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 $({\ensuremath{\tau}}_s)$ in the frequency domain. A time-dependent spin imbalance is created by injecting spin-polarized 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 ${f}_{\text{rf}}$ shows a cutoff at ${f}_{\text{rf}}\ensuremath{\approx}1/(2\ensuremath{\pi}{\ensuremath{\tau}}_s)$. 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, ${\ensuremath{\tau}}_s$ is consistent with previous measurements and of the order of the electron-electron scattering time ${\ensuremath{\tau}}_ee$. Our data are qualitatively well described by a theoretical model taking into account all quasiparticle tunneling processes from a normal metal into a superconductor.