Reservoir computing in a lithium-based magneto-ionic device

TL;DR

This work addresses low-power, real-time time-series forecasting by integrating reservoir computing directly into a magneto-ionic device. A Ta/CoFeB/Ta/MgO/Ta crossbar with LiPON/Pt top electrode enables voltage-driven Li$^+$ migration that modulates magnetic anisotropy and domain patterns, with outputs read from radially averaged 2D Fourier spectra of MOKE images. The Mackey-Glass time series is used as a chaotic benchmark and parameterized by $a$, $b$, $\tau$, and $n$. Systematic variation of input rate, reservoir dimensionality, smoothing, and training length reveals two computational regimes: short-term forecasts favor smoothed, low-dimensional reservoirs with minimal training, while predictions around the Mackey-Glass delay time $\tau$ benefit from unsmoothed, high-dimensional reservoirs and longer training. The results quantify a fundamental nonlinearity–memory trade-off and provide concrete design principles for matching reservoir characteristics to input statistics, highlighting potential for magneto-ionic neuromorphic processors in real-time, low-power time-series forecasting.

Abstract

In-materio computing exploits the intrinsic physical dynamics of materials to perform complex computations, enabling low-power, real-time data processing by embedding computation directly within physical layers. Here, we demonstrate a voltage-controlled magneto-ionic device that functions as a reservoir computer capable of forecasting chaotic time series. The device consists of a crossbar structure with a Ta/CoFeB/Ta/MgO/Ta bottom electrode and a LiPON/Pt top electrode. A chaotic Mackey-Glass time series is encoded into a voltage signal applied to the device, while 2D Fourier transforms of voltage-dependent magnetic domain patterns form the output. Performance is influenced by the input rate, smoothing of the output, the number of elements in the reservoir state vector, and the training duration. We identify two distinct computational regimes: short-term prediction is optimized using smoothed, low-dimensional states with minimal training, whereas prediction around the Mackey-Glass delay time benefits from unsmoothed, high-dimensional states and extended training. Reservoir computing metrics reveal that slower input rates are more tolerant to output smoothing, while faster input rates degrade both memory capacity and nonlinear processing. These findings demonstrate the potential of magneto-ionic systems for neuromorphic computing and offer design principles for tuning performance in response to input signal characteristics.

Figures (6)

• Figure 1: (a) Schematic of the magneto-ionic device, comprising a crossbar junction with a layered Ta/CoFeB/Ta/MgO/Ta bottom electrode and LiPON/Pt top electrode. Application of a positive voltage to the top electrode drives Li$^+$ ions from the LiPON layer toward the bottom electrode, enabling voltage-controlled modulation of the magnetic domain state in the CoFeB layer. (b) Out-of-plane magnetic hysteresis loops measured by MOKE microscopy under different applied voltages, illustrating voltage-induced changes in magnetic behavior. (c)-(e) MOKE microscopy images showing the magnetic domain structure in the CoFeB layer at a fixed out-of-plane magnetic field of 0.3 mT under applied voltages of (c) -2 V, (d) 0 V, and (e) +2 V.
• Figure 2: (a) Delay-embedded trajectory of the Mackey-Glass signal used in this study. The inset shows the same 100-step segment of the signal as a time series. (b) Representative voltage waveforms used to drive the magneto-ionic reservoir, obtained by linearly mapping the Mackey-Glass signal onto a voltage range of -2 V to +2 V. The input rates shown are 0.04 (top), 0.20 (middle), and 0.41 (bottom) Mackey-Glass steps per MOKE microscopy frame. (c)-(e) Zoom-ins of MOKE microscopy images captured at the (c) 1000th, (d) 1050th, and (e) 1100th frame in a video recorded at an input rate of 0.20 Mackey-Glass steps per frame.
• Figure 3: (a) Radially averaged 2D Fourier transforms of the full-size versions of the MOKE microscopy images from Fig. 2, recorded at an input rate of 0.20 Mackey-Glass steps per frame. (b) Temporal evolution of the reservoir signal for selected wavenumber components as a function of video frame number, recorded at an input rate of 0.20 Mackey-Glass steps per frame. The corresponding input signal is shown for comparison. (c) Effect of causal Savitzky-Golay filtering on the reservoir states for an input rate of 0.20 Mackey-Glass steps per frame. Reservoir responses are shown for second-order polynomial smoothing with window lengths of 0, 11, 21, 31, 41, and 51 data points at 0.22 $\upmu$m$^{-1}$. The input signal is again shown for reference.
• Figure 4: Predictions of the Mackey-Glass signal under varying input and model parameters. The time step is referenced to the video frame rate. (a) One-step ahead prediction at an input rate of 0.04 Mackey-Glass steps per frame, using the full 64-component reservoir state vector, 20 training frames, and a 51-point Savitzky-Golay filter. (b) 50-step-ahead prediction at the same input rate, performed with a reduced 16-component state vector, 400 training frames, and no smoothing. (c) Five-step-ahead prediction at a higher input rate of 0.33 Mackey-Glass steps per frame, using a 64-component state vector, 1000 training frames, and no smoothing.
• Figure 5: Optimization results for predicting the Mackey-Glass signal across various prediction horizons and input rates. The prediction step is referenced to the video frames. (a) Minimum mean squared error (MSE) achieved for each combination of prediction horizon and input rate, determined by scanning over all combinations of state vector sizes, training lengths, and smoothing parameters. The black dots mark the number of steps in the reference time of the video frames equal to $\tau$. (b) Optimal maximum wavenumber component (i.e., number of wave vector components) that minimizes the prediction error for each setting. (c) Optimal Savitzky-Golay smoothing window length yielding the lowest prediction error across all conditions. The black dots mark the number of steps in the reference time of the video frames equal to $\tau$. (d) Optimal number of training frames resulting in the smallest prediction error for each prediction horizon and input rate.