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Physical reservoir computing and deep neural networks using artificial and natural noncollinear spin textures

Haotian Li, Liyuan Li, Rongxin Xiang, Wei Liu, Chunjie Yan, Zui Tao, Lei Zhang, and Ronghua Liu

Phys. Rev. Applied 22, 014027 – Published 11 July 2024

Abstract

The growing demand for artificial intelligence has motivated research into nontraditional physical devices that enable efficient learning in various tasks. This requires the devices to exhibit natural nonlinear dynamics with minimal power consumption. Here we present the application of artificial spin ice (ASI) and an as-grown chiral helimagnet (CHM) as the nonlinear component in physical reservoir computing (RC) and deep neural networks (DNNs). Their complex nonlinear magnetodynamics can be easily characterized by the broadband coplanar waveguide–based ferromagnetic resonance technique, originating from the specifically geometrical frustration effect and intrinsic multiple magnetic interactions competition, respectively. On the basis of the experimentally obtained nonlinear magnetodynamic response curves of these two noncollinear spin textures, we build ASI- and CHM-based physical reservoirs for RC and use the absorption and differential ferromagnetic resonance spectra as the activation function and its derivatives to perform nonlinear transformation of inputs for DNNs. The results demonstrate that physical RC and DNNs can accomplish time-series prediction and image-recognition tasks, respectively, with high accuracy and low power consumption. Our findings provide valuable insights and a promising pathway toward neuromorphic hardware using abundant artificial or natural nontrivial magnetic systems.

Received 13 December 2023
Revised 14 March 2024
Accepted 17 June 2024

DOI:https://doi.org/10.1103/PhysRevApplied.22.014027

Physics Subject Headings (PhySH)

Artificial spin ice Neuromorphic computing Spin texture Spintronics

Artificial neural networks Chiral magnets

Deep learning Ferromagnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Haotian Li¹, Liyuan Li¹, Rongxin Xiang¹, Wei Liu ³, Chunjie Yan¹, Zui Tao¹, Lei Zhang ^4,5, and Ronghua Liu ^1,2,*

¹National Laboratory of Solid State Microstructures, Jiangsu Provincial Key Laboratory for Nanotechnology, and School of Physics, Nanjing University, Nanjing, 210093, China
²National Key Laboratory of Spintronics, Nanjing University, Suzhou, 215163, China
³Institutes of Physical Science and Information Technology, Anhui University, Hefei, 230601, China
⁴Anhui Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, 230031, China
⁵The High Magnetic Field Laboratory of Anhui Province, Hefei, 230031, China

^*Corntact author: [email protected]

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Vol. 22, Iss. 1 — July 2024

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Figure 1
Differential FMR experimental setup and two nonlinear dynamics of magnetic devices. (a) The sample is fixed to the center signal line of the CPW consisting of two ground parts and one center signal line and the purple and red arrows represent the injection of microwave current and external magnetic field, respectively. (b) Scanning-electron-microscope images of the ASI. (c) Three-dimensional schematic spin configurations of the CSL.
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Figure 2
Magnetic dynamic characteristics of ASI and the CHM. (a) Pseudocolor map of the experimental FMR spectra of ASI at room temperature. Five series of resonance peaks are represented by the dotted lines to guide the eye. (b) Representative FMR absorbed power spectra of ASI obtained by simulation at three selected in-plane fields $H = 0.5$ , 0.6 and 0.7 kOe. (c) Spatial profiles of the power spectrum density (PSD) for two high-frequency (upper panel) and two low-frequency (lower panel) peaks correspond to the bulk and edge spin-wave modes, respectively. (d) Pseudocolor map of the experimental FMR spectra of the CHM single crystal ${Cr Nb}_{3} S_{6}$ obtained at $T = 4$ K. The critical field $H_{c} = 1.72 kOe$ , represented by the vertical dashed line, separates the low-field CSL state from the high-field forced ferromagnetic state in the FMR spectra. The dotted lines are guides for the eye, marking different spin-wave modes. (e) Representative experimental differential FMR spectra of the CSL state measured at three selected in-plane fields $H_{ext} = 1.3$ , 1.4, and 1.5 kOe below $H_{c}$ . These different peaks corresponding to distinct spin-wave modes are represented by “CSL-LF,” “CSL-FM,” and “CSL-OP”, which are defined in the main text. (f) Spatial distributions (amplitude abbreviated as “amp” and phase) and three-dimensional schematic precession trajectory of the ferromagnetic (FM) and CSL-OP modes, respectively.
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Figure 3
Reservoir-computing scheme and training results. (a) The input time-series data $x (t) \in R^{N}$ are linearly mapped to the time series of the magnetic field $H (t) \in R^{N}$ in the input layer. (b) Magnetic field–dependent differential FMR spectra $d P / d H |_{H_{i}} (f_{j})$ as the physical reservoir. $H (t_{i})$ is the input of the physical reservoir at each time step. After the physical reservoir, $H (t)$ is nonlinearly transformed into a reservoir state matrix $R_{out} \in R^{N \times M}$ . (c) $R_{out}$ is connected to the output layer by a trainable weight matrix $W_{out}$ . The error between prediction and target results is used to update $W_{out}$ by ridge regression. After the training phase, the $W_{out}$ matrix is fixed for the testing phase.
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Figure 4
Prediction results for two nonlinear dynamic systems obtained by ASI- and CHM-based physical RC. (a),(b) Prediction results obtained by ASI-based physical RC for the Mackey-Glass dataset (a) and the NARMA10 dataset (b). (c),(d) Prediction results obtained by CHM-based physical RC for the Mackey-Glass dataset (c) and the NARMA10 dataset (d). The theoretical target results (black) and the prediction results obtained by the physical RC (red) are both in the testing phase.
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Figure 5
NRMSE results for (a) the Mackey-Glass dataset and (b) the NARMA10 dataset dependent on prediction time $τ$ for ASI and the CHM.
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Figure 6
Architecture diagram of the DFA-based DNN and its performance in the handwritten-digit-recognition task. (a) Schematic network structure of the DFA-based DNN. Differing from the layer-by-layer updating process for the weight in the conventional BP algorithm, the DFA simultaneously updates weights ( $W_{0}$ , $W_{1}$ , and $W_{2}$ ) on the basis of an arbitrary matrix as the initial weight according to the error between the output value and the target value. (b) Representative FMR absorption spectrum (for forward propagation) and differential FMR spectrum (for backward propagation) are directly obtained by the FMR experiments. (c) Testing results for the physical DFA-based DNN with 10 000 test sets of handwritten-digit images. (d) Comparison of results for the recognition error rate as a function of the number of testing epochs between the conventional BP algorithm and our physical DFA algorithm.
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Physical Review Applied

Physical reservoir computing and deep neural networks using artificial and natural noncollinear spin textures

Haotian Li, Liyuan Li, Rongxin Xiang, Wei Liu, Chunjie Yan, Zui Tao, Lei Zhang, and Ronghua Liu

Phys. Rev. Applied 22, 014027 – Published 11 July 2024

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