Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays

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Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays

D. Ray, C. J. Olson Reichhardt, B. Jankó, and C. Reichhardt

Phys. Rev. Lett. 110, 267001 – Published 24 June 2013

Abstract

Conformal crystals are nonuniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of local ordering in the conformally transformed hexagonal lattice and the arching arrangement of the pinning also play crucial roles. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.

Received 3 October 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.267001

Authors & Affiliations

D. Ray^1,2, C. J. Olson Reichhardt², B. Jankó¹, and C. Reichhardt²

¹Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
²Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Vol. 110, Iss. 26 — 28 June 2013

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Images

Figure 1
A conformal transformation is applied to the semiannular section of a regular hexagonal lattice shown in (a) to create the conformal crystal structure shown in (b) (see the Supplemental Material [25]). Points A–F in (a) are mapped by the transformation to points a–f in (b), respectively. The straight contour lines connecting nearest neighbor lattice points in (a) are bent into arcs in (b), but the local sixfold ordering of the lattice points is maintained. Pinning sites are placed at the vertices formed by the intersections of the contour lines in (b).Reuse & Permissions
Figure 2
The gradient-driven sample geometry consists of two conformal crystals facing each other in the pinned region. Open circles are pinning site locations. Vortex addition and subtraction occurs in the pin-free region labeled $A$ .Reuse & Permissions
Figure 3
The magnetization $M$ versus $H / H_{ϕ}$ . The outer dark (black) curve represents a sample with a CPA, the inner light (red) curve a sample with a uniformly dense random arrangement of pinning sites, and the middle light (green) curve a random arrangement of pinning sites with a pinning gradient equivalent to the CPA.Reuse & Permissions
Figure 4
(a),(b) $M_{HW}$ , the half-width of the magnetization loop, measured at $H / H_{ϕ} = 1.0$ (filled symbols) and at $H / H_{ϕ} = 1.4$ (open symbols) and normalized to $M_{HW}$ for the random pinning array (squares). The circles represent the CPA, the triangles the random array with CPA-equivalent pinning gradient. (a) $M_{HW}$ versus $F_{p}$ for fixed $r_{p} = 0.12$ . (b) $M_{HW}$ versus $r_{p}$ for fixed $F_{p} = 0.55$ . (c) $⟨ V_{x} ⟩$ versus $F_{d}$ for vortices driven across a CPA (right curve, black), a random array (center curve, red), and a random array with a pinning gradient (left curve, green). (d) Magnetization loops for the CPA (outer curve, black) compared to periodic pinning arrays, square (center curve, blue) and triangular (inner curve, purple), at $F_{p} = 0.55$ and $r_{p} = 0.12$ .Reuse & Permissions
Figure 5
(a) $P (n_{m})$ , the distribution of the number of vortices $n_{m}$ in individual avalanches occurring as the field $H / H_{ϕ}$ is raised from 0.65 to 2.0, for the CPA (circles), uniform random pinning (squares), and random pinning with gradient (triangles). (b),(c) High-field behavior of pinning arrays on the initial ramp-up only: in (b), magnetization $M$ , and in (c), the fraction of occupied pinning sites $P$ . The CPA is represented by the upper (black) curve, the uniform random array by the lower (red) curve, and random with gradient by the middle (green) curve. The dotted line indicates $H / H_{ϕ} = 2$ , where $M$ and $P$ both drop for the CPA.Reuse & Permissions

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