Threefold onset of vortex loops in superconductors with a magnetic core

A magnetic inclusion inside a superconductor gives rise to a fascinating complex of {it vortex loops}. Our calculations, done in the framework of the Ginzburg-Landau theory, reveal that {it 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 {it vortex pairs} piercing through the sample surface.