Confined vortex loops in superconductors with a magnetic core

A magnetic moment inside an extreme type II superconductor gives rise to confined vortex states in its neighborhood. We show how the presence of such states can be tracked down in the I-V characteristic curve, thus providing a simple method to their detection. The Lorentz force causes their growth and periodic evolution, passing through a long range ordered state (bulk) or an external vortex pair state (sub-micron particle). For a small magnetic moment there are exactly three confined vortex loops whereas for a large more elaborate vortex arrangements arise are possible. Their onset from the upper critical field core in sets of threes is proved to be energetically favorable over the growth of just one or two confined vortex loops independently of boundary conditions. All our results are derived in the context of the time-dependent and of the time-independent Ginzburg-Landau theory applied to a superconductor with periodic (bulk) and superconductor-insulator (sub-micron particle) boundary conditions, using three independent numerical methods.