Positional memory of skyrmions in magnetic bilayers

TL;DR

The study investigates how skyrmions in synthetic antiferromagnet bilayers respond to magnetic field gradients. By combining numerical simulations, a moduli-space (Thiele) framework, and an exact dynamical treatment, it reveals a characteristic motion perpendicular to the gradient and a robust positional memory: after removing the gradient, skyrmions nearly return to their original positions. The work shows that an equilibrium interlayer separation emerges from a balance of external gradient forces and interlayer coupling, and that the guiding-center dynamics underpin the memory effect, with only small deviations possible due to nonadiabatic transients. This contributes a distinct dynamical paradigm for SAF skyrmions, with potential implications for memory- and neuromorphic-inspired devices.

Abstract

We numerically and analytically study the transient dynamics of magnetic skyrmions in synthetic antiferromagnets under a magnetic field gradient. We consider skyrmions in a bilayer with antiferromagnetic coupling between the layers. The skyrmions in the two layers move almost perpendicular to the field gradient and the motion is eventually halted with the two skyrmions at a distance from each other. We find that the skyrmion displacement is proportional to the field gradient, while the time it takes to reach their final position is almost independent of it. Below a critical magnetic field gradient strength, the system displays an unusual 'remembering' dynamics: when the magnetic field gradient is removed, the skyrmions return to their original positions to a high degree of accuracy. We explain this observation and other quantitative features using a moduli space dynamics approximation. We further provide an exact treatment of the dynamics that indicates that deviations from exact memory of the skyrmion position can arise.

Figures (6)

• Figure 1: A bilayer skyrmion for parameter value $\lambda=0.5$. (Left) The skyrmion magnetization $\mathbf{L}$ in the lower layer and (Right) the skyrmion magnetization $\mathbf{U}$ in the upper layer, where $\mathbf{U} = -\mathbf{L}$. The skyrmion configurations are identical to skyrmions in a monolayer with the same intralayer parameter values. Vectors show the projection of the magnetization on the $xy$ plane and the third component of the magnetization is shown via a colour code.
• Figure 2: Snapshots of the bilayer skyrmions propagating under a magnetic field gradient with $g=0.05$ (lower in red, upper in blue). Shown are the contours for $L_3=0.75,\, U_3=-0.75$. (Note that the skyrmion radius, measured at $U_3=0, L_3=0$, is 1.4.) The simulation starts from the static skyrmion, for parameter value $\lambda=0.5$ and damping parameter $\alpha=0.1$, The field is switched on at time $\tau=0$.
• Figure 3: Motion of the centers of the two skyrmions (lower in red, upper in blue) in the bilayer according to definition \ref{['eq:XY']}. The simulation is the same as in Fig. \ref{['fig:skyrmionBL_diffgradient']}. A field gradient is applied for times $0 < \tau < 400$ with $g=0.05$ and the field is switched off at $\tau=400$. Solid lines represent motion under the applied field gradient, while dashed lines show the trajectories after the field is switched off.
• Figure 4: The trajectories of the two skyrmions for the same simulation as in Figs. \ref{['fig:skyrmionBL_gradientDamping']},\ref{['fig:XY_trajectory']}. The trajectories for the lower and upper layer skyrmion are shown with red and blue lines, respectively. Solid lines represent motion under the applied field gradient, while dashed lines show the trajectories after the field is switched off. The trajectories of the guiding centres $(R_1, R_2)$ are shown by strong lines. The faded lines show the trajectories for $(X_1, X_2)$ which were also presented in Fig. \ref{['fig:XY_trajectory']} and are drawn here for comparison.
• Figure 5: The guiding centre component $R_2$ for skyrmions in both layers as a function of time under various field gradient strengths $g$. The field gradient is switched on at $\tau = 0$ and switched off at $\tau = 400$.