  The Josephson effect in superconductor / diffusive ferromagnet /
superconductor (SFS) junctions is studied using the recursive Green function
method in the regime of large exchange energy in a ferromagnet. Motivated by
recent experiment [R. S. Keizer, et. al., Nature 439, 825 (2006)] we also
address the case of superconductor / diffusive half metal / superconductor
junctions. The pairing function in spin-singlet and triplet channels, the
Josephson current and their mesoscopic fluctuations are calculated. We show
that the spin-flip scattering at the junction interfaces opens the Josephson
channel of the odd-frequency spin-triplet Cooper pairs. As a consequence, the
local density of states in half metals has a large peak at the Fermi energy.
Therefore odd-frequency pairs can be detected experimentally by using the
scanning tunneling spectroscopy.
