Collective Directional Locking of Colloidal Monolayers on a Periodic Substrate

Ralph L. Stoop, Arthur V. Straube, Tom H. Johansen, and Pietro Tierno

Phys. Rev. Lett. 124, 058002 – Published 4 February 2020

Abstract

We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred.

Received 3 September 2019
Accepted 16 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.058002

Physics Subject Headings (PhySH)

Ballistic transport Domain walls Transport phenomena

Magnetic colloids

Polymers & Soft Matter

Authors & Affiliations

Ralph L. Stoop ¹, Arthur V. Straube^2,3,1, Tom H. Johansen ^4,5, and Pietro Tierno ^1,6,7,*

¹Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
²Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
³Group “Dynamics of Complex Materials”, Zuse Institute Berlin, 14195 Berlin, Germany
⁴Department of Physics, University of Oslo, P. O. Box 1048 Blindern, 0316 Oslo, Norway
⁵Institute for Superconducting and Electronic Materials, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia
⁶Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
⁷Institut de Nanociència i Nanotecnologia, IN2UB, Universitat de Barcelona, 08028 Barcelona, Spain

^*ptierno@ub.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 124, Iss. 5 — 7 February 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Polarization microscope image showing a small portion of a magnetic bubble lattice with a schematic of the 12 possible directions. The particles are driven toward left along the $- 1 - 1$ direction; the basic lattice vectors are chosen as $a_{\pm} = (\sqrt{3} a / 2, \pm a / 2)$ . Scale bar is $10 μ m$ . (b) Energy landscape of the magnetic lattice calculated at an elevation $z = 0.7 a$ ( $H_{0} = 0.06 M_{s}$ ) for $t = 0$ , $t = 3 π / (4 ω)$ , $t = π / ω$ , and $t = 2 π / ω$ (from left to right, the particle moves from right to left). Schematics at the bottom shows one bubble in the FGF during the different phases of the applied field. See Ref. [32] for details on the calculation. (c) Microscope image of the same region showing paramagnetic colloids driven towards left by a rotating field with $H_{0} = 720 {Am}^{- 1}$ , $ω = 25.1 rad s^{- 1}$ and $β = - 1 / 3$ . Superimposed are two trajectories of an individual particle (blue path) and one in a dense collection (green path). Scale bar is $10 μ m$ , see also video 1 in the Supplemental Material [32].
Reuse & Permissions
Figure 2
Longitudinal velocity $⟨ v_{x} ⟩$ (blue open symbols) and transversal one $⟨ v_{y} ⟩$ (black filled symbols) versus normalized particle density $ρ$ for paramagnetic colloids driven toward left. Error bars are obtained from the statistical analysis of different experimental realizations.
Reuse & Permissions
Figure 3
Experimental images with superimposed particle trajectories for (a) $ρ = 0.02$ ; (b) $ρ = 0.23$ (c) $ρ = 0.16$ ; (d) $ρ = 0.58$ . Lateral graphs show the distribution of the transversal displacement of the particles $P (δ y)$ for three different regions of the diagram with $ρ < 0.025$ (top left), $ρ \in [0.55, 0.65]$ (bottom left), and $ρ \in [0.17, 0.27]$ (right). The $P (δ y)$ at the top ( $R^{2} = 0.85$ ) and at the bottom ( $R^{2} = 0.99$ ) are fitted with a Gaussian distribution, while the middle curve is a bimodal fit ( $R^{2} = 0.82$ ), with $R^{2}$ the coefficient of determination.
Reuse & Permissions
Figure 4
Normalized average distance between nearest neighbors $⟨ Δ r ⟩$ versus time calculated for four densities.
Reuse & Permissions
Figure 5
Velocities versus time for a dilute system driven to the left, where density is slowly decreasing in time from $ρ = 0.06$ ( $t = 0 s$ ) to $ρ = 0.06$ ( $t = 250 s$ ). The shaded regions indicate the presence of an additional magnetic field $H_{y} = 200 {Am}^{- 1}$ (blue) and $- H_{y}$ (pink). Right graph denotes the corresponding evolution of the normalized particle density $ρ$ . Inset shows the direction of the applied bias fields with respect to the magnetic lattice.
Reuse & Permissions

Physical Review Letters