Magnetic exchange coupling through superconductors: A trilayer study

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 occur three prima facie 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. Under these conditions, when the superconductor is cooled to below its critical temperature, the magnetic coupling changes. The appearance of the superconducting gap introduces a new length scale (the coherence length of the superconductor) and modifies the temperature dependence of the indirect exchange coupling existent in the normal state. The magnetic coupling is oscillatory both above and below the the critical temperature of the superconductor, as well as strongly temperature-dependent. However, at low temperatures the indirect exchange coupling decay length is controlled by the coherence length of the superconductor, while at temperatures close to and above the critical temperature of the superconductor the magnetic coupling decay length is controlled by the thermal length.