Proximity effects in a superconductor/ferromagnet junction

Abstract

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 ( Ψ s ) and spin-triplet pair amplitude ( Ψ t ) are induced in FM and both amplitudes depend on the frequency in the Matsubara representation. Ψ s is an even function and Ψ t is an odd function with respect to the Matsubara frequency ( ω n ). 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 ω n as in the case of the SC/FM junction. We discuss that in our tunneling model the pair amplitude of even function of ω n only contributes to a Josephson current.