Excluded Volume Causes Integer and Fractional Plateaus in Colloidal Ratchet Currents

Pietro Tierno and Thomas M. Fischer

Phys. Rev. Lett. 112, 048302 – Published 31 January 2014

Abstract

We study the collective transport of paramagnetic colloids driven above a magnetic bubble lattice by an external rotating magnetic field. We measure a direct ratchet current which rises in integer and fractional steps with the field amplitude. The stepwise increase is caused by excluded volume interactions between the particles, which form composite clusters above the bubbles with mobile and immobile occupation sites. Transient energy minima located at the interstitials between the bubbles cause the colloids to hop from one composite cluster to the next with synchronous and period doubled modes of transport. The colloidal current may be polarized to make selective use of type up or type down interstitials.

Received 28 November 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.048302

Authors & Affiliations

Pietro Tierno^1,2,* and Thomas M. Fischer³

¹Estructura i Constituents de la Matèria, Universitat de Barcelona, Avenida Diagonal 647, 08028 Barcelona, Spain
²Institut de Nanociència i Nanotecnologia IN2UB, Universitat de Barcelona, 08028 Barcelona, Spain
³Institute of Physics, Universität Bayreuth, 95440 Bayreuth, Germany

^*ptierno@ub.edu

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Vol. 112, Iss. 4 — 31 January 2014

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Images

Figure 1
(a) Schematic of the FGF film ( $a = 8.6 μ m$ ) covered with a polymer film ( $h = 1 μ m$ ), with one Wigner-Seitz unit cell shaded. Potential particle paths between the bubbles pass the type up (blue) and type down (red) interstitial regions. (b) Polarization microscopy image of the FGF loaded with one particle per unit cell. Crystal directions are indicated in white, type up and type down interstitial wells are marked in blue and in red, and nucleate at the beginning of the arrows, annihilate at the end. Central region has been magnified for clarity. (c) Magnetic potential energy of a paramagnetic particle during different phases of the applied field (inset). Energy maxima are colored in yellow, minima in red.
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Figure 2
(a) Time sequence of polarization microscopy images showing a row of bubbles subsequently filled with paramagnetic particles of diameter $d = 1 μ m$ (a), and $d = 2.8 μ m$ (b). Particle motion occurs from left to right. In (a) the magnetic bubble in the shaded column requires a filling of $\tilde{ρ} > 8$ particles to emit particles towards the next bubble. In (b) the particle transport occurs when the bubbles are filled with $\tilde{ρ} > 1$ particles. (c) Normalized current $\tilde{j}$ for particles of size $d = 1 μ m$ , blue symbols, and of $d = 2.8 μ m$ , black symbols, as a function of the overloading, $\tilde{ρ} - N_{c}$ (d) Partially filled integer plateaus in the normalized current for $d = 2.8 μ m$ particles as a function of the amplitude of $H_{z}$ . (movie, ad Fig. 2.WMV [22]).
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Figure 3
(a) Polarization microscopy images showing the time evolution of the doublet $d$ modes and triplet $t$ modes. The orientation of the external magnetic field during the different stages is shown in the top row. In the images where interstitial wells exist, the stored particles are marked in green, particles in the type up or type down interstitial are marked in blue or red, respectively, and particles hopping from annihilated emitter bubbles are marked in purple. The $t 12$ and $t 23$ modes are period doubled modes, where the second cycle (columns 5 and 6) differs from the first cycle. (b) Dimensionless current $\tilde{j}$ as a function of $H_{z}$ for a density of $\tilde{ρ} = 2.75$ exhibiting different kind of plateaus: partially filled integer plateaus in red, fully filled integer plateaus in green, and partially filled fractional plateaus in blue, together with the dominating modes (movie, ad Fig. 3.WMV [22]).
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Figure 4
(a) The polarization $P$ measured as a function of time without (squares) and with (circles) an additional field along the $y $ direction for the $d 1$ mode. (b) Four microscopy images corresponding to the first cycle doublet storage ( $t = 1.25 s$ ), hopping in type down interstitial ( $t = 1.4 s$ ), second cycle doublet storage ( $t = 1.6 s$ ), and hopping in type up interstitial period ( $t = 1.75 s$ ). (c) The polarization per unit cell measured as a function of time with the field along the $y $ direction for the $t 1$ mode. (d) Four microscopy images corresponding to the first cycle hopping $t = 0.5 s$ , triplet storage $t = 0.8 s$ , and a similar second cycle. Hopping particles are marked in blue or red when moving into an interstitial of type up or down, while particles stored in bubbles are marked in green (movie, ad Fig. 4.WMV [22]).
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