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Vortices and the lower critical field for a Ginzburg–Landau model of superconductors with ferromagnetic interactions

Published online by Cambridge University Press:  12 July 2007

Stan Alama
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Lia Bronsard
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada

Abstract

We study a Ginzburg–Landau functional for a vector-valued order parameter that carries a spin and couples directly to the magnetic field. We verify that spin coupling reduces the lower critical field Hc1, the smallest value of the applied field strength at which vortices penetrate the superconductor, and discuss the related phenomena of a ‘spontaneous vortex phase’ for sufficiently strong spin coupling, predicted by physicists. The method uses energy methods and a priori bounds to confine the vortices and spin transitions to very small balls

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2005

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