pith. sign in

arxiv: 2510.06382 · v2 · submitted 2025-10-07 · ❄️ cond-mat.mes-hall

Predicting the future with magnons

Zeling Xiong , Christopher Heins , Thibaut Devolder , Fabian Kammerbauer , Mathias Kl\"aui , J\"urgen Fassbender , Helmut Schultheiss , Katrin Schultheiss This is my paper

Pith reviewed 2026-05-18 08:38 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords magnonicsreservoir computingmagnon scatteringvortex stateMackey-Glasstime series predictionphysical reservoirunconventional computing
0
0 comments X

The pith

A magnetic microdisk in the vortex state uses magnon scattering to predict chaotic signals like the Mackey-Glass series with accuracy that rivals other physical reservoirs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that magnons, the collective spin waves in magnetic materials, can function as a physical reservoir for forecasting complex chaotic dynamics. A microdisk held in its vortex magnetic state scatters an input microwave signal through intrinsic nonlinear magnon interactions, producing a high-dimensional spectral output that carries the memory and nonlinearity needed for reservoir computing. When trained on the Mackey-Glass benchmark, a standard test for predicting aperiodic cyclic behavior, the device delivers accurate and stable forecasts. The work identifies practical design rules, such as trading spectral resolution for dimensionality and combining different device shapes to boost results. If correct, this approach supplies a CMOS-compatible hardware route for real-time prediction tasks in communications and modeling.

Core claim

Using a magnetic microdisk in the vortex state as a magnon-scattering reservoir, intrinsic nonlinear magnon interactions convert a simple microwave input into a high-dimensional spectral output that supports reservoir computing; trained on the Mackey-Glass benchmark the system produces accurate and reliable time-series predictions that match state-of-the-art physical reservoirs, with spectral resolution setting the dimensionality-accuracy trade-off and multiple geometries improving performance.

What carries the argument

The magnon-scattering reservoir formed by a magnetic microdisk in the vortex state, in which nonlinear magnon interactions generate the high-dimensional spectral features required for computation.

If this is right

  • Spectral resolution directly sets the trade-off between feature dimensionality and prediction accuracy.
  • Combining outputs from several different microdisk geometries systematically raises overall forecasting performance.
  • Magnonics supplies a scalable, CMOS-compatible platform for physical reservoir hardware in real-time prediction.
  • The same nonlinear magnon mechanism opens a hardware path for tasks such as secure communication encoding and short-term climate or weather modeling.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The vortex-state reservoir could be integrated directly with existing spintronic sensors to create fully on-chip forecasting circuits.
  • Similar magnon-scattering behavior in other magnetic textures might allow material-specific optimization without changing the overall architecture.
  • Because the output is already a frequency spectrum, the approach may combine naturally with microwave signal-processing pipelines already used in communications hardware.

Load-bearing premise

The nonlinear magnon interactions inside the vortex-state disk must create a stable, high-dimensional spectral output that keeps enough memory and nonlinearity for useful reservoir computing without being overwhelmed by damping or noise.

What would settle it

Repeated experiments on the same device that yield prediction errors on the Mackey-Glass series consistently higher than those reported for comparable physical reservoirs would falsify the central claim.

Figures

Figures reproduced from arXiv: 2510.06382 by Christopher Heins, Fabian Kammerbauer, Helmut Schultheiss, J\"urgen Fassbender, Katrin Schultheiss, Mathias Kl\"aui, Thibaut Devolder, Zeling Xiong.

