G\ae{}nice: a general model for magnon band structure of artificial spin ices

Arrays of artificial spin ices exhibit reconfigurable ferromagnetic resonance frequencies that can be leveraged and designed for potential applications.However, analytical and numerical studies of the frequency response of artificial spin ices have remained somewhat limited due to the need of take into account nonlocal dipole fields in theoretical calculations or by long computation times in micromagnetic simulations. Here, we introduce Gaenice, a framework to compute magnon dispersion relations of arbitrary artificial spin ice configurations. Gaenice makes use of a tight-binding approach to compute the magnon bands. It also provides the user complete control of the interaction terms included, e.g., external field, anisotropy, exchange, and dipole, making it useful also to compute ferromagnetic resonances for a variety of structures, such as multilayers and ensembles of weakly or non-interacting nanoparticles. Because it relies on a semi-analytical model, Gaenice is computationally inexpensive and efficient, making it an attractive tool for the exploration of large parameter spaces

Ultrastrong Magnon-Magnon Coupling and Chiral Symmetry Breaking in a 3D Magnonic Metamaterial

Strongly-interacting nanomagnetic arrays are ideal systems for exploring the frontiers of magnonic control. They provide functional reconfigurable platforms and attractive technological solutions across storage, GHz communications and neuromorphic computing. Typically, these systems are primarily constrained by their range of accessible states and the strength of magnon coupling phenomena. Increasingly, magnetic nanostructures have explored the benefits of expanding into three dimensions. This has broadened the horizons of magnetic microstate spaces and functional behaviours, but precise control of 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial, compatible with widely-available fabrication and characterisation techniques. By combining independently-programmable artificial spin-systems strongly coupled in the z-plane, we construct a reconfigurable 3D metamaterial with an exceptionally high 16N microstate space and intense static and dynamic magnetic coupling. The system exhibits a broad range of emergent phenomena including ultrastrong magnon-magnon coupling with normalised coupling rates of $\frac{\Delta \omega}{\gamma} = 0.57$ and magnon-magnon cooperativity up to C = 126.4, GHz mode shifts in zero applied field and chirality-selective magneto-toroidal microstate programming and corresponding magnonic spectral control