Paramagnetic Meissner effect in superconductors from self-consistent solution of Ginzburg-Landau equations

The paramagnetic Meissner effect (PME) is observed in small superconducting samples, and a number of controversial explanations of this effect are proposed, but there is as yet no clear understanding of its nature. In the present paper the PME is considered on the basis of Ginzburg-Landau (GL) theory. The one-dimensional solutions are obtained in a model case of a long superconducting cylinder for different cylinder radii R, GL parameters, kappa and vorticities m. According to GL theory, the PME is caused by the presence of vortices inside the sample. The superconducting current flows around the vortex to screen the vortex internal field from the bulk of the sample. Another current flows at the boundary to screen the external field H from entering the sample. These screening currents flow in opposite directions and contribute with opposite signs to the total magnetic moment (or magnetization) of the sample. Depending on H, the total magnetization M may be either negative (diamagnetism) or positive (paramagnetism). A detailed study of a very complicated sawlike dependence M(H) (and of other characteristics), which follow from the self-consistent solutions of the GL equations, is presented.