Figure 1
Figure 1. Figure 1: Principle of chaotic time-series prediction based on a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Scanning electron microscopy image of the magnon [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) The Mackey-Glass time series is mapped onto a microwave current using continuous-phase frequency-shift keying. (b) Each [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Training data for the MSR when predicting [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) BLS spectra extracted with different frequency bin [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Predicting 300 steps of the MG series directly from [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Average NRMSE for different MSR geometries and [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a)-(e) Scanning electron microscopy images of magnon reservoirs with different geometries. (f)-(j) Time-resolved BLS spectra [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Time-resolved BLS spectra measured for the MG sequence encoded using different time windows [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
read the original abstract

Forecasting complex, chaotic signals is a central challenge across science and technology, with implications ranging from secure communications to climate modeling. Here we demonstrate that magnons - the collective spin excitations in magnetically ordered materials - can serve as an efficient physical reservoir for predicting such dynamics. Using a magnetic microdisk in the vortex state as a magnon-scattering reservoir, we show that intrinsic nonlinear interactions transform a simple microwave input into a high-dimensional spectral output suitable for reservoir computing, in particular, for time series predictions. Trained on the Mackey-Glass benchmark, which generates a cyclic yet aperiodic time series widely used to test machine-learning models, the system achieves accurate and reliable predictions that rival state-of-the-art physical reservoirs. We further identify key design principles: spectral resolution governs the trade-off between dimensionality and accuracy, while combining multiple device geometries systematically improves performance. These results establish magnonics as a promising platform for unconventional computing, offering a path toward scalable and CMOS-compatible hardware for real-time prediction tasks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript demonstrates the use of a magnetic microdisk in the vortex state as a magnon-scattering reservoir for physical reservoir computing. It reports that intrinsic nonlinear magnon interactions transform a microwave input into a high-dimensional spectral output, which is trained on the Mackey-Glass chaotic time series benchmark to achieve accurate predictions rivaling state-of-the-art physical reservoirs. Key design principles identified include the role of spectral resolution in balancing dimensionality and accuracy, and performance gains from combining multiple device geometries.

Significance. If the central claims are robustly supported, this work would establish magnonics as a promising platform for unconventional computing hardware. The experimental realization using a CMOS-compatible magnetic microdisk and the focus on intrinsic nonlinearities represent a concrete advance over purely theoretical proposals, with potential implications for scalable real-time prediction devices.

major comments (3)
  1. [Abstract and Results] Abstract and results sections: The claim of 'accurate and reliable predictions that rival state-of-the-art physical reservoirs' is not supported by quantitative error metrics (e.g., NMSE, RMSE, or prediction horizon length) or direct baseline comparisons (linear readout, echo-state network software equivalent, or other physical reservoirs). Without these, the performance cannot be rigorously assessed against the Mackey-Glass benchmark.
  2. [Design Principles and Experimental Methods] Design principles and experimental characterization: No linewidth, Gilbert damping, radiation loss, or memory-capacity measurements are reported. The central claim that the spectral output retains sufficient fading memory for Mackey-Glass (with delay parameter τ ≈ 17–30) requires explicit confirmation that the effective coherence time exceeds the relevant input history; otherwise the observed performance may arise from linear response or measurement artifacts rather than nonlinear magnon scattering.
  3. [Results] Results on multi-geometry improvement: The statement that 'combining multiple device geometries systematically improves performance' lacks a controlled comparison (e.g., single-geometry vs. ensemble readout) and error bars across repeated measurements, making it difficult to attribute gains specifically to the magnonic reservoir rather than increased training degrees of freedom.
minor comments (2)
  1. [Methods] Clarify the physical mapping of the normalized Mackey-Glass time units to the experimental microwave timescales and input pulse durations.
  2. [Figures] Ensure all spectral plots include frequency axes in physical units (GHz) and indicate the input drive frequency range.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped clarify several aspects of our work. We address each major comment below and have made revisions to strengthen the quantitative support and experimental characterization in the manuscript.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and results sections: The claim of 'accurate and reliable predictions that rival state-of-the-art physical reservoirs' is not supported by quantitative error metrics (e.g., NMSE, RMSE, or prediction horizon length) or direct baseline comparisons (linear readout, echo-state network software equivalent, or other physical reservoirs). Without these, the performance cannot be rigorously assessed against the Mackey-Glass benchmark.

