Magnetic Exchange Coupling in Ferromagnet/Superconductor/Ferromagnet Multilayers

The possibility of magnetic exchange coupling between two ferromagnets (F) separated by a superconductor (S) spacer is analyzed using the functional integral method. For this coupling to happen three basic conditions need to be satisfied. First, an indirect exchange coupling between the ferromagnets must exist when the superconductor is in its normal state. Second, superconductivity must not be destroyed due to the proximity to ferromagnetic boundaries. Third, roughness of the $F/S$ interfaces must be small. The appearance of the superconducting gap causes a reduction of the indirect exchange coupling existent in the normal state. This reduction is temperature dependent, being weaker near the critical temperature and stronger at zero temperature.