Directional mode-locking of driven two-dimensional active magnetized colloids with periodic pinning centers

Li, Xiaodan; Wu, Chun; Cao, Tingting; Cao, Yigang

doi:10.1016/j.physa.2018.09.058

“…In a square lattice of obstacles, these angles include φ = 0 • , 45 • and 90 • , and they are more generally described by the relation φ = arctan(n/m) where n and m are integers [1][2][3][4]. Dynamical directional locking effects have been studied for vortices interacting with square and triangular pinning arrays [1,5,6], electrons moving through antidot arrays [2,7] and colloidal assemblies moving on two dimensional periodic substrates [3,4,[8][9][10][11][12][13][14]. In these systems, as the angle of the drive is varied with respect to the symmetry direction of the substrate, the velocity vector or velocity-force curves show a series of steps corresponding to drive angle intervals over which the direction of the motion of the particles remains locked to the substrate instead of following the drive direction.…”

Section: Introductionmentioning

confidence: 99%

Skyrmion dynamics and topological sorting on periodic obstacle arrays

Vizarim

¹

,

Reichhardt

²

,

Venegas

³

2020

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We examine skyrmions under a dc drive interacting with a square array of obstacles for varied obstacle size and damping. When the drive is applied in a fixed direction, we find that the skyrmions are initially guided in the drive direction but also move transverse to the drive due to the Magnus force. The skyrmion Hall angle, which indicates the difference between the skyrmion direction of motion and the drive direction, increases with drive in a series of quantized steps as a result of the locking of the skyrmion motion to specific symmetry directions of the obstacle array. On these steps, the skyrmions collide with an integer number of obstacles to create a periodic motion. The transitions between the different locking steps are associated with jumps or dips in the velocity-force curves. In some regimes, the skyrmion Hall angle is actually higher than the intrinsic skyrmion Hall angle that would appear in the absence of obstacles. In the limit of zero damping, the skyrmion Hall angle is 90 • , and we find that it decreases as the damping increases. For multiple interacting skyrmion species in the collective regime, we find jammed behavior at low drives where the different skyrmion species are strongly coupled and move in the same direction. As the drive increases, the species decouple and each can lock to a different symmetry direction of the obstacle lattice, making it possible to perform topological sorting in analogy to the particle sorting methods used to fractionate different species of colloidal particles moving over two-dimensional obstacle arrays. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische GesellschaftNew J. Phys. 22 (2020) 053025 N P Vizarim et alfrequency of the oscillations generated by the motion of the particle over the periodic substrate locks or comes into resonance with the ac drive frequency and its higher harmonics for a fixed range of drive intervals, producing steps in the velocity-force curves of the type found in Josephson junctions (which are known as Shapiro steps) [15,16], incommensurate sliding charge density waves [17], driven Frenkel-Kontorova systems [18], vortices in type-II superconductors moving over a periodic pinning substrate [19][20][21], and colloidal particles driven over periodic substrates [22,23]. In the case of the directional locking, there is no ac driving; however, two frequencies are still present, where one is associated with motion in the direction parallel to the drive and the other is associated with motion in the direction perpendicular to the drive. Directional locking can also arise in a system with a quasiperiodic substrate, where there are five or seven symmetry locking directions [24,25]. The locking can be harnessed for applications such as the sorting of different species of particles which have different sizes, charges, or damping, where a spatial separation of the species is achieved over time when one species locks to one angle while the other species locks to a different angl...

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“…In a square lattice of obstacles, these angles include φ = 0 • , 45 • and 90 • , and they are more generally described by the relation φ = arctan(n/m) where n and m are integers [1,2,3,4]. Dynamical directional locking effects have been studied for vortices interacting with square and triangular pinning arrays [1,5,6], electrons moving through antidot arrays [2,7] and colloidal assemblies moving on two dimensional periodic substrates [3,4,8,9,10,11,12,13,14]. In these systems, as the angle of the drive is varied with respect to the symmetry direction of the substrate, the velocity vector or velocity-force curves show a series of steps corresponding to drive angle intervals over which the direction of the motion of the particles remains locked to the substrate instead of following the drive direction.…”

Section: Introductionmentioning

confidence: 99%

Skyrmion Dynamics and Topological Sorting on Periodic Obstacle Arrays

Vizarim,

Reichhardt,

Reichhardt

et al. 2020

Preprint

2

6

0

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We examine skyrmions under a dc drive interacting with a square array of obstacles for varied obstacle size and damping. When the drive is applied in a fixed direction, we find that the skyrmions are initially guided in the drive direction but also move transverse to the drive due to the Magnus force. The skyrmion Hall angle, which indicates the difference between the skyrmion direction of motion and the drive direction, increases with drive in a series of quantized steps as a result of the locking of the skyrmion motion to specific symmetry directions of the obstacle array. On these steps, the skyrmions collide with an integer number of obstacles to create a periodic motion. The transitions between the different locking steps are associated with jumps or dips in the velocity-force curves. In some regimes, the skyrmion Hall angle is actually higher than the intrinsic skyrmion Hall angle that would appear in the absence of obstacles. In the limit of zero damping, the skyrmion Hall angle is 90 • , and we find that it decreases as the damping increases. For multiple interacting skyrmion species in the collective regime, we find jammed behavior at low drives where the different skyrmion species are strongly coupled and move in the same direction. As the drive increases, the species decouple and each can lock to a different symmetry direction of the obstacle lattice, making it possible to perform topological sorting in analogy to the particle sorting methods used to fractionate different species of colloidal particles moving over two-dimensional obstacle arrays.

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“…Passive particles driven over a periodic substrate can undergo directional locking in which the motion becomes locked to certain symmetries of the lattice. Here, the direction of particle motion does not change smoothly as the angle of the external drive is rotated with respect to the substrate, but remains fixed for finite intervals of drive angle, producing steps in a plot of the direction of particle motion versus drive direction [48][49][50][51][52][53][54][55][56][57][58][59][60]. For a particle moving on a square lattice, the directional locking occurs when the particle moves p lattice constants in one direction and q lattice constants in the perpendicular direction, giving locking steps centered at angles of θ = arctan(p/q).…”

Section: Introductionmentioning

confidence: 99%

Directional Locking Effects for Active Matter Particles Coupled to a Periodic Substrate

Reichhardt,

Reichhardt

2020

Preprint

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Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45 • directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ = arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is non-monotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

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Directional mode-locking of driven two-dimensional active magnetized colloids with periodic pinning centers

Cited by 10 publications

References 42 publications

Skyrmion dynamics and topological sorting on periodic obstacle arrays

Skyrmion dynamics and topological sorting on periodic obstacle arrays

Skyrmion Dynamics and Topological Sorting on Periodic Obstacle Arrays

Directional Locking Effects for Active Matter Particles Coupled to a Periodic Substrate

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