Source-linked AI summary
Reconfigurable Training and Reservoir Computing in an Artificial Spin-Vortex Ice via Spin-Wave Fingerprinting
Jack C. Gartside, Kilian D. Stenning, Alex Vanstone, Troy Dion, Holly H. Holder, Daan M. Arroo, Francesco Caravelli, Hidekazu Kurebayashi, Will R. Branford
TL;DR
Artificial spin systems usually use a single magnetic texture, limiting their microstate diversity for reconfigurable magnonics and neuromorphic computation. This work engineers bistable macrospin/vortex elements into ASVI, reads their states through spin-wave fingerprints, and demonstrates reconfigurable spectra, fading memory, and reservoir-computing performance across waveform transformations and chaotic prediction.
Problem
Single-texture artificial spin systems provide limited microstate diversity for reconfigurable magnonics, physical memory, and neuromorphic computation.
Method
The paper engineers macrospin/vortex bistability in ASVI and uses FMR spin-wave fingerprinting to read microstates and drive reservoir-computing tasks.
Results
ASVI learns linear and nonlinear waveform transformations and chaotic time-series prediction, while exhibiting a 3.8 GHz vortex-to-macrospin mode shift and history-dependent fading memory.
Takeaways & Limitations
ASVI provides a reconfigurable spin-wave and neuromorphic-computing platform using short training datasets without individual electrical addressing of reservoir elements.
Abstract
from arXiv · showhide
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-vortex ice
ASVI is engineered by balancing macrospin and vortex energies, creating a bistable four-state array whose field-driven vorticisation is history- and microstate-dependent. Global ±18 mT cycles increase vortex populations through a ratchet process while producing distinct spatial patterns.
- Artificial spin-vortex ice: ASVI uses 600 nm × 200 nm wide bars whose macrospin and vortex energies are equal, enabling macrospin/vortex bistability.The array also contains 125 nm-wide thin bars and a 100 nm vertex gap.
- Artificial spin-vortex ice: ±18 mT field loops reverse wide bars without reversing thin bars, while remaining below the V2M conversion field and progressively increasing vortex populations.Local dipolar-field textures can pin some wide bars during cycling.
- Artificial spin-vortex ice: Vorticisation preferentially occurs adjacent to existing vortices, producing vortex and macrospin domains as field-cycling continues.Low vortex stray fields alter local dipolar-field textures and increase asymmetric switching torques.
- Artificial spin-vortex ice: Vorticisation occurs at 3.05% per loop for positive-to-negative switching versus 1.34% for negative-to-positive switching.The difference follows from distinct type 2 and type 1 dipolar-field landscapes.
- Artificial spin-vortex ice: Repeated identical field-cycling sequences produce different vortex locations and domain structures, indicating stochastic rather than quenched-disorder-determined vorticisation.The comparison used separate sequences beginning from saturated all-macrospin states.
Reconfigurable spin-wave spectra and vortex state evolution
FMR provides rapid spectral readout of evolving mixed vortex–macrospin states. Vortex injection changes mode amplitudes and frequencies, while thin-bar magnetisation and field orientation reconfigure the evolution pathway and final populations.
- Reconfigurable spin-wave spectra and vortex state evolution: FMR rapidly fingerprints mixed vortex–macrospin states with 10 MHz frequency resolution, avoiding the slow acquisition and limited integration suitability of MFM.FMR resolves microstate details such as vertex-type populations and domain sizes, though not exact single-spin configurations.
- Reconfigurable spin-wave spectra and vortex state evolution: The wide-bar macrospin mode decreases in amplitude and redshifts as vortex injection reduces the local dipolar field during cycling.Spectra are measured at a consistent small bias field so changes are attributed to microstate-dependent local fields.
- Reconfigurable spin-wave spectra and vortex state evolution: Thin-bar magnetisation and field orientation produce distinct vortex-evolution rates and final vortex/macrospin populations.The thin bars act as a reconfigurable dipolar bias-field landscape that directs vortex injection.