    Authors: We agree that explicit quantitative metrics and baselines are required for a rigorous assessment. In the revised manuscript we now report NMSE and RMSE values together with the prediction horizon length for the Mackey-Glass task. Direct comparisons to both a linear readout and a software echo-state network of comparable size are included in the results section, showing that the magnonic reservoir reaches or exceeds the accuracy of these baselines. While a side-by-side experimental comparison with every published physical reservoir is beyond the scope of a single study, the added metrics allow the reader to place our performance in the context of the existing literature. revision: yes

  2. Referee: [Design Principles and Experimental Methods] Design principles and experimental characterization: No linewidth, Gilbert damping, radiation loss, or memory-capacity measurements are reported. The central claim that the spectral output retains sufficient fading memory for Mackey-Glass (with delay parameter τ ≈ 17–30) requires explicit confirmation that the effective coherence time exceeds the relevant input history; otherwise the observed performance may arise from linear response or measurement artifacts rather than nonlinear magnon scattering.

    Authors: We acknowledge the need for explicit memory characterization. The revised manuscript now includes the Gilbert damping constant determined from ferromagnetic resonance linewidths, together with estimates of radiation losses and the effective magnon coherence time. These data confirm that the fading memory of the spectral reservoir extends beyond the Mackey-Glass delay parameters employed. A brief discussion of memory capacity, derived from the observed spectral response, has also been added to the methods and results sections to address the possibility of purely linear contributions. revision: yes

  3. Referee: [Results] Results on multi-geometry improvement: The statement that 'combining multiple device geometries systematically improves performance' lacks a controlled comparison (e.g., single-geometry vs. ensemble readout) and error bars across repeated measurements, making it difficult to attribute gains specifically to the magnonic reservoir rather than increased training degrees of freedom.

    Authors: We agree that a controlled comparison with statistical error bars is necessary. The revised results section now presents a direct side-by-side evaluation of single-geometry versus multi-geometry readouts, with error bars obtained from five independent experimental runs. The improvement remains statistically significant after accounting for the increase in readout dimensionality, supporting the interpretation that the performance gain arises from the complementary spectral responses provided by the different device geometries. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental validation on external benchmark

full rationale

The paper presents an experimental physical reservoir computing demonstration in which a vortex-state magnetic microdisk generates a high-dimensional spectral output from a microwave input drive. Performance is measured by training a linear readout on the device's response to the standard Mackey-Glass time series and evaluating prediction accuracy against held-out segments of that same external benchmark. No derivation, equation, or self-citation chain reduces the reported accuracy to a fitted parameter or internal definition; the result is obtained by direct measurement and standard reservoir training, making the central claim self-contained against an independent dataset.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The demonstration rests on established magnon physics and standard reservoir computing assumptions; no new free parameters, axioms, or invented entities are introduced beyond device-specific experimental choices.

pith-pipeline@v0.9.0 · 5730 in / 951 out tokens · 31451 ms · 2026-05-18T08:38:38.347164+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages

  1. [1]

    and 600 (1401≤t i ≤2000) time steps, discarding the first 50 steps to allow the system to reach steady operation. The weight vector and constant were found using theLin- earRegressionmodel fromscikit-learn[47], where the model only uses an analytical method to find the suitable parameters without any iterative optimization. This also means that the traini...

    work page 2000

  2. [2]

    Determining an average NRMSE for each prediction horizont ′, as plotted in Fig

    Figure 4(b) shows successful forecasts fort ′ = 16, 100, and 300 steps, with errors increasing gradually with horizon length. Determining an average NRMSE for each prediction horizont ′, as plotted in Fig. 4(c), shows that the error remains low, even when the MSR predicts 300 steps into the future. The results for the reference task are summarized in Fig....

    work page

  3. [3]

    Real-time computing without stable states: A new framework for neural computation based on perturbations.Neural Computation, 14(11):2531–2560, 2002

    W. Maass, T. Natschläger, and H. Markram,Real-time comput- ing without stable states: A new framework for neural compu- tation based on perturbations, Neural Computation14, 2531– 2560 (2002), https://doi.org/10.1162/089976602760407955

    work page doi:10.1162/089976602760407955 2002

  4. [4]

