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We study Josephson current in superconductor / diffusive ferromagnet/superconductor junctions by using the recursive Green function method. Whenthe exchange potential in a ferromagnet is sufficiently large as compared tothe pair potential in a superconductor, an ensemble average of Josephsoncurrent is much smaller than its mesoscopic fluctuations. The Josephson currentvanishes when the exchange potential is extremely large so that a ferromagnetis half-metallic. Spin-flip scattering at junction interfaces drasticallychanges the characteristic behavior of Josephson current. In addition tospin-singlet Cooper pairs, equal-spin triplet pairs penetrate into a halfmetal. Such equal-spin pairs have an unusual symmetry property calledodd-frequency symmetry and carry the Josephson current through a half metal.The penetration of odd-frequency pairs into a half metal enhances the lowenergy quasiparticle density of states, which could be detected experimentallyby scanning tunneling spectroscopy. We will also show that odd-frequency pairsin a half metal cause a nonmonotonic temperature dependence of the criticalJosephson current.

Odd-frequency Pairs and Josephson Current through a Strong Ferromagnet