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 (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(rf) shows a cutoff at f(rf) approximate to 1/(2 pi 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, tau(s) is consistent with previous measurements and of the order of the electron-electron scattering time 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.