Revisiting the spin-orbit scattering in small-sized superconducting particles in the magnetic field

TL;DR

This paper investigates how the coupling between superconducting currents and spin-orbit scattering in small particles enhances paramagnetic susceptibility and shifts electron paramagnetic resonance frequency, revealing a larger-than-expected effect.

Contribution

It introduces the concept of interference coupling between