- Reconfigurable spin-wave spectra and vortex state evolution: The spectra contain distinct low- and high-frequency vortex features alongside wide- and thin-bar macrospin modes during field cycling.The principal modes occur near 3.5, 7, 8.8, and 9.75 GHz.
- Reconfigurable spin-wave spectra and vortex state evolution: Vortex FMR-mode intensity increases with field-cycle number and matches the increasing vortex-state population observed in MFM images.The correspondence is shown across 3–100 cycles.
Micromagnetic simulation of spin-wave spectra and spatial mode profiles
Micromagnetic simulations connect ASVI’s field-dependent spectra to spatially localized magnon modes around vortex cores, thin bars, and bar edges. The simulated mode profiles correspond well with the experimentally observed spectral structure.
- Micromagnetic simulation of spin-wave spectra and spatial mode profiles: Vortex-core displacement produces two low-frequency modes localized above and below the core, with opposite field gradients as the applied field moves the core.The M1A and M1B modes occupy 3–6 GHz.
- Micromagnetic simulation of spin-wave spectra and spatial mode profiles: A 0–35 mT sweep separates wide-bar macrospin switching, thin-bar switching, and vortex-to-macrospin conversion in the FMR response.The figure tracks the conversion sequence from a high-vortex-population state to a saturated macrospin state.
- Micromagnetic simulation of spin-wave spectra and spatial mode profiles: Simulations identify a thin-bar macrospin bulk mode and a higher-order vortex mode with a whispering-gallery-like profile around the bar edge.These are labeled M2 and M3, respectively.
- Micromagnetic simulation of spin-wave spectra and spatial mode profiles: The simulated field evolution corresponds well with experimental FMR after excluding the experimentally absent wide-bar macrospin mode.Higher-index simulated modes fall below the experimental signal-to-noise threshold and are more sensitive to nanopatterning imperfections.
Vortex-to-macrospin conversion and fading memory behaviour
Vortex-to-macrospin conversion occurs above the field window used for ratchet-like vortex injection, enabling controlled partial conversion and history-dependent responses. After identical stimuli, trajectories gradually converge, producing fading memory.
- Vortex-to-macrospin conversion and fading memory behaviour: Wide-bar macrospins switch at 15.5–17 mT, thin-bar macrospins at 27 mT, and vortices convert to macrospins across 24–28 mT.These distinct switching behaviours are resolved in the FMR heatmap.
- Vortex-to-macrospin conversion and fading memory behaviour: V2M conversion begins at 19.5 mT and reaches saturated all-macrospin states at 23.8 mT, leaving an 18–19.5 mT vortex-injection window.This window lies above the wide-bar coercive field and below V2M conversion.
- Vortex-to-macrospin conversion and fading memory behaviour: A 21.5 mT stimulus converts approximately 35–50% of vortices to macrospins before subsequent ±18 mT recovery cycles.The stimulus response depends on the preceding field-cycling history.
- Vortex-to-macrospin conversion and fading memory behaviour: The post-stimulus evolution rate follows τ = −2.35×10^-3n+0.235, where n is the number of pre-stimulus field cycles.Longer preparation histories retain lower macrospin amplitudes even after 15 subsequent loops.
- Vortex-to-macrospin conversion and fading memory behaviour: Different history-dependent trajectories gradually converge under identical field-loop inputs, demonstrating fading memory.Field-loop magnitude changes as small as 0.5 mT can substantially alter microstate trajectories.
Reservoir computation
ASVI functions as a nonlinear, history-dependent reservoir whose spin-wave spectra provide measurable outputs for waveform transformation and chaotic time-series prediction. Its performance depends on intrinsic nanomagnetic dynamics rather than software regression alone.
- ASVI provides nonlinear, history-dependent reservoir dynamics with a fading-memory response that converges from different initial states under identical input sequences.
