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Magnonic crystals are metamaterials whose magnon behavior can be controlled for specific applications. To date, most magnonic crystals have relied on nanopatterning and magnetostatic waves. Here, we analytically and numerically investigate magnonic crystals defined by modulating magnetic parameters at the nanoscale, which predominantly act on exchange-dominated, sub-100 nm magnons. We focus on two cases: the variation in the exchange constant, and the DMI constant. We found that the exchange constant modulation gives rise to modest band gaps in the forward volume wave and surface wave configurations. The modulation of the DMI constant was found to have little effect on the magnonic band structure, leading instead to a behavior expected for unpatterned thin films. We believe that our results will be interesting for future experimental investigations of nano-designed magnonic crystals and magnonic devices, where material parameters can be locally controlled, e.g., by thermal nano-lithography. 

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. 

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.