Spin/magnetisation relaxation and coherence times, respectively T_{1} and T_{2}, initially defined in the context of nuclear magnetic resonance (NMR), are general concepts applicable to a wide range of systems. If one thinks of spins as classical magnetic moments, T_{1} is the time over which they align with an external magnetic field, while T_{2} is the time over which Larmor-like precessions of the spins around the external field remain phase coherent.

In a typical electron spin resonance (ESR) experiment, electrons are immersed in an external homogenous static magnetic field, H. Microwave radiation creates a perturbative transverse magnetic field (perpendicular to the static field) of frequency f_{RF}. The power P(H,f_{RF}) absorbed by the spins from the microwave field is determined, usually by measuring the fraction of the incident microwaves that is *not* absorbed, i.e. either transmitted or reflected.

When H is tuned to its resonance value, H_{res}=2πf_{RF}/γ – with γ the gyromagnetic ratio – the electron spins precess around H and P(H,f_{RF}) is maximal. P(H,f_{RF}) is proportional to the imaginary part of the transverse magnetic susceptibility and to [(H-H_{res})^{2}+1/(γT_{2} )^{2} ]^{-1} in the case of a linearly polarised field. Thus, T_{2}=2/(γΔH), where ΔH is the full-width at half-maximum of the power resonance as a function of H.

* a, b, Scanning electron micrograph of a typical device (scale bar = 1µm )and schematic drawings of the two measurement setups. In both cases a static magnetic field, H is applied parallel to a superconducting bar (S, Al) and a sinusoidal signal of rms amplitude V_{RF} and frequency f_{RF} in the microwave range applied across the length of S (with a lossy coaxial cable in series), resulting in a high-frequency field perpendicular to H. To detect the spin precession of the quasiparticles in S, two on-chip detection methods are used. a, (Detection Scheme 1) A voltage V_{DC} is applied between S and a normal electrode (N_{1}, thick Al) with which it is in contact via an insulating tunnel barrier (I, Al_{2}O_{3}). The differential conductance G=dI/dV_{DC} is measured, where I is the current between N_{1} and S. b, (Detection Scheme 2) A current I_{DC} is injected along the length of S. We measure either the voltage V between the ends of the S bar or the differential resistance R=dV/dI_{DC}. We record in particular the switching current I_{S} at which S first becomes resistive. c, NIS junction conductance G as a function of H at V_{DC} = -288µV and V_{RF}= V_{RF}^{0} for different f_{RF}. The black vertical line indicates the critical field of N. H_{res} and ∆H are obtained for each f_{RF} by fitting a Lorentzian with a linear background. The fit for f_{RF} = 10.56GHz is shown (thin red line) and H_{res} is indicated with a red vertical line. d, H_{res} and ∆H the resonance linewidth (full-width at half-maximum) as a function of f_{RF} red and blue circles respectively). A linear fit to H_{res} (f_{RF}) gives a Landé g-factor of 1.95±0.2. The black dots indicate values obtained at different powers or with the second detection scheme. The circles (squares) are from devices in which S is 8.5nm (6nm) thick.*

Our measurements of quasiparticle spin resonance were performed on thin film superconducting aluminium using two novel on-chip microwave detection techniques, which allow us to overcome technical difficulties arising from the short penetration depth of magnetic fields in Type I superconductors (~16nm for bulk aluminium).

The spin decoherence time we obtain (~100ps), and its dependence on the sample thickness, are consistent with Elliott-Yafet spin-orbit scattering as the main decoherence mechanism. The striking divergence between the spin coherence time and the previously measured spin imbalance relaxation time (~10ns) suggests that the latter is limited instead by inelastic processes.

These results open up new possibilities for investigating the dynamics of the exchange interaction between excitations and condensate in conventional mesoscopic superconductors.

### Reference:

Quasiparticle spin resonance and coherence in superconducting aluminium

C. H. L. Quay, M. Weideneder, Y. Chiffaudel, C. Strunk & M. Aprili*Nature Communications* **6**, 8660 (2015).