Magnetic hysteresis from the geometrical barrier in type-II superconducting strips

The magnetic hysteresis due to the geometrical barrier in a type-II superconducting strip placed in a perpendicular applied field is examined theoretically. We first consider ideal strips with no bulk pinning and show results for the average flux density as a function of the applied field for both flux entry and exit. The magnetization is found to be nearly inversely proportional to the applied field upon flux entry and to be proportional to the applied field upon flux exit. We also present results showing the time evolution of magnetic-flux and current-density profiles during initial flux entry for samples that are bulk-pinning free and those with pinning characterized by a critical current ${\mathit{J}}_{\mathit{c}}$. As predicted theoretically in pinning-free strips, the vortices collect in a dome-shaped magnetic flux profile, within which the current density is zero. A vortex-free region develops near the edges, where a high current density flows. With bulk pinning, the vortices pile up in two symmetric dome-shaped magnetic flux profiles, within which the current density is equal to the critical current density, whereas the regions near the center and the edges of the strip remain vortex-free. © 1996 The American Physical Society.