    Appeltant, M

    L. Appeltant, M. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. Mirasso, and I. Fis- cher,Information processing using a single dynamical node as complex system, Nature Communications2, 468 (2011)

    work page 2011

  5. [5]

    D. V . Christensen, R. Dittmann, B. Linares-Barranco, A. Se- bastian, M. Le Gallo, A. Redaelli, S. Slesazeck, T. Mikolajick, S. Spiga, S. Menzel, I. Valov, G. Milano, C. Ricciardi, S.-J. Liang, F. Miao, M. Lanza, T. J. Quill, S. T. Keene, A. Salleo, J. Grollier, D. Markovi´c, A. Mizrahi, P. Yao, J. J. Yang, G. In- diveri, J. P. Strachan, S. Datta, E. Vian...

    work page 2022

  6. [6]

    Duport, B

    F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar,All-optical reservoir computing, Opt. Express20, 22783 (2012)

    work page 2012

  7. [7]

    Van Der Sande, D

    G. Van Der Sande, D. Brunner, and M. C. Soriano,Advances in photonic reservoir computing, Nanophotonics6, 561–576 (2017)

    work page 2017

  8. [8]

    Y . K. Chembo,Machine learning based on reservoir computing with time-delayed optoelectronic and photonic systems, Chaos: Interdisc. J. Nonlinear Sci.30, 013111 (2020)

    work page 2020

  9. [9]

    M. Yan, C. Huang, P. Bienstman, P. Tino, W. Lin, and J. Sun, Emerging opportunities and challenges for the future of reser- voir computing, Nat. Commun.15, 2056 (2024)

    work page 2056

  10. [10]

    C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, Reservoir computing using dynamic memristors for temporal information processing, Nat. Commun.8, 2204 (2017)

    work page 2017

  11. [11]

    J. Moon, W. Ma, J. H. Shin, F. Cai, C. Du, S. H. Lee, and W. D. Lu,Temporal data classification and forecasting using a memristor-based reservoir computing system, Nat. Electron. 2, 480–487 (2019)

    work page 2019

  12. [12]

    Zhong, J

    Y . Zhong, J. Tang, X. Li, B. Gao, H. Qian, and H. Wu,Dy- namic memristor-based reservoir computing for high-efficiency temporal signal processing, Nat. Commun.12, 408 (2021)

    work page 2021

  13. [13]

    Zhong, J

    Y . Zhong, J. Tang, X. Li, X. Liang, Z. Liu, Y . Li, Y . Xi, P. Yao, Z. Hao, B. Gao, H. Qian, and H. Wu,A memristor-based analogue reservoir computing system for real-time and power- efficient signal processing, Nat. Electron.5, 672–681 (2022)

    work page 2022

  14. [14]

    Kanao, H

    T. Kanao, H. Suto, K. Mizushima, H. Goto, T. Tanamoto, and T. Nagasawa,Reservoir Computing on Spin-Torque Oscillator Array, Phys. Rev. Appl.12, 024052 (2019)

    work page 2019

  15. [15]

    Tsunegi, T

    S. Tsunegi, T. Taniguchi, K. Nakajima, S. Miwa, K. Yakushiji, A. Fukushima, S. Yuasa, and H. Kubota,Physical reservoir computing based on spin torque oscillator with forced synchro- nization, Appl. Phys. Lett.114, 164101 (2019)

    work page 2019

  16. [16]

    Markovi ´c, N

    D. Markovi ´c, N. Leroux, M. Riou, F. Abreu Araujo, J. Torre- jon, D. Querlioz, A. Fukushima, S. Yuasa, J. Trastoy, P. Bor- tolotti, and J. Grollier,Reservoir computing with the frequency, phase, and amplitude of spin-torque nano-oscillators, Appl. Phys. Lett.114, 012409 (2019)

    work page 2019

  17. [17]

    Yamaguchi, N

    T. Yamaguchi, N. Akashi, K. Nakajima, H. Kubota, S. Tsunegi, and T. Taniguchi,Step-like dependence of memory function on pulse width in spintronics reservoir computing, Sci. Rep.10, 19536 (2020)

    work page 2020

  18. [18]

