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Resonant spins in a conventional superconductor (aluminium)

Conventional superconductors were long thought to be spin-inert, in large part due to the singlet spin structure of the Cooper pairs (of electrons) which make up the ground state condensate. We recently demonstrated the existence of long-lived spin-polarised excitations (quasiparticles) in superconducting aluminium, and have now performed spin resonance measurements on these. This work contributes to the fast-developing field of spin-based electronics with superconductors, or superconducting spintronics. In addition to work such as ours on spin-polarised excitations, complementary efforts in this field focus on manipulating the internal spin structure of the superconducting condensate.

Spin/magnetisation relaxation and coherence times, respectively T1 and T2, 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, T1 is the time over which they align with an external magnetic field, while T2 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 fRF. The power P(H,fRF) 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, Hres=2πfRF/γ – with γ the gyromagnetic ratio – the electron spins precess around H and P(H,fRF) is maximal. P(H,fRF) is proportional to the imaginary part of the transverse magnetic susceptibility and to [(H-Hres)2+1/(γT2 )2 ]-1 in the case of a linearly polarised field. Thus, T2=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 VRF and frequency fRF 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 VDC is applied between S and a normal electrode (N1, thick Al) with which it is in contact via an insulating tunnel barrier (I, Al2O3). The differential conductance G=dI/dVDC is measured, where I is the current between N1 and S. b, (Detection Scheme 2) A current IDC 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/dIDC. We record in particular the switching current IS at which S first becomes resistive. c, NIS junction conductance G as a function of H at VDC = -288µV and VRF= VRF0 for different fRF. The black vertical line indicates the critical field of N. Hres and ∆H are obtained for each fRF by fitting a Lorentzian with a linear background. The fit for fRF = 10.56GHz is shown (thin red line) and Hres is indicated with a red vertical line. d, Hres and ∆H the resonance linewidth (full-width at half-maximum) as a function of fRF red and blue circles respectively). A linear fit to Hres (fRF) 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).

Contact :

Charis Quay