[Paper Review] Frequency-dependent spin accumulation in out-of-equilibrium mesoscopic superconductors

Denis Chevallier, C. Dutreix+4 more|arXiv (Cornell University)|Aug 8, 2014

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper extends the theoretical framework for spin accumulation in mesoscopic superconductors under out-of-equilibrium conditions, showing that while time-averaged spin accumulation is frequency-independent, the spin chemical potential and non-local spin-accumulation voltage exhibit strong frequency dependence. This enables experimental extraction of the superconducting spin relaxation time via frequency-domain measurements.

ABSTRACT

We study the spin accumulation in a junction between a superconductor and a ferromagnet or a normal metal in presence of a Zeeman magnetic field applied to the superconductor, and when the junction is taken out of equilibrium by applying a voltage bias. We extend the formalism presented in C.H.L. Quay and al., Nature Physics 9, 84 (2013) to obtain the most general formulas for the spin accumulation for an applied DC bias, and we calculate the time-dependence of the spin accumulation for an applied AC voltage. We study both sinusoidal and rectangular AC pulses. We find that the time-averaged accumulated spin does not depend on the frequency of the applied bias, however the spin chemical potential, as well as the non-locally measured spin-accumulation voltage depend on the frequency. This dependence allows one to extract experimentally the spin relaxation time in a superconductor from measurements in the frequency domain.

Motivation & Objective

• To extend the formalism of spin accumulation in superconductor-ferromagnet or superconductor-normal metal junctions under DC and AC voltage bias.
• To investigate how spin accumulation evolves dynamically under time-varying voltage excitation in the presence of a Zeeman field.
• To determine whether frequency-dependent measurements can provide access to the superconducting spin relaxation time.
• To derive general analytical expressions for spin accumulation under both sinusoidal and rectangular AC pulses.

Proposed method

• Adapt and extend the formalism from Quay et al. (Nature Physics 9, 2013) to include time-dependent voltage bias.
• Apply linear response theory and Keldysh non-equilibrium Green's function techniques to model spin accumulation in superconducting junctions.
• Calculate the time-dependent spin accumulation for both sinusoidal and rectangular AC voltage pulses.
• Derive expressions for the spin chemical potential and non-locally measured spin-accumulation voltage as functions of frequency.
• Use the frequency dependence of the spin response to extract the spin relaxation time experimentally.
• Analyze the distinction between time-averaged spin accumulation and frequency-dependent spin potential.

Experimental results

Research questions

• RQ1 How does the time-dependent spin accumulation respond to AC voltage bias in a superconductor under a Zeeman field?
• RQ2 Does the frequency of the applied AC bias affect the time-averaged spin accumulation in the system?
• RQ3 Can the frequency dependence of the spin chemical potential be used to extract the spin relaxation time in superconductors?
• RQ4 How do sinusoidal and rectangular AC pulses differentially influence the spin accumulation dynamics?
• RQ5 What is the relationship between non-locally measured spin-accumulation voltage and the driving frequency?

Key findings

• The time-averaged spin accumulation remains independent of the frequency of the applied AC bias.
• The spin chemical potential exhibits a strong frequency dependence, which is absent in the time-averaged spin accumulation.
• The non-locally measured spin-accumulation voltage also depends on the frequency of the applied AC signal.
• This frequency dependence provides a direct experimental pathway to extract the superconducting spin relaxation time.
• The results hold for both sinusoidal and rectangular AC voltage pulses, indicating robustness of the frequency-domain response.
• The formalism enables quantitative prediction of spin accumulation dynamics in out-of-equilibrium mesoscopic superconducting devices.