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

TL;DR

This paper investigates how interface spin-flip scatterings induce odd triplet pairing in superconductor/ferromagnet bilayers, affecting the critical temperature's dependence on ferromagnet thickness and interface properties.

Contribution

It derives boundary conditions incorporating spin-flip scatterings for the Usadel equation, revealing how triplet components influence the critical temperature in S/F bilayers.

Findings

Spin-flip scatterings induce odd-frequency triplet pairing components.

The critical temperature exhibits non-monotonic behavior with ferromagnet thickness.

Increased interface resistance raises T_C and suppresses non-monotonic features.

Abstract

The superconducting critical temperature $T_C$ of a superconductor/ferromagnet (S/F) bilayer with spin-flip scatterings at the interface is calculated as a function of the ferromagnet thickness $d_F$ 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 $\Delta$ 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 $T_C$ of an S/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 increased from 0 and shows a shallow minimum and then saturates slowly as $d_F$ is further increased. It is well established that as the interface resistance (parameterized in terms of $\gamma_b$) is increased, the $T_C$ is increased for a given $d_F$ and the non-monotonic feature in $T_C(d_F)$ is strongly suppressed. 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 even enhanced, through the formation of the spin triplet components.