Distinct memory properties in spin-wave reservoir computing based on synthetic antiferromagnet

Abstract

Spin-wave-based physical reservoir computing (RC) is a promising candidate for energy-efficient physical implementations of artificial intelligence because of its potential for nanoscale integration with low power consumption. Most of the previous studies on spin-wave RC have utilized spin waves excited in a single-layer ferromagnet. In this study, we focused on spin waves in a synthetic antiferromagnet (SAF), consisting of two ferromagnetic layers coupled antiferromagnetically, and investigated additional memory properties of spin-wave RC. We theoretically and numerically demonstrate the emergence of two distinct memory properties in the SAF device due to the distinct spin-wave characteristics of the acoustic and optical modes inherent in SAFs.

Figures (9)

• Figure 1: (a)Schematic illustration of spin-wave physical reservoir computing using synthetic antiferromagnets. Magnetization dynamics is excited by spin-transfer torque to inject time-series data as spin waves and the spin-wave information is detected by magnetoresistance effect. Complex characteristics of spin-wave propagation in synthetic antiferromagnet enable to make distinct memory properties which can keep past input time-series with different time length. (b)Length scale to evaluate memory properties of spin-wave physical reservoir computing used in this study. Higher damping parameter is set at an edge of rectangle to prevent reflection of spin waves.
• Figure 2: Memory curves of spin-wave physical reservoir computing using synthetic antiferromagnet. Capacity to reconstruct delayed input $C_k$ plotted as a function of delay $k$ of input time-series for the case when external magnetic field ${\bf B}$ and spin-wave wavevector ${\bf q}$ are parallel and Néel vector ${\bf n} = {\bf m}_1 -{\bf m}_2$ is along $+{\bf y}$ direction [(a)-(c)], the case when ${\bf B}$ and ${\bf q}$ are orthogonal [(d)-(f)], and the case when ${\bf B}$ and ${\bf q}$ are parallel and ${\bf n}$ is along $-{\bf y}$ [(g)-(i)]. Magnetization of one ferromagnetic layer ${\bf m}_1$ is used as output [(a), (d), (g)] while summations ${\bf m}_1+{\bf m}_2$ [(b), (e), (h)] and differences ${\bf m}_1-{\bf m}_2$ [(c), (f), (i)] of two ferromagnetic layers are used. Here, $B$ = 0.2 T is applied. Solid curve in (a) is average value of $C_k$ obtained in (b) and (c). Solid and broken lines in (a)-(i) are the threshold $\varepsilon$ to avoid overestimation and $N_{\rm v}/N_{\rm T}$ expected value when there is no correlation between outputs and the data reconstructed by the magnetization.
• Figure 3: (a) Average delay $\left< k \right>$ and memory time $N_{\rm v}\theta \left< k \right>$ plotted as a function of external magnetic field $B$ for the case when Néel vector ${\bf m}_1 -{\bf m}_2$ is along $+{\bf y}$ direction. (b) $\left< k \right>$ and $N_{\rm v}\theta \left< k \right>$ plotted as a function of $B$ when ${\bf m}_1 -{\bf m}_2$ is along $-{\bf y}$.
• Figure 4: (a)The relative angles $\varphi_{1}$ and $\varphi_{2}$ between $\mathbf{B}$ and $\mathbf{m}_{1,2}$. The solid and dashed lines represent $\varphi_{1}$ and $\varphi_{2}$, respectively. and (b) frequency at ${\bf q}$ = 0 for AC and OP modes calculated as a function of in-plane external magnetic field $B$.
• Figure 5: (a) Efficiency of spin-wave excitation $|h(q_{\rm x})|$ plotted as a function of wavenumber $q_x$ with a parameter $a$ = 40 nm. (b), (c) Calculated memory time $d\left< v_{\rm g}^{-1}\right>$ for AC and OP modes based on the group velocity calculation of spin waves in SAFs with different Néel vector orientations (b) $+{\bf y}$ and (c) $-{\bf y}$ corresponding to Figs. 3(a) and 3(b). Solid and broken curves are the values evaluated with analytical calculation of spin-wave dispersion relation while circle and square symbols are the values evaluated with the dispersion relation obtained by micromagnetic simulations.