Vortex structure of thin mesoscopic disks in the presence of an inhomogeneous magnetic field

The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ``model'' magnetic-field profiles with zero average field, which may result from a ferromagnetic disk or circulating currents in a loop near the superconductor. We calculated the dependences of both the ground and metastable states on the magnitude and shape of the magnetic-field profile for different values of the order-parameter angular moment, i.e., the vorticity. The regions of existence of the multivortex state and the giant-vortex state are found. We analyzed the phase transitions between these states and studied the contribution from ring-shaped vortices. An additional transition between different multivortex configurations and the ground state is found. Furthermore, we found a vortex state consisting of a central giant vortex surrounded by a collection of antivortices which are located in a ring around this giant vortex. The limit to a disk with an infinite radius, i.e., a film, will also be discussed. We also extended our results to ``real'' magnetic-field profiles and to the case in which an external homogeneous magnetic field is present.