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Physical reservoir computing (PRC) is a computing framework that harnesses the intrinsic dynamics of physical systems for computation. It offers a promising energy-efficient alternative to traditional von Neumann computing for certain tasks, particularly those demanding both memory and nonlinearity. As PRC is implemented across a broad variety of physical systems, the need increases for standardised tools for data processing and model training. In this manuscript, we introduce PRCpy, an open-source Python library designed to simplify the implementation and assessment of PRC for researchers. The package provides a high-level interface for data handling, preprocessing, model training, and evaluation. Key concepts are described and accompanied by experimental data on two benchmark problems: nonlinear transformation and future forecasting of chaotic signals. Throughout this manuscript, which will be updated as a rolling release, we aim to facilitate researchers from diverse disciplines to prioritise evaluating the computational benefits of the physical properties of their systems by simplifying data processing, model training and evaluation., Comment: 19 pages, 5 figures

With the growing prevalence of AI, demand increases for efficient machine learning hardware. Physical systems are sought which combine image feature detection with the essential nonlinearity for tasks such as image classification. Existing physical hardware typically detects features linearly, then employs digital processing for nonlinear activation. Biological vision systems excel at nonlinear image processing. The retina detects features in ganglion cells via lateral inhibition, where cells nonlinearly compete for neuronal firing while supressing neighbouring cells. We present a bio-inspired 'retinomorphic' machine vision platform using an on-chip semiconductor network laser. The system detects multiple features in parallel via spatially-overlapping lasing modes, with integrated nonlinearity provided by antagonistic gain competition between modes - a photonic analogue of retinal inhibition. Parallel feature-detection enhances efficiency relative to feature-detection schemes which operate sequentially or via multiple device copies, with Si-compatible processing and a compact micron-scale footprint relative to existing mm-scale systems. We report 98.05% accuracy on MNIST-digits and 87.85% on Fashion-MNIST, with strong performance on short training datasets.

Physical computing has the potential to enable widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction. While individual devices provide basic data processing capabilities, networks of interconnected devices can perform more complex and varied tasks. However, designing networks to perform dynamic tasks is challenging without physical models and accurate quantification of device noise. We propose a novel, noise-aware methodology for training device networks using Neural Stochastic Differential Equations (Neural-SDEs) as differentiable digital twins, accurately capturing the dynamics and associated stochasticity of devices with intrinsic memory. Our approach employs backpropagation through time and cascade learning, allowing networks to effectively exploit the temporal properties of physical devices. We validate our method on diverse networks of spintronic devices across temporal classification and regression benchmarks. By decoupling the training of individual device models from network training, our method reduces the required training data and provides a robust framework for programming dynamical devices without relying on analytical descriptions of their dynamics.

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.

Reservoir computing is a neuromorphic architecture that potentially offers viable solutions to the growing energy costs of machine learning. In software-based machine learning, neural network properties and performance can be readily reconfigured to suit different computational tasks by changing hyperparameters. This critical functionality is missing in ``physical" reservoir computing schemes that exploit nonlinear and history-dependent memory responses of physical systems for data processing. Here, we experimentally present a `task-adaptive' approach to physical reservoir computing, capable of reconfiguring key reservoir properties (nonlinearity, memory-capacity and complexity) to optimise computational performance across a broad range of tasks. As a model case of this, we use the temperature and magnetic-field controlled spin-wave response of Cu$_2$OSeO$_3$ that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to a host of different physical reservoir responses. We quantify phase-tunable reservoir performance, characterise their properties and discuss the correlation between these in physical reservoirs. This task-adaptive approach overcomes key prior limitations of physical reservoirs, opening opportunities to apply thermodynamically stable and metastable phase control across a wide variety of physical reservoir systems, as we show its transferable nature using above(near)-room-temperature demonstration with Co$_{8.5}$Zn$_{8.5}$Mn$_{3}$ (FeGe)., Comment: Main manuscript: 14 pages, 5 figures. Supplementary materials: 13 pages, 10 figures

Recent studies in magnetic nanolithography show that a variety of complex magnetic states emerge as a function of a single magnetic island's aspect ratio. We propose a model which, in addition to fitting experiments, predicts magnetic states with continuous symmetry at particular aspect ratios and reveals a duality between vortex and vertex states. Our model then opens new means of engineering novel types of artificial spin systems, and their application to complex magnetic textures in devices and computing., Comment: 3 pages + epsilon + 18 supplementary material

All-optical magnetic switching promises ultrafast, high-resolution magnetisation control with the technological attraction of requiring no magnetic field. Existing all-optical switching schemes are driven by ultrafast transient effects, typically requiring power-hungry femtosecond-pulsed lasers and complex magnetic materials. Here, we demonstrate deterministic, all-optical magnetic switching in simple ferromagnetic nanomagnets (Ni$_{81}$Fe$_{19}$, Ni$_{50}$Fe$_{50}$) with sub-diffraction limit dimensions using a focused low-power, linearly-polarised continuous-wave laser. Isolated nanomagnets are switched across a range of dimensions, laser wavelengths and powers. All square-geometry artificial spin ice vertex configurations are written, including ground-state and energetically-unfavourable `monopole-like' states at powers as low as 2.74 mW. Usually, magnetic switching with linearly polarised light is symmetry-forbidden; however, here the laser spot has a similar size to the nanomagnets, producing an absorption distribution dependent on the relative nanoisland-spot displacement. We attribute the observed deterministic switching to the transient dynamics of this asymmetric absorption. No switching is observed in Co samples, suggesting the multi-species nature of NiFe alloys plays a role in reversal. The results presented here usher in cheap, low-power optically-controlled devices with impact across data storage, neuromorphic computation and reconfigurable magnonics.

