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We consider superconductivity nucleation in multiply connected mesoscopicsamples such as thin-walled cylinders or rings placed in electrical contactwith a ferromagnet. The superconducting critical temperature and orderparameter structure are studied on the basis of linearized Usadel equations. Wesuggest a mechanism of switching between the superconducting states withdifferent vorticities caused by the exchange field and associated with theoscillatory behavior of the Cooper pair wave function in a ferromagnet.

Vortex States Induced by Proximity Effect in Hybrid Ferromagnet-Superconductor Systems