Odd triplet pairing effects induced by interface spin-flip scatterings: critical temperature of superconductor/ferromagnet bilayers

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The superconducting critical temperature TC of a superconductor/ferromagnet (S/F) bilayer with spin-flip scatterings at the interface is calculated as a function of the ferromagnet thickness dF in the dirty limit employing the Usadel equation. The appropriate boundary conditions from the spin-flip scatterings at the S/F interface are derived for the Usadel equation which includes the spin triplet pairing components as well as the spin singlet one. The spin-flip processes induce the spin triplet pairing components with s-wave in momentum and odd symmetry in frequency from the s-wave singlet order parameter Δ of the superconductor region. The induced triplet components alter the singlet order parameter in the superconductor through boundary conditions at the interface and, consequently, change the TC of an S/F bilayer system. The calculated TC(dF), like the case of no spin-flips, shows non-monotonic behavior which typically decreases as dF is increased from 0 and shows a shallow minimum and then saturates slowly as dF is further increased. It is well established that as the interface resistance (parameterized in terms of γb) is increased, the TC is increased for a given dF and the non-monotonic feature in TC(dF) is strongly suppressed. As the spin flip scattering (parameterized in terms of γₘ) is increased, on the other hand, the TC is also increased for a given dF, but the non-monotonic feature in TC(dF) is less suppressed or even enhanced, through the formation of the spin triplet components.