are constructed as periodically width-modulated microwave transmission slot-lines placed in between thin ferrite and ferroelectric films. Dispersion characteristics of the spin-electromagnetic waves (SEWs) in the investigated periodic waveguiding structure were derived using the method of approximate boundary conditions and the coupled-mode approach. The transmission-loss characteristics (TLCs) were calculated by the transfer-matrix method. The results show that the TLCs of the structures consist of pass-bands and stop-bands. The stop-bands are due to Bragg reflections in the structure. The magnetic and electric fields control the stop-band frequencies. The ferroelectric film polarization produced with the application of control voltage to the slot-line electrodes reduces its dielectric permittivity and provides up-shift of the stop-band frequencies. The most effective electric tuning is achieved in the area of the maximum hybridization of SEWs. As a result, the investigated multiferroic MCs combine the advantages of thin-film planar topology and dual tunability of magnonic band-gaps.

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