Paramagnetic Meissner effect in multiply-connected superconductors

Abstract

We have measured a paramagnetic Meissner effect in $\mathrm{Nb}--{\mathrm{Al}}_{2}{\mathrm{O}}_{3}--\mathrm{Nb}$ Josephson-junction arrays using a scanning superconducting quantum interference device microscope. The arrays exhibit diamagnetism for some cooling fields and paramagnetism for other cooling fields. The measured mean magnetization is always small, $〈{\ensuremath{\Phi}}_{\mathrm{tot}}\ensuremath{-}{\ensuremath{\Phi}}_{\mathrm{ext}}〉<0.3{\ensuremath{\Phi}}_{0}$ (in terms of flux per unit cell of the array, where ${\ensuremath{\Phi}}_{0}$ is the flux quantum), for the range of cooling fields investigated $(\ensuremath{-}12{\ensuremath{\Phi}}_{0}$ to $12{\ensuremath{\Phi}}_{0}).$ We demonstrate that a different model of magnetic screening, valid for multiply-connected superconductors, reproduces all of the essential features of paramagnetism that we observe and that no exotic mechanism, such as d-wave superconductivity, is needed for paramagnetism.