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Register a new userAnomalously Weak Cooper Pair-breaking by Exchange Energy in Ferromagnet/Superconductor Bilayers
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We report the superconducting transition temperature $T_c$ vs. thickness $d_F$ of Ferromagnet/Superconductor (F/S) bilayers, where F is a strong $3d$ ferromagnet (Ni, Ni$_{0.81}$Fe$_{0.19}$ (Permalloy), Co$_{0.5}$Fe$_{0.5}$) and S = Nb, taken from superfluid density measurements rather than resistivity. By regrouping the many physical parameters that appear in theory, we show that the effective exchange energy is determined from the F film thickness $d_F$ where $T_c$ vs. $d_F$ begins to flatten out. Using this rearranged theory we conclude: 1) the effective exchange energy, $E_{ex}$, is about 15 times smaller than measured by ARPES and 5 times smaller than deduced in previous studies similar to ours; 2) the dirty-limit coherence length, $xi_{F}$, for Cooper pairs in F is larger than the electron mean free path, $ell_F$; and 3) the $3d$-F/Nb interface is enough of a barrier that Cooper pairs typically must hit it several times before getting through. The Py/Nb and CoFe/Nb interfaces are more transparent than the Ni/Nb interface.
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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.
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