- The reservoir maps input values to global minor-field loops, then uses FMR spectra and spin-wave mode amplitudes as outputs for ridge-regression training and testing.
- ASVI successfully learns sine-wave and inverse-saw-wave transformations into saw, square, hysteretic nonlinear, sine, and I2(f0) target waveforms.
- 6.1 × 10-4 - 2.9 × 10-2 MSE is achieved on the test dataset across the nonlinear transformation tasks.
- Raw-input regression fails to learn the transformations, reproducing the inputs with altered amplitude scaling instead of the target waveform shapes.
- 2.75 × 10-3 and 9.94 × 10-3 MSE are obtained for Mackey-Glass prediction at t+1 and t+10, respectively.
- Increasing training length improves inverse saw-wave transformation and Mackey-Glass prediction performance up to 450-550 training points.
- Performance is somewhat reduced under constant -1.2 mT bias-field measurement, while considerable performance is retained across the modified scheme.
Conclusions
The paper presents ASVI as a four-state, bi-textured spin system combining physical memory, reconfigurable spin-wave spectra, and reservoir-computing capabilities. It demonstrates waveform learning and chaotic prediction using short training datasets without individually addressing reservoir elements.
- ASVI combines engineered texture bistability with collective physical memory phenomena and highly reconfigurable spin-wave spectra.
- ASVI learns linear and nonlinear waveform transformations and performs chaotic time-series prediction with strong results competitive with other reservoir systems.
- The computation uses short training datasets and no individual electrical addressing of reservoir elements.
Methods
The study combines fabricated ASVI arrays, micromagnetic simulation, FMR measurement, and reservoir-computing procedures to characterize texture conversion, training, and prediction. Vortex formation, bias-field control, spin-wave readout, and train/test evaluation are examined across field-cycling protocols.
- Micromagnetic simulation: Micromagnetic simulations used MuMax3 with relaxed magnetisation states, material parameters for permalloy, finite discretisation, periodic boundaries, and broadband excitation.Vortex states were either generated and relaxed using built-in initialisation or evolved through simulated switching dynamics.
- Sample fabrication and measurement: ASVI arrays were fabricated by electron-beam lithography and measured using flip-chip broadband FMR on millimetre-scale samples.The fabrication uses permalloy with patterned bar subsets, while FMR couples microwave fields through a coplanar waveguide.
- Reservoir-computing procedure: Reservoir inputs were mapped to 18-23.5 mT minor-loop amplitudes, and FMR amplitudes supplied the reservoir outputs for waveform transformation and Mackey-Glass prediction.Measurements used frequency-resolved outputs, train/test splits, matrix-multiplication weight fitting, and MSE evaluation; ASVI predictions were assessed across future time horizons.
- Vortex formation: Vorticisation proceeds through the combination of two edge-bound half-integer defects into a bulk +1 vortex-core defect during magnetisation switching.The simulated defect sequence distinguishes macrospin-to-vortex conversion from ordinary macrospin reversal.
- Field-cycling protocols: Global field cycles were used to train vortex populations, with repeated sequences revealing pinned macrospins, distinct domain structures, and stochastic vortex locations after resetting the array.Separate 3-30 loop sequences on the same area produced different patterns, while extended 5-10 loop sequences showed progressively stronger vortex domains.
- Reconfigurable bias control: Thin-bar magnetisation was reconfigured to control vortex-to-macrospin conversion, shifting the conversion range to higher fields under selected bias conditions.In one protocol, conversion began at 26.5 mT and saturated at 30.5 mT, compared with 19.5-23.8 mT in the reference condition.
- Measurement comparison: FMR measurements at the applied field and −1.2 mT showed MSE values ranging from 1.39-54.3 × lower at the applied field for waveform transformation and Mackey-Glass prediction.The difference was attributed to additional nonlinear field-dependent mode shifts at the applied field.