Learning-Performance Evaluation of a Physical Reservoir Based on a Vortex Spin-Torque Oscillator with a Modified Free Layer

Abstract

In this study, we numerically evaluate the learning performance of a vortex spin-torque oscillator with a modified free layer, called a modified VSTO (m-VSTO), in which an additional layer (AL) of smaller radius is stacked on the free layer, for physical reservoir computing. The vortex-core dynamics are computed using the Thiele equation incorporating the potential deformation induced by the AL. We identify the edge of chaos from the maximal Lyapunov exponent and quantify the short-term memory capacity (STMC) as well as the information processing capacity (IPC) in a time-multiplexed reservoir scheme. We find that the m-VSTO exhibits finite STMC and IPC in a low-current and low-field regime below the threshold current of the conventional VSTO, and can achieve up to approximately twice the IPC with about one quarter of the power consumption. Furthermore, when the input pulse width is set comparable to or longer than the transient time, the parameter region with high STMC and IPC expands, and the optimal operating region is located not at the edge of chaos but in a stable regime with long transients. These results suggest that engineering the potential landscape and the driving conditions enables low-power spintronic physical reservoirs.

Figures (5)

• Figure 1: (a) Schematic of the modified vortex spin-torque oscillator (m-VSTO). A circular ferromagnetic additional layer (AL) of radius $R_a$ and thickness $L_a$ is concentrically stacked on the free layer (radius $R$, thickness $L$) of a ferromagnet/insulator/ferromagnet trilayer. A dc current $I$ is injected perpendicular to the film plane, and an in-plane magnetic field $\bm{H}=(h_x,0,0)$ is applied along the $x$ axis; $\bm{m}$ denotes the magnetization direction of the reference layer. (b),(c) Representative vortex-core dynamics under an $x$-directed sinusoidal ac magnetic field at $I=0$: (b) phase portrait of the normalized vortex-core position $(X/R,\,Y/R)$ after discarding an initial transient and (c) the corresponding time trace of the normalized gyration amplitude $s(t)$. The aperiodic trajectory and irregular amplitude fluctuations indicate a chaotic response enabled by the AL-induced deformation of the confinement potential.
• Figure 2: Dependence of Lyapunov exponent $\lambda$ on input strength $h_0$ (Oe) and current $I$ (mA) for (a) without AL and (b) with AL radius $R_a=40$ nm. White indicates a region where $\lambda$ is very close to zero, which we regard as corresponding to the edge of chaos.
• Figure 3: Dependence of short-term memory capacity $C_{\mathrm{STM}}$ and information processing capacity (IPC) on input strength $h_0$ (Oe) and current $I$ (mA) for (a)(c) without AL and (b)(d) with AL radius $R_a=40$ nm. The purple dashed line indicates the threshold current of a conventional VSTO.
• Figure 4: Dependence of Lyapunov exponent $\lambda$ on input strength $h_0$ (Oe) and current $I$ (mA) for $R_a=40$ nm with pulse widths (a) $t_p=5$ ns, (b) $t_p=7$ ns, (c) $t_p=8$ ns, and (d) $t_p=10$ ns. White indicates a region where $\lambda$ is very close to zero, which we regard as corresponding to the edge of chaos.
• Figure 5: Dependence of information processing capacity on input strength $h_0$ (Oe) and current $I$ (mA) for $R_a=40$ nm with pulse widths (a) $t_p=7$ ns and (b) $t_p=10$ ns.