We study theoretically the effect of spin relaxation on the spin transport in a ferromagnet/superconductor (FM/SC) tunnel junction. When spin-polarized electrons are injected into the SC from the FM, nonequilibrium spin accumulation as well as spin current are created in the range of the spin diffusion length in the SC. We find that the spin diffusion length in the superconducting state is the same as that in the normal state. We examine a FM/SC/SC double tunnel junction, and show that the spin current is detected by the Joule heat generated at the Josephson junction. This provides a method to obtain the spin diffusion length by probing the spin current in SC's.
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