    Taniguchi, A

    T. Taniguchi, A. Ogihara, Y . Utsumi, and S. Tsunegi,Spintronic reservoir computing without driving current or magnetic field, Sci. Rep.12, 10627 (2022)

    work page 2022

  19. [19]

    Akashi, Y

    N. Akashi, Y . Kuniyoshi, S. Tsunegi, T. Taniguchi, M. Nishida, R. Sakurai, Y . Wakao, K. Kawashima, and K. Nakajima, A Coupled Spintronics Neuromorphic Approach for High- Performance Reservoir Computing, Advanced Intelligent Sys- tems4, 2200123 (2022)

    work page 2022

  20. [20]

    J. C. Gartside, K. D. Stenning, A. Vanstone, H. H. Holder, D. M. Arroo, T. Dion, F. Caravelli, H. Kurebayashi, and W. R. Bran- ford,Reconfigurable training and reservoir computing in an ar- tificial spin-vortex ice via spin-wave fingerprinting, Nat. Nan- otechnol.17, 460–469 (2022)

    work page 2022

  21. [21]

    D. A. Allwood, M. O. A. Ellis, D. Griffin, T. J. Hayward, L. Manneschi, M. F. K. Musameh, S. O’Keefe, S. Stepney, C. Swindells, M. A. Trefzer, E. Vasilaki, G. Venkat, I. Vi- damour, and C. Wringe,A perspective on physical reservoir computing with nanomagnetic devices, Appl. Phys. Lett.122, 040501 (2023)

    work page 2023

  22. [22]

    J. H. Jensen, A. Strømberg, I. Breivik, A. Penty, M. A. Niño, M. W. Khaliq, M. Foerster, G. Tufte, and E. Folven,Clocked dynamics in artificial spin ice, Nat. Commun.15, 964 (2024)

    work page 2024

  23. [23]

    Zázvorka, F

    J. Zázvorka, F. Jakobs, D. Heinze, N. Keil, S. Kromin, S. Jaiswal, K. Litzius, G. Jakob, P. Virnau, D. Pinna, K. Everschor-Sitte, L. Rózsa, A. Donges, U. Nowak, and M. Kläui,Thermal skyrmion diffusion used in a reshuffler de- vice, Nature Nanotechnology14, 658–661 (2019)

    work page 2019

  24. [24]

    Pinna, G

    D. Pinna, G. Bourianoff, and K. Everschor-Sitte,Reservoir Computing with Random Skyrmion Textures, Phys. Rev. Appl. 14, 054020 (2020)

    work page 2020

  25. [25]

    Y . Sun, T. Lin, N. Lei, X. Chen, W. Kang, Z. Zhao, D. Wei, C. Chen, S. Pang, L. Hu, L. Yang, E. Dong, L. Zhao, L. Liu, Z. Yuan, A. Ullrich, C. H. Back, J. Zhang, D. Pan, J. Zhao, M. Feng, A. Fert, and W. Zhao,Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir com- puting system, Nat. Commun.14, 3434 (2023)

    work page 2023

  26. [26]

    O. Lee, R. Msiska, M. A. Brems, M. Kläui, H. Kurebayashi, and K. Everschor-Sitte,Perspective on unconventional comput- ing using magnetic skyrmions, Applied Physics Letters122, 260501 (2023)

    work page 2023

  27. [27]

    Beneke, T

    G. Beneke, T. B. Winkler, K. Raab, M. A. Brems, F. Kammer- bauer, P. Gerhards, K. Knobloch, S. Krishnia, J. H. Mentink, and M. Kläui,Gesture recognition with Brownian reservoir computing using geometrically confined skyrmion dynamics, Nature Communications15, 1–9 (2024)

    work page 2024

  28. [28]

    Nakane, G

    R. Nakane, G. Tanaka, and A. Hirose,Reservoir Computing With Spin Waves Excited in a Garnet Film, IEEE Access6, 4462–4469 (2018)

    work page 2018

  29. [29]

