Magnetization of a type-I superconducting slab in the thermodynamic and the metastable phases

Fortini, A.; Hairie, A.; Paumier, E.

doi:10.1103/physrevb.21.5065

Cited by 26 publications

(8 citation statements)

References 14 publications

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“…It was directly observed in single crystals of Sn back in 1958 [20], Hg [8] and Pb [8,24]. The tubular pattern was reproduced numerically [19] and metastability of slabs was theoretically analyzed [21]. Ginzburg -Landau equations have stable multiquanta solution for arbitrary tube size [9].…”

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confidence: 97%

Equilibrium Topology of the Intermediate State in Type-I Superconductors of Different Shapes

Prozorov

2007

Phys. Rev. Lett.

128

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High-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes -cones, hemispheres and discs. Combined with the measurements of macroscopic magnetization these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to topological hysteresis -flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region in both regimes. It is concluded that flux tubes represent the equilibrium topology of the intermediate state and that the laminar structure is unstable towards Lorentz or condensation energy forces. Real-time video is available in [24].

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confidence: 97%

Equilibrium Topology of the Intermediate State in Type-I Superconductors of Different Shapes

Prozorov

2007

Phys. Rev. Lett.

128

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“…25 Geometrical barriers, however, should emerge in any nonellipsoidal shape whatever the aspect ratio might be. [3][4][5]15 The interplay between such barriers and the applied magnetic field would then also be the reason for the ability of lamellae to leave sample A on decreasing H from the normal state. 12 In this context, the absence of irreversibility when the applied field is perpendicular to the revolution axis in samples A to C should be a consequence of the fact that the sample edges that generate the geometrical barriers become irrelevant in this configuration.…”

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confidence: 99%

“…This problem was first studied by Landau 1 and since then different authors have tried to deepen the understanding of magnetic-flux dynamics and equilibrium structures following both theoretical and experimental approaches. [2][3][4][5][6][7][8][9][10] Magnetic hysteresis in type-I superconductors has been attributed historically to impurities, defects, dislocations, and edge barriers. 2 In the last years, thanks to the emergence of high-resolution magneto-optical imaging, this field has been deeply revised, [11][12][13][14][15][16][17] and different ideas have come to light.…”

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confidence: 99%

Topological magnetic irreversibility in superconducting Pb samples of various shapes

et al. 2008

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The magnetic-field dependence of the magnetization of cylinders, disks, and spheres of pure type-I superconducting lead was investigated by means of isothermal measurements of first magnetization curves and hysteresis cycles. Depending on the geometry of the sample and the direction and intensity of the applied magnetic field, the intermediate state exhibits different irreversible features that become particularly highlighted in minor hysteresis cycles. The irreversibility is noticeably observed in cylinders and disks only when the magnetic field is parallel to the axis of revolution and is very subtle in spheres. When the magnetic field decreases from the normal state, the irreversibility appears at a temperature-dependent value whose distance to the thermodynamic critical field depends on the sample geometry. The irreversible features in the disks are altered when they are submitted to an annealing process. These results agree well with very recent highresolution magneto-optical experiments in similar materials that were interpreted in terms of transitions between different topological structures for the flux configuration in the intermediate state. A discussion of the relative role of geometrical barriers for flux entry and exit and pinning effects as responsible for the magnetic irreversibility is given. One of the most important questions to be yet answered univocally in type-I superconductors is the emergence of irreversibility when the flux enters and leaves the material in the intermediate state. This problem was first studied by Landau 1 and since then different authors have tried to deepen the understanding of magnetic-flux dynamics and equilibrium structures following both theoretical and experimental approaches.2-10 Magnetic hysteresis in type-I superconductors has been attributed historically to impurities, defects, dislocations, and edge barriers.2 In the last years, thanks to the emergence of high-resolution magneto-optical imaging, this field has been deeply revised, [11][12][13][14][15][16][17] and different ideas have come to light. This is the case, for example, of the very recent works of Menghini and Wijngaarden 14 and Prozorov et al. [15][16][17] In both cases, the main conclusions refer to the existence of topological irreversibility associated to the formation of tubular structures, when the flux enters the material, and laminar patterns in the case of flux exit. In real-time videos shown in Ref. 16, it is also possible to follow the dynamics of the flux structures that help elucidate the physics of irreversibility in the intermediate state of type-I superconductors. In this paper we have extended these studies to investigate the emergence of magnetic irreversibility for flux entering and leaving bulk samples of lead for different configurations of the external magnetic field.We present here results for a cylinder with a radius of 1.5 mm and a height of 3 mm ͑sample A͒, two disks of octagonal cross section with a surface area of 40 mm 2 and a thickness of 0.2 mm ͑samples B and C͒, and a s...

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“…(30) Recall that the growth of flux domes when the dome radius b obeys β = b/a ≪ 1 is determined by Eqs. (9) and (10). For larger domes, the dome-generated local field at the outer edge can be obtained with good accuracy from Eqs.…”

Section: Initial Growth Of Small Flux Domesmentioning

confidence: 88%

Geometrical Barriers and the Growth of Flux Domes in Thin Ideal Superconducting Disks

Clem

2008

J Supercond Nov Magn

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When an ideal (no bulk pinning) flat type-II superconducting disk is subjected to a perpendicular magnetic field Ha, the first vortex nucleates at the rim when Ha = H0, the threshold field, and moves quickly to the center of the disk. As Ha increases above H0, additional vortices join the others, and together they produce a domelike field distribution of radius b. In this paper I present analytic solutions for the resulting magnetic-field and sheet-current-density distributions. I show how these distributions vary as b increases with Ha, and I calculate the corresponding field-increasing magnetization.

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Magnetization of a type-I superconducting slab in the thermodynamic and the metastable phases

Cited by 26 publications

References 14 publications

Equilibrium Topology of the Intermediate State in Type-I Superconductors of Different Shapes

Equilibrium Topology of the Intermediate State in Type-I Superconductors of Different Shapes

Topological magnetic irreversibility in superconducting Pb samples of various shapes

Geometrical Barriers and the Growth of Flux Domes in Thin Ideal Superconducting Disks

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