Paramagnetic moment in field-cooled superconducting plates: Paramagnetic Meissner effect

We calculate the magnetic moment for thin superconducting plates after field cooling. We consider the situation when the whole magnetic flux is trapped within the strip and compressed due to inhomogeneous cooling. We demonstrate that the magnetic moment in such a state is paramagnetic. For a thin superconducting strip we found exact solutions for the field and current distributions at any degree of flux compression. The cases of complete and partial Bean states were considered. For a thin superconducting disk we found an approximate solution for the case of weak compression and a complete Bean state. The mechanism considered can explain the paramagnetic Meissner effect observed recently in some high-Tc superconductors and in Nb