PACS 74.25.Ha -Magnetic properties PACS 74.25.Op -Mixed state, critical fields, and surface sheath PACS 74.78.Na -Mesoscopic and nanoscale systemsAbstract. -A magnetic inclusion inside a superconductor gives rise to a fascinating complex of vortex loops. Our calculations, done in the framework of the Ginzburg-Landau theory, reveal that loops always nucleate in triplets around the magnetic core. In a mesoscopic superconducting sphere, the final superconducting state is characterized by those confined vortex loops and the ones that eventually spring to the surface of the sphere, evolving into vortex pairs piercing through the sample surface.

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The vortex state of mesoscopic three-dimensional superconductors is determined using a minimization procedure of the Ginzburg-Landau free energy. We obtain the vortex pattern for a mesoscopic superconducting sphere and find that vortex lines are naturally bent and are closest to each other at the equatorial plane. For a superconducting disk with finite height, and under an applied magnetic field perpendicular to its major surface, we find that our method gives results consistent with previous calculations. The matching fields, the magnetization and H c3 , are obtained for models that differ according to their boundary properties. A change of the Ginzburg-Landau parameters near the surface can substantially enhance H c3 , as shown here.