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Frequency-Domain Measurement of the Spin Imbalance Lifetime in Superconductors

In conventional superconductors, the ground state is made up of ‘Cooper pairs’ of electrons in a spin singlet state, whereas the excitations are Bogolyubov quasiparticles. These quasiparticles are spin-1/2 fermions; however, unlike electrons, both their group velocity and charge are energy-dependent. In particular, at the superconducting gap edge, both are zero.

The quasiparticle populations of superconductors driven out-of-equilibrium have been extensively studied since the advent of thin-film technologies in the 1960s, then in mm-sized devices. A recent revival of interest has been driven by efforts to improve the performance of sub-micron sized superconducting quantum circuits. Nevertheless, comparatively little attention has been paid to the quasiparticles’ spin degree of freedom.

A few years ago, we (the ‘Nanostructures at the Nanosecond timescale’ group) and another group (at the Karlsruhe Institute of Technology) independently demonstrated the existence of a long-lived (τs 10ns) almost-chargeless spin imbalance in the quasiparticle population of a mesoscopic superconductor with a Zeeman-split density of states. This imbalance exists as a result of the dynamic equilibrium between spin injection (enabled by the Zeeman effect) and relaxation. The spin imbalance lifetime was then estimated from a fit of the nonlocal DC spin signal as a function of quasiparticle injection current or voltage.

We have now independently confirmed this estimation in frequency domain measurements. The idea of our experiment is as follows: We inject spin-polarized quasiparticles into a superconductor, in a Zeeman field, at a finite frequency frf = ω/2π while measuring the time average of the nonlocal signal due to the resulting spin imbalance S(ω,t). We observe a cutoff at ω ≈ α/τs, with α a constant close to 1, in agreement with theory. This cutoff is visible because of the highly nonlinear current-voltage characteristic of our detector. The thickness dependence of τs, as well as its value, suggest that the spin imbalance lifetime is limited by electron-electron scattering.

(a) Scanning electron micrograph of a typical device (scale bar = 1 μm) and schematic drawing of the measurement setup. S = superconductor (8.5 nm thick Al film with a native oxide), N = normal metal (100 nm Al), F = ferromagnet (40 nm Co, with a 4.5 nm Al capping layer). The native oxide on S constitutes a tunnel barrier between it and any other given electrode. Quasiparticles are injected into S across a tunnel barrier by applying a voltage Vdc across J1. These are spin polarized because of the Zeeman field in S. The nonlocal voltage Vnl and differential nonlocal signal dVnl/dVdc are measured between F and S (at J2) as a function of magnetic field and temperature, as well as a function of the amplitude Vrf and frequency frf = ω/2π of high-frequency (1–50 MHz) voltages applied to the injection electrode. The local conductance dI/dVdc is measured simultaneously at the injection electrode.
(b), (c) Respectively, local conductance dI/dVdc measured at J1 and differential nonlocal signal dVnl/dVdc measured at J2 as a function of Vrf at frf = 1 MHz and H = 680 mT (dotted lines). The Vrf given here is the value at the output of the generator. Vrf at the device can be estimated from the classical rectification of features in the Vrf = 0 trace. The solid lines are calculations based on the superconducting density of states (DOS) extracted from the measured local conductance at Vrf = 0; they agree qualitatively with the data.
(d) Differential nonlocal signal dVnl/dVdc measured at J2 with injection at J1 as a function of Vdc with constant-power excitations (of ∼ 250 μV at the device) at frf = 1 and 50 MHz.
(e) dVnl/dVdc at the Vdc values indicated in (d) as a function of frf. We subtract “opposing” peaks to obtain the antisymmetric part of the signal, which is due to spin. Fits to numerical calculations yield τs = 3.2 (P4-P1) and 6.4 ns (P3-P2) with a fitting error of 10%–20%. Note that the cutoff does not occur exactly at 1/(2πτs).


Frequency domain measurement of the spin-imbalance lifetime in superconductors
C. H. L. Quay, C. Dutreix, D. Chevallier, C. Bena, and M. Aprili
Physical Review B 93, 220501R (2016)


Charis Quay Huei Li