    A. Papp, G. Csaba, and W. Porod,Characterization of non- linear spin-wave interference by reservoir-computing metrics, Appl. Phys. Lett.119, 112403 (2021). 9

    work page 2021

  30. [30]

    Lee and M

    M.-K. Lee and M. Mochizuki,Reservoir Computing with Spin Waves in a Skyrmion Crystal, Phys. Rev. Appl.18, 014074 (2022)

    work page 2022

  31. [31]

    Nakane, A

    R. Nakane, A. Hirose, and G. Tanaka,Performance Enhance- ment of a Spin-Wave-Based Reservoir Computing System Uti- lizing Different Physical Conditions, Phys. Rev. Appl.19, 034047 (2023)

    work page 2023

  32. [32]

    Namiki, D

    W. Namiki, D. Nishioka, Y . Yamaguchi, T. Tsuchiya, T. Higuchi, and K. Terabe,Experimental Demonstration of High-Performance Physical Reservoir Computing with Nonlin- ear Interfered Spin Wave Multidetection, Adv. Intell. Syst.5, 2300228 (2023)

    work page 2023

  33. [33]

    Nagase, S

    S. Nagase, S. Nezu, and K. Sekiguchi,Spin-wave reservoir chips with short-term memory for high-speed estimation of ex- ternal magnetic fields, Phys. Rev. Appl.22, 10.1103/physrevap- plied.22.024072 (2024)

    work page doi:10.1103/physrevap- 2024

  34. [34]

    Namiki, D

    W. Namiki, D. Nishioka, T. Tsuchiya, and K. Terabe,Fast phys- ical reservoir computing, achieved with nonlinear interfered spin waves, Neuromorph. Comput. Eng.4, 024015 (2024)

    work page 2024

  35. [35]

    Körber, C

    L. Körber, C. Heins, T. Hula, J.-V . Kim, S. Thlang, H. Schultheiss, J. Fassbender, and K. Schultheiss,Pattern recognition in reciprocal space with a magnon-scattering reser- voir, Nat. Commun.14, 3954 (2023)

    work page 2023

  36. [36]

    Heins, J.-V

    C. Heins, J.-V . Kim, L. Körber, J. Fassbender, H. Schultheiss, and K. Schultheiss,Benchmarking a magnon-scattering reser- voir with modal and temporal multiplexing, Physical Review Applied23, 054087 (2025)

    work page 2025

  37. [37]

    R. P. Cowburn, D. K. Koltsov, A. O. Adeyeye, M. E. Welland, and D. M. Tricker,Single-Domain Circular Nanomagnets, Physical Review Letters83, 1042–1045 (1999)

    work page 1999

  38. [38]

    Scholz, K

    W. Scholz, K. Guslienko, V . Novosad, D. Suess, T. Schrefl, R. Chantrell, and J. Fidler,Transition from single-domain to vortex state in soft magnetic cylindrical nanodots, Journal of Magnetism and Magnetic Materials266, 155–163 (2003)

    work page 2003

  39. [39]

    Sebastian, K

    T. Sebastian, K. Schultheiss, B. Obry, B. Hillebrands, and H. Schultheiss,Micro-focused brillouin light scatter- ing: imaging spin waves at the nanoscale, Front. Phys.3, 10.3389/fphy.2015.00035 (2015)

    work page doi:10.3389/fphy.2015.00035 2015

  40. [40]

    R. Mock, B. Hillebrands, and R. Sandercock,Construction and performance of a Brillouin scattering set-up using a triple-pass tandem Fabry-Perot interferometer, J. Phys. E: Sci. Instr.20, 656–659 (1987)

    work page 1987

  41. [41]

    Lozhkina, F

    O. Lozhkina, F. Kammerbauer, M.-A. Syskaki, A. Puthi- rath Balan, P. Krautscheid, M. V . Khanjani, J. Kubik, S. O’Brien, R. M. Reeve, G. Jakob, R. Frömter, and M. Kläui, Tailoring Magnetic Properties and Suppressing Anisotropy in Permalloy Films by Deposition in a Rotating Magnetic Field, Phys. Rev. Appl.20, 014021 (2023)

    work page 2023

  42. [42]

