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 (FM) 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 the equal magnitude but in the opposite
direction in SC, because of no quasiparticle charge current in 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.Comment: 3 pages, 2 figure