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Abstract Magnons, the quantum-mechanical fundamental excitations of magnetic solids, are bosons whose number does not need to be conserved in scattering processes. Microwave-induced parametric magnon processes, often called Suhl instabilities, have been believed to occur in magnetic thin films only, where quasi-continuous magnon bands exist. Here, we reveal the existence of such nonlinear magnon-magnon scattering processes and their coherence in ensembles of magnetic nanostructures known as artificial spin ice. We find that these systems exhibit effective scattering processes akin to those observed in continuous magnetic thin films. We utilize a combined microwave and microfocused Brillouin light scattering measurement approach to investigate the evolution of their modes. Scattering events occur between resonance frequencies that are determined by each nanomagnet’s mode volume and profile. Comparison with numerical simulations reveals that frequency doubling is enabled by exciting a subset of nanomagnets that, in turn, act as nanosized antennas, an effect that is akin to scattering in continuous films. Moreover, our results suggest that tunable directional scattering is possible in these structures. 

We show how, by changing the polarization value of ferroelectric domains, it is possible to tune the magnon conductivity in the ferromagnetic film layer of a multiferroic magnonic system. In particular, we suggest how to switch from a metal behavior (zero frequency gap and linear frequency-wavevector dispersion) to an insulator behavior (around 1 GHz frequency gap and parabolic dispersion). The ferroelectric film is prepared with a sequence of ferroelectric domains with a periodic variation of their polarization direction. Through inverse magnetostriction, they induce in the ferromagnetic layer a periodic magnetic anisotropy and a consequent sinusoidal magnetization. The amplitude of the sinusoidal magnetization can be varied by varying the induced magnetic anisotropy. This allows for a fine and reversible control over the curvature of the dispersion relations at the Brillouin zone boundary, as well as the width of the frequency gap. We suggest the extension of Dirac’s magnon picture to our system, finding interesting implications in terms of magnon mobility. This work expands the possible implementations of the voltage-controlled-bandgap meta-materials, marks the conditions for the occurrence of a magnonic metal behavior in a ferromagnetic film, and outlines how a same unpatterned film can be reversibly turned from a magnonic metal to a magnonic insulator. 

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16^Nmicrostate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates of$$\frac{\Delta f}{\nu }=0.57$$ $\frac{\Delta f}{\nu }=0.57$, GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.