Odd-frequency Pairs and Josephson Current through a Strong Ferromagnet

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