Irreversible magnetization of pin-free type-II superconductors

Abstract

The magnetization curve of a type II superconductor in general is hysteretic even when the vortices exhibit no volume or surface pinning. This geometric irreversibility, caused by an edge barrier for flux penetration, is absent only when the superconductor has precisely ellipsoidal shape or is a wedge with a sharp edge where the flux lines can penetrate. A quantitative theory of this irreversibility is presented for pin-free disks and strips with constant thickness. The resulting magnetization loops are compared with the reversible magnetization curves of ideal ellipsoids.PACS numbers: 74.60. Ec, 74.60.Ge, 74.55.+h The magnetic moment of most superconductors is well known to be irreversible. After Abrikosov's [1] prediction of quantized flux lines it became clear [2] that the magnetic hysteresis is caused by pinning of these vortex lines at inhomogeneities in the material. Flux-line pinning and the related critical state [3] were subsequently confirmed quantitatively in numerous papers [4]. However, similar hysteresis effects were also observed [5] in type I superconductors, which do not contain flux lines but normal conducting domains, and in type II superconductors with negligible pinning. In these two cases the magnetic irreversibility is caused by a geometric (specimen-shape dependent) barrier which delays the penetration of magnetic flux but not its exit. In this respect the geometric barrier behaves similar to the Bean-Livingston barrier [6,7] for vortices penetrating a parallel surface.The geometric irreversibility is most pronounced for thin films of constant thickness in a perpendicular field. It is absent only when the superconductor is of exactly ellipsoidal shape or is tapered like a wedge with a sharp edge where flux penetration is facilitated. In ellipsoids the inward directed driving force exerted on the vortex ends by the surface screening currents is exactly compensated by the vortex line tension [8], and thus the magnetization is reversible. In specimens with constant thickness (i.e. rectangular cross-section) this line tension opposes the penetration of flux lines at the four corner lines, thus causing an edge barrier; but as soon as two penetrating vortex segments join at the equator they contract and are driven to the specimen center by the surface currents, see Fig. 1 below. As opposed to this, when the specimen profile is tapered and has a sharp edge, the driving force even in very weak applied field exceeds the restoring force of the line tension such that there is no edge barrier. The resulting absence of hysteresis in wedge-shaped samples was nicely shown by Morozov et al. [9].An elegant analytical theory of the field and current profiles in thin superconductor strips with an edge barrier has been presented by Zeldov et al. [10], see also the extensions [11]. With increasing applied field H a , the magnetic flux does not penetrate until an entry field H en is reached; at H a = H en the flux immediately jumps to the center, from where it gradually fills the entire strip or disk. This ...

Superconducting state in the metastable binary bismuthide Rh3Bi14single crystals

“…21 We estimate demagnetization factors 0.47, 0.23 and 0.59 for H a, H b and H c by using H c1 = H * c1 /tanh( 0.36b/a), where a and b are width and thickness of a plate-like superconductor. 22 The corrected data are plotted in Fig. 3(b), (c) and (d).…”

Superconductors in realistic geometries: geometric edge barrier versus pinning

“…This method in general is fast and elegant; but so far the algorithm is restricted to aspect ratios 0.03 ≤ b/a ≤ 30, and to a number of grid points not exceeding 1400 (on a Personal Computer). Improved accuracy is expected by combining the methods [17] (working best for small b/a) and [18]. Here I shall use the method [18] and simplify it to the two-dimensional (2D) geometry of thick strips and disks.…”

“…While method [17] considers a magnetic charge density on the specimen surface which causes an effective field H i (r) inside the superconductor, our method [18] couples the arbitrarily shaped superconductor to the external field B(r, t) via surface screening currents: In a first step the vector potential A(r, t) is calculated for given current density J; then this linear relation (a matrix) is inverted to obtain J for given A and given H a ; next the induction law is used to obtain the electric field [in our symmetric geometry one has E(J, B) = −∂A/∂t ], and finally the constitutive law E = E(J, B) is used to eliminate A and E and obtain one single integral equation for J(r, t) as a function of H a (t), without having to compute B(r, t) outside the specimen. This method in general is fast and elegant; but so far the algorithm is restricted to aspect ratios 0.03 ≤ b/a ≤ 30, and to a number of grid points not exceeding 1400 (on a Personal Computer).…”

“…Appropriate continuum equations and algorithms have been proposed recently by Labusch and Doyle [17] and by the author [18], based on the Maxwell equations and on constitutive laws which describe flux flow and pinning or thermal depinning, and the equilibrium magnetization in absence of pinning, M (H a ; 0). For arbitrary specimen shape these two methods proceed as follows.…”

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