Ratchet motion of magnetic skyrmions driven by surface acoustic sawtooth waves

TL;DR

This work addresses the challenge of deterministically transporting skyrmions without Joule heating by leveraging surface acoustic waves. The authors propose a sawtooth SAW profile that creates an asymmetric strain gradient, enabling depinning and unidirectional hopping of skyrmions between pinning centers, with net motion roughly perpendicular to the SAW direction. They develop a rigid-Néel skyrmion analytical model including magnetoelastic coupling and pinning potentials, derive a depinning threshold $\Delta\varepsilon_{xx,\min}$, and predict a ratchet regime confirmed by micromagnetic simulations. The simulations, conducted for nanoscale skyrmions and realistic pinning landscapes, reproduce the threshold behavior and demonstrate ratcheting under a sawtooth SAW, supported by an energy landscape analysis and Fourier-synthesis route to experimental implementation. Overall, the results indicate feasible strain requirements and provide a route to SAW-assisted, directional skyrmion control for spintronic devices.

Abstract

The manipulation of skyrmions by surface acoustic waves (SAW) has garnered significant interest in the field of spintronic devices. Previous studies established that skyrmions can be generated and moved by strain pulses. In this study, we propose that sawtooth-SAWs can be used to drive a ratchet motion of magnetic skyrmions in the presence of pinning centers. This results in a net motion of the skyrmions orthogonal to the continuously applied SAW. The ratchet motion is fundamentally caused by non-vanishing pinning, so that a certain strain gradient magnitude is required to overcome pinning and start skyrmion motion. We demonstrate the feasibility of our concept by micromagnetic simulations and analytical model calculations.

Figures (4)

• Figure 1: a) Schematic of the proposed experiment. An interdigital transducer (IDT) launches a sawtooth-shaped surface acoustic wave (SAW) to a skyrmion in a pinning center. This depins the skyrmion and moves it to the next pinning center. The pinning center is modeled as a donut-shaped region with reduced anisotropy. The image on the top left shows the applied strain $\varepsilon$ and the bottom left image the resulting strain gradient $\Delta\varepsilon$ resulting from a sinusoidal-SAW (orange) and a sawtooth-shaped SAW (blue) over time $t$. The dashed black line in the bottom left image indicates the strain gradient $\Delta\varepsilon_\text{depin}$ needed to depin the skyrmion from a pinning site. b) depicts the micromagnetically simulated skyrmion velocities (black and red dots) of a pinned nm-scale skyrmion in a single pinning site in dependence of an applied strain gradient in x-direction. The black and red lines indicate the analytically calculated skyrmion velocity for $r_\text{SkX}=12.6nm$ and $w = 4.7nm$ obtained from Eq. (\ref{['eq:vx']}, \ref{['eq:vy']}).
• Figure 2: Anisotropy landscape used for simulating the response of the skyrmion to a surface-acoustic-wave. The anisotropy is reduced by a value of $2$ % in a donut shaped form. The regions of reduced anisotropy create a chain like structure. The anisotropy landscape creates a energy landscape which induces pinning to the system. The red circles correspond to skyrmions in the landscape after $t_\text{1} = 0ns$, $t_\text{2} = 30ns$ and $t_\text{3} = 40ns$ after applying a sawtooth-shaped SAW. The energy landscape for a region of $100\times100$ nm is shown in on the right.
• Figure 3: a) Shape of the resulting strain $\epsilon_{xx}$ (bottom) and the straingradient $\Delta\epsilon_{xx}$ (top) due to the applied sawtooth SAW. b) Anisotropy landscape created by $10nm$ sized grains with random anisotropy reduction between 0 and $1\%$. On the right the resulting energy landscape in a $100\times100$$nm\squared$ region. c) Movement of the skyrmion placed in the anisotropy landscape with an sawtooth-shaped SAW applied in the positive x-direction after a time of $t = 0ns$, $t = 10ns$ and $t = 30ns$.
• Figure 4: Force on the skyrmion in dependence of the skyrmion size $s = 2\cdot r_\text{SkX}+ w$ obtained from micromagnetic simulations (black circles) and from an analytical calculation from Eq. \ref{['eq:force_sky_ana']}. $r_\text{SkX}$ and $w$ for the analytical calculation are determined by fitting the normalized $m_z$ component from Eq. \ref{['eq:m']} to the skyrmion profile of the micromagnetically simulated skyrmion. The inset is a zoom in on small skyrmion sizes $s$.