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Artificial spin ice, arrays of strongly interacting nanomagnets, are complex magnetic systems with many emergent properties, rich microstate spaces, intrinsic physical memory, high-frequency dynamics in the GHz range, and compatibility with a broad range of measurement approaches. This Tutorial article aims to provide the foundational knowledge needed to understand, design, develop, and improve the dynamic properties of artificial spin ice. Special emphasis is placed on introducing the theory of micromagnetics, which describes the complex dynamics within these systems, along with their design, fabrication methods, and standard measurement and control techniques. The article begins with a review of the historical background, introducing the underlying physical phenomena and interactions that govern artificial spin ice. We then explore the standard experimental techniques used to prepare the microstate space of the nanomagnetic array and to characterize magnetization dynamics, both in artificial spin ice and more broadly in ferromagnetic materials. Finally, we introduce the basics of neuromorphic computing applied to the case of artificial spin ice systems with a goal to help researchers new to the field grasp these exciting new developments. 

Abstract The transition from planar to three-dimensional (3D) magnetic nanostructures represents a significant advancement in both fundamental research and practical applications, offering vast potential for next-generation technologies like ultrahigh-density storage, memory, logic, and neuromorphic computing. Despite being a relatively new field, the emergence of 3D nanomagnetism presents numerous opportunities for innovation, prompting the creation of a comprehensive roadmap by leading international researchers. This roadmap aims to facilitate collaboration and interdisciplinary dialogue to address challenges in materials science, physics, engineering, and computing. The roadmap comprises eighteen sections, roughly divided into three blocks. The first block explores the fundamentals of 3D nanomagnetism, focusing on recent trends in fabrication techniques and imaging methods crucial for understanding complex spin textures, curved surfaces, and small-scale interactions. Techniques such as two-photon lithography and focused electron beam-induced deposition enable the creation of intricate 3D architectures, while advanced imaging methods like electron holography and synchrotron x-ray tomography provide nanoscale spatial resolution for studying magnetization dynamics in three dimensions. Various 3D magnetic systems, including coupled multilayer systems, artificial spin-ice, magneto-plasmonic systems, topological spin textures, and molecular magnets are discussed. The second block introduces analytical and numerical methods for investigating 3D nanomagnetic structures and curvilinear systems, highlighting geometrically curved architectures, interconnected nanowire systems, and other complex geometries. Finite element methods are emphasized for capturing complex geometries, along with direct frequency domain solutions for addressing magnonic problems. The final block focuses on 3D magnonic crystals and networks, exploring their fundamental properties and potential applications in magnonic circuits, memory, and spintronics. Computational approaches using 3D nanomagnetic systems and complex topological textures in 3D spintronics are highlighted for their potential to enable faster and more energy-efficient computing. 

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. 

Abstract We demonstrate direct probing of strong magnon–photon coupling using Brillouin light scattering (BLS) spectroscopy in a planar geometry. The magnonic hybrid system comprises a split-ring resonator loaded with epitaxial yttrium iron garnet thin films of 200 nm and 2.46  μ m thickness. The BLS measurements are combined with microwave spectroscopy measurements where both biasing magnetic field and microwave excitation frequency are varied. The cooperativity for the 200 nm-thick YIG films is 1.1, and larger cooperativity of 29.1 is found for the 2.46 μ m-thick YIG film. We show that BLS is advantageous for probing the magnonic character of magnon–photon polaritons, while microwave absorption is more sensitive to the photonic character of the hybrid excitation. A miniaturized, planar device design is imperative for the potential integration of magnonic hybrid systems in future coherent information technologies, and our results are a first stepping stone in this regard. Furthermore, successfully detecting the magnonic hybrid excitation by BLS is an essential step for the up-conversion of quantum signals from the microwave to the optical regime in hybrid quantum systems. 

Terahertz (THz) sciences and technologies have contributed to a rapid development of a wide range of applications and expanded the frontiers in fundamental science. Spintronic terahertz emitters offer conceptual advantages since the spin orientation in the magnetic layer can be easily controlled either by the externally applied magnetic field or by the internal magnetic field distribution determined by the specific shape of the magnetic elements. Here, we report a switchable terahertz source based on micropatterned magnetic heterostructures driven by femtosecond laser pulses. We show that the precise tunability of the polarization state is facilitated by the underlying magnetization texture of the magnetic layer that is dictated by the shape of the microstructure. These results also reveal the underlying physical mechanisms of a nonuniform magnetization state on the generation of ultrafast spin currents in the magnetic heterostructures. Our findings indicate that the emission of the linearly polarized THz waves can be switched on and off by saturating the sample using a biasing magnetic field, opening fascinating perspectives for integrated on-chip THz devices with wide-ranging potential applications.