We theoretically study the spin-polarized current flowing through a Josephson junction (JJ) in a spin injection device. When the spin-polarized current is injected from a ferromagnet in a superconductor (SC), the charge current is carried by the superconducting condensate (Cooper pairs), while the spin-up and spin-down currents flow in equal magnitude but in the opposite direction in a SC, because of no quasiparticle charge current in the SC. This indicates that not only the Josephson current but also the spin current flow across JJ at zero bias voltage, thereby generating Joule heating by the spin current. The result provides a new method for detecting the spin current by measuring Joule heating at JJ.
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