Proximity effects in a superconductor/ferromagnet junction

A proximity effect in an s-wave superconductor/ferromagnet (SC/F) junction is theoretically studied using the second order perturbation theory for the tunneling Hamiltonian and Green's function method. We calculate a pair amplitude induced by the proximity effect in a weak ferromagnetic metal (FM) and a half-metal (HM). In the SC/FM junction, it is found that a spin-singlet pair amplitude (Ψs) and spin-triplet pair amplitude (Ψt) are induced in FM and both amplitudes depend on the frequency in the Matsubara representation. Ψs is an even function and Ψt is an odd function with respect to the Matsubara frequency (ωn). In the SC/HM junction, we examine the proximity effects by taking account of magnon excitations in HM. It is found that the triplet-pair correlation is induced in HM. The induced pair amplitude in HM shows a damped oscillation as a function of the position and contains the terms of even and odd functions of ωn as in the case of the SC/FM junction. We discuss that in our tunneling model the pair amplitude of even function of ωn only contributes to a Josephson current.