Topological magnetic irreversibility in superconducting Pb samples of various shapes

Abstract

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...

Polarized neutron imaging and three-dimensional calculation of magnetic flux trapping in bulk of superconductors

“…In this work we show, for the first time, that it is a true bulk effect. It will be interesting to compare the results of S. Velez et al 40 with our technique, because they could show that the geometry of the sample and the direction and amount of the magnetic field lead to certain irreversible features of the intermediate state.…”

“…Several publications describe and calculate a geometry--dependent magnetic energy barrier and that the magnetization of type--I superconductors samples showed an irreversible behavior, 11,12,21 assuming a migration of flux tubes toward the center of the sample. Recent calculations concerning confinement effects on intermediate--state flux patterns in mesoscopic type--I superconductors predict tubular and laminar structures, and that they are strongly influenced by the geometry of the sample.…”

Magnetic field dependence of the quantum tunneling of normal-superconductor interfaces in a type-I Pb superconductor

“…However, if the sample also contains other irreversibility sources, metastability develops and a good amount of magnetic flux can be trapped at zero field [12,15]. The isothermal evolution of such remnant state has been reported to follow a logarithmic law with time in flat disks of Pb with stress defects [14].…”

“…The existence of these phenomena has been attributed to the presence of a geometrical barrier, which controls both the penetration and the expulsion of the magnetic flux. To be precise, when the magnetic field increases from zero the flux penetrates in the form of bubbles that tend quickly to fill the whole sample to reach the so-called suprafroth state [9], but when the magnetic field is reduced from the normal state the system exhibits random labyrinthine patterns that make the expulsion to be more difficult than the penetration [8,12].…”

“…The properties of type-I superconductors have been studied, both theoretically and experimentally, for nearly one century [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Historically, the presence of irreversible phenomena in the magnetic hysteresis cycle had been associated to physical or chemical defects such as dislocations or impurities [2].…”