  The Josephson current in the presence of a precessing spin between various
types of superconductors is studied. It is shown that the Josephson current
flowing between two spin-singlet pairing superconductors is not modulated by
the precession of the spin. When both superconductors have equal-spin-triplet
pairing state, the flowing Josephson current is modulated with twice of the
Larmor frequency by the precessing spin. It was also found that up to the
second tunneling matrix elements, no Josephson current can occur with only a
direct exchange interaction between the localized spin and the conduction
electrons, if the two superconductors have different spin-parity pairing
states.
