Using the non-linear Ginzburg-Landau (GL) theory, we study the magnetic response of different shaped samples in the field-cooled regime (FC). For high external magnetic fluxes, the conventional diamagnetic response under cooling down can be followed by the paramagnetic Meissner effect (PME). A second-order transition from a giant vortex state to a multi-vortex state, with the same vorticity, occurs at the second critical field which leads to the suppression of PME.
@article{arxiv.cond-mat/0001110,
title = {Paramagnetic Meissner effect in mesoscopic samples},
author = {V. A. Schweigert and F. M. Peeters},
journal= {arXiv preprint arXiv:cond-mat/0001110},
year = {2007}
}