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Frequency-Domain Measurement of the Spin Imbalance Lifetime in Superconductors

We have measured the lifetime of spin imbalances in the quasiparticle population of a superconductor ($τ_s$) in the frequency domain. A time-dependent spin imbalance is created by injecting spin-polarised electrons at finite excitation frequencies into a thin-film mesoscopic superconductor (Al) in an in-plane magnetic field (in the Pauli limit). The time-averaged value of the spin imbalance signal as a function of excitation frequency, $f_{RF}$ shows a cut-off at $f_{RF} \approx 1/(2πτ_s)$. The spin imbalance lifetime is relatively constant in the accessible ranges of temperatures, with perhaps a slight increase with increasing magnetic field. Taking into account sample thickness effects, $τ_s$ is consistent with previous measurements and of the order of the electron-electron scattering time $τ_{ee}$. Our data are qualitatively well-described by a theoretical model taking into account all quasiparticle tunnelling processes from a normal metal into a superconductor.