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

摘要

The superconducting critical temperature $T_C$ of asuperconductor/ferromagnet (S/F) bilayer with spin-flip scatterings at theinterface is calculated as a function of the ferromagnet thickness $d_F$ in thedirty limit employing the Usadel equation. The appropriate boundary conditionsfrom the spin-flip scatterings at the S/F interface are derived for the Usadelequation which includes the spin triplet pairing components as well as the spinsinglet one. The spin-flip processes induce the spin triplet pairing componentswith s-wave in momentum and odd symmetry in frequency from the s-wave singletorder parameter $\Delta$ of the superconductor region. The induced tripletcomponents alter the singlet order parameter in the superconductor throughboundary conditions at the interface and, consequently, change the $T_C$ of anS/F bilayer system. The calculated $T_C(d_F)$, like the case of no spin-flips,shows non-monotonic behavior which typically decreases as $d_F$ is increasedfrom 0 and shows a shallow minimum and then saturates slowly as $d_F$ isfurther increased. It is well established that as the interface resistance(parameterized in terms of $\gamma_b$) is increased, the $T_C$ is increased fora given $d_F$ and the non-monotonic feature in $T_C(d_F)$ is stronglysuppressed. As the spin flip scattering (parameterized in terms of $\gamma_m$)is increased, on the other hand, the $T_C$ is also increased for a given $d_F$,but the non-monotonic feature in $T_C(d_F)$ is less suppressed or evenenhanced, through the formation of the spin triplet components.