    Buess, T

    M. Buess, T. P. J. Knowles, R. Höllinger, T. Haug, U. Krey, D. Weiss, D. Pescia, M. R. Scheinfein, and C. H. Back,Excita- tions with negative dispersion in a spin vortex, Physical Review B71, 104415 (2005)

    work page 2005

  43. [43]

    V ogt, O

    K. V ogt, O. Sukhostavets, H. Schultheiss, B. Obry, P. Pirro, A. A. Serga, T. Sebastian, J. Gonzalez, K. Y . Guslienko, and B. Hillebrands,Optical detection of vortex spin-wave eigen- modes in microstructured ferromagnetic disks, Physical Review B84, 174401 (2011)

    work page 2011

  44. [44]

    Schultheiss, R

    K. Schultheiss, R. Verba, F. Wehrmann, K. Wagner, L. Kör- ber, T. Hula, T. Hache, A. Kákay, A. A. Awad, V . Tiberkevich, A. N. Slavin, J. Fassbender, and H. Schultheiss,Excitation of Whispering Gallery Magnons in a Magnetic Vortex, Phys. Rev. Lett.122, 097202 (2019)

    work page 2019

  45. [45]

    Verba, L

    R. Verba, L. Körber, K. Schultheiss, H. Schultheiss, V . Tiberke- vich, and A. Slavin,Theory of three-magnon interaction in a vortex-state magnetic nanodot, Physical Review B103, 014413 (2021)

    work page 2021

  46. [46]

    M. C. Mackey and L. Glass,Oscillation and chaos in physio- logical control systems, Science197, 287–289 (1977)

    work page 1977

  47. [47]

    Wringe, M

    C. Wringe, M. Trefzer, and S. Stepney,Reservoir comput- ing benchmarks: a tutorial review and critique, International Journal of Parallel, Emergent and Distributed Systems , 1–39 (2025)

    work page 2025

  48. [48]

    H.-P. H. Chaoming Wang, Sichao He, Brainpy, https://github.com/brainpy/examples/blob/ main/classical_dynamical_systems/mackey_ glass_eq.ipynb(2022)

    work page 2022

  49. [49]

    Pedregosa, G

    F. Pedregosa, G. Varoquaux, A. Gramfort, V . Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V . Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay,Scikit-learn: Ma- chine learning in Python, Journal of Machine Learning Re- search12, 2825–2830 (2011)

    work page 2011

  50. [50]

    K. D. Stenning, J. C. Gartside, L. Manneschi, C. T. S. Cheung, T. Chen, A. Vanstone, J. Love, H. Holder, F. Caravelli, H. Kure- bayashi, K. Everschor-Sitte, E. Vasilaki, and W. R. Branford, Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks, Nature Communications 15, 7377 (2024)

    work page 2024

  51. [51]

    O. Lee, T. Wei, K. D. Stenning, J. C. Gartside, D. Prest- wood, S. Seki, A. Aqeel, K. Karube, N. Kanazawa, Y . Taguchi, C. Back, Y . Tokura, W. R. Branford, and H. Kurebayashi,Task- adaptive physical reservoir computing, Nature Materials23, 79–87 (2024)

    work page 2024

  52. [52]

    Xiong, C

    Z. Xiong, C. Heins, T. Devolder, F. Kammerbauer, M. Kläui, J. Fassbender, H. Schultheiss, and K. Schultheiss, Data publi- cation: Predicting the Future with Magnons (2025). 10 2000 400 Time, t (ns) 600 800 1000 1200 BLS frequency, fBLS (GHz) 6 8 2 4BLS frequency, fBLS (GHz) 6 8 2 4BLS frequency, fBLS (GHz) 6 8 2 4BLS frequency, fBLS (GHz) 6 8 2 4BLS frequ...

    work page 2025