Skyrmion behavior in attractive-repulsive square array of pinning centers

TL;DR

The work addresses steering a single skyrmion through a square lattice of mixed pinning centers (attractive and repulsive) under an applied drive. It uses a particle-based model with Gaussian pinning potentials and a Magnus term to map how the Hall-angle-like direction $\theta_{\rm sk}$ evolves as $F_D$ increases, revealing a robust $-45^\circ$ locking plateau that can be broadened or suppressed by defect strengths and radii. Key findings show that weaker attraction lowers depinning, stronger repulsion stabilizes $-45^\circ$ locking and broadens its force window, and defect size enables a sequence of locking angles including $-45^\circ$, $-50^\circ$, $-55^\circ$, and near $-59^\circ$ at low drives, with high drives returning to the intrinsic SkHE angle $\theta_{\rm sk}^{\rm int}$. These results propose a practical knob set for directing skyrmion transport and tailoring the effective Hall response, offering design principles for skyrmion-based memory and logic devices, while noting limitations of zero-temperature, rigid-skyrmion modeling and potential extensions to continuum or finite-temperature regimes.

Abstract

We investigate the driven dynamics of a single skyrmion in a square lattice of mixed pinning sites, where attractive and repulsive defects coexist using a particle-based model. The mixed landscape yields directional locking at $θ_{\rm sk}=-45^\circ$ and flow at locked angles near the intrinsic skyrmion Hall angle. By mapping defect strengths, we show that weaker attraction lowers the depinning threshold, whereas stronger repulsion stabilizes and broadens the $-45^\circ$ locking plateau. Moreover, combinations of attractive and repulsive defect strengths allows control of directional lockings and their force ranges. Defect size further tunes the response, selecting among $-45^\circ$, $-50^\circ$, $-55^\circ$, and $\approx-59^\circ$. These results establish mixed pinning as a practical knob to steer skyrmion trajectories and the effective Hall response, providing design guidelines for skyrmion-based memory and logic devices.

Figures (7)

• Figure 1: Schematic of the square array of periodic defects in our system that interact with the skyrmion. Red circles correspond to repulsive obstacles, while black circles to attractive pinning sites.
• Figure 2: Results for a system with a single skyrmion in mixture of repulsive and attractive pinning sites as shown in Fig. \ref{['fig:rede_quadrad']}, using $a_{at} = a_{rep}=0.65$, $C_{\rm rep}=-0.5$ and $C_{\rm rep}=1.0$. (a) $\langle V_{\parallel} \rangle$ and $\langle V_{\perp} \rangle$ as a function $F_D$. (b) The corresponding Hall angle $\theta_{sk}$ as a function of $F_D$.
• Figure 3: Illustration of the skyrmion trajectory (blue line) under the defect array for different values of the external driving force $F_D$ for the system shown in Figs. \ref{['fig:rede_quadrad']}. and \ref{['fig:vel_fatr0.5_frep1']}. In (a) $F_D = 0.70$, where a directional locking regime occurs with $\theta_{\rm sk}=-45^{\circ}$; (b) $F_D = 1.60$, regime dominated by a directional locking $\theta_{\rm sk}=-59^{\circ}$ very close to the intrinsic Hall angle $\theta_{\rm sk}^{\rm int}\approx-60^{\circ}$.
• Figure 4: (a,b) Skyrmion Hall angle $\theta_{\rm sk}$ as a function of the driving force, $F_D$ and (c,d) the range of forces $\Delta F_D$ vs. the defect strengths. (a) Results for fixed $C_{\rm rep}= 1.0$ and varied $C_{\rm at}$, and (b) for fixed $C_{\rm at}= -1.0$ and varied $C_{\rm rep}$. (c) $\Delta F_D$ vs. $C_{\rm at}$ with fixed $C_{\rm rep}= 0.5$ and (d) $\Delta F_D$ vs. $C_{\rm rep}$ with $C_{\rm at}= -0.5$. Simulations were performed with the ratio $\alpha_m/\alpha_d = 1.732$ and $a_{\rm at}=a_{\rm rep} = 0.65$.
• Figure 5: Skyrmion trajectories in a periodic lattice of attractive and repulsive defects for different combinations of potential strengths and driving force, $F_D$. (a) $C_{\rm at} = -1.0$, $C_{\rm rep} = 1.0$ and $F_D=1.50$, where the skyrmion motion is locked at $\theta_{\rm sk}=-57^{\circ}$. (b) $C_{\rm at}=-0.75$, $C_{\rm at}=1.0$ and $F_D=1.60$, where the skyrmion motion is in a transient state, between locked states $\theta_{\rm sk}=-57^{\circ}$ and $-59^{\circ}$.