Joule heating generated by spin current through Josephson junctions

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.