Strongly-interacting artificial spin systems are moving beyond mimicking naturally-occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically artificial spin systems comprise nanomagnets with a single magnetisation texture: collinear macrospins or chiral vortices. By tuning nanoarray dimensions we achieve macrospin/vortex bistability and demonstrate a four-state metamaterial spin-system 'Artificial Spin-Vortex Ice' (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions, and weakly-coupled vortices with low stray dipolar-field. Vortices and macrospins exhibit starkly-differing spin-wave spectra with analogue-style mode-amplitude control and mode-frequency shifts of df = 3.8 GHz. The enhanced bi-textural microstate space gives rise to emergent physical memory phenomena, with ratchet-like vortex training and history-dependent nonlinear fading memory when driven through global field cycles. We employ spin-wave microstate fingerprinting for rapid, scaleable readout of vortex and macrospin populations and leverage this for spin-wave reservoir computation. ASVI performs linear and non-linear mapping transformations of diverse input signals as well as chaotic time-series forecasting. Energy costs of machine learning are spiralling unsustainably, developing low-energy neuromorphic computation hardware such as ASVI is crucial to achieving a zero-carbon computational future.

Artificial spin ices are magnetic metamaterials comprising geometrically-tiled interacting nanomagnets. There is significant interest in these systems for reconfigurable magnonics due to their vast microstate landscape. Studies to-date have focused on the in-field GHz spin-wave response, convoluting effects from applied field, nanofabrication-imperfections ('quenched disorder') and microstate-dependent dipolar field landscapes. Here, we study artificial spin ices in pure and disordered microstates and evaluate their zero-field spectra. Removing the applied field allows us to deconvolute contributions to reversal dynamics and spin-wave spectra, directly measuring the dipolar field landscape and quenched disorder. Mode-amplitude provides population readout of nanomagnet magnetisation direction, and hence net magnetisation as well as local vertex populations. We demonstrate microstate-fingerprinting via distinct spectral-readout of three microstates with identical (zero) magnetisation, supported by simulation. These results establish remanence 'spectral-fingerprinting' as a rapid, scalable on-chip readout of both magnetic state and nanoscale dipolar field texture, a critical step in realising next-generation functional magnonic devices., Comment: 32 pages, 6 figures

Artificial spin ice systems have seen burgeoning interest due to their intriguing physics and potential applications in reprogrammable memory, logic and magnonics. Integration of artificial spin ice with functional magnonics is a relatively recent research direction, with a host of promising results. As the field progresses, direct in-depth comparisons of distinct artificial spin systems are crucial to advancing the field. While studies have investigated the effects of different lattice geometries, little comparison exists between systems comprising continuously connected nanostructures, where spin-waves propagate via dipole-exchange interaction, and systems with nanobars disconnected at vertices where spin-wave propagation occurs via stray dipolar-field. Gaining understanding of how these very different coupling methods affect both spin-wave dynamics and magnetic reversal is key for the field to progress and provides crucial system-design information including for future systems containing combinations of connected and disconnected elements. Here, we study the magnonic response of two kagome spin ices via Brillouin light scattering, a continuously connected system and a disconnected system with vertex gaps. We observe distinct high-frequency dynamics and magnetization reversal regimes between the systems, with key distinctions in spin-wave localization and mode quantization, microstate-trajectory during reversal and internal field-profiles. These observations are pertinent for the fundamental understanding of artificial spin systems and broader design and engineering of reconfigurable functional magnonic crystals.

Strongly-interacting nanomagnetic arrays are finding increasing use as model host systems for reconfigurable magnonics. The strong inter-element coupling allows for stark spectral differences across a broad microstate space due to shifts in the dipolar field landscape. While these systems have yielded impressive initial results, developing rapid, scaleable means to access abroad range of spectrally-distinct microstates is an open research problem.We present a scheme whereby square artificial spin ice is modified by widening a 'staircase' subset of bars relative to the rest of the array, allowing preparation of any ordered vertex state via simple global-field protocols. Available microstates range from the system ground-state to high-energy 'monopole' states, with rich and distinct microstate-specific magnon spectra observed. Microstate-dependent mode-hybridisation and anticrossings are observed at both remanence and in-field with dynamic coupling strength tunable via microstate-selection. Experimental coupling strengths are found up to g / 2$\pi$ = 0.15 GHz. Microstate control allows fine mode-frequency shifting, gap creation and closing, and active mode number selection.

The spin-wave dynamics of the ferromagnetic nanoarrays termed artificial spin ice (ASI) are known to vary depending on their magnetic microstate. However, little work has been done to characterise this relationship. Recent advances in control over the magnetic configuration of ASI bring designs harnessing the interplay between spin-wave eigenmodes and the microstate within reach, offering diverse applications including reconfigurable magnonic crystals, microwave filters and microstate read-out probes. These designs hinge on a strong understanding of the underlying spin wave-microstate correspondence. Here, we analyse the effects of the magnetic microstate on spin-wave spectra of honeycomb ASI systems via micromagnetic simulation. We find the spin-wave spectrum to be highly-tunable via the microstate to an enhanced degree relative to existing magnonic crystals, with mode shifting and (de)activation realised by reversing individual nanoislands. Symmetries of ASI systems and the chirality of magnetic defects are found to play important roles in determining the high-frequency response.