Magnetization of mesoscopic superconducting disks

Solutions of Ginzburg-Landau equations coupled with three-dimensional Maxwell equations reveal an intriguing magnetic response of small superconducting particles, qualitatively different from the two-dimensional approximation but in agreement with recent experiments. Depending on the radius and thickness, first or second order transitions are found for the normal to superconducting state. For a sufficiently large radius of the disk, several transitions in the superconducting phase are obtained which correspond to different angular momentum giant vortex states. The incorporation of the finite thickness in the calculation is crucial in order to obtain agreement with the position and the size of these jumps, and the line shape and magnitude of the magnetization curves.