Josephson current through a half metal at low temperatures

We study the Josephson effect in the superconductor/diffusive half metal/superconductor junctions by using the recursive Green function method. In the presence of spin-flip scatterings at the interface, odd-frequency spin-triplet Cooper pairs penetrate deeply into a half metal and carry Josephson current. The critical Josephson current increases with decreasing temperatures near the transition temperature. At low temperatures, however, the critical current decreases with decreasing temperatures. Such reentrant behavior is unusual in the case of s-wave superconductor junctions. The penetration of odd-frequency pairs modifies quasiparticle density of states in a half metal near the Fermi energy, which is responsible for the nonmonotonic temperature dependence of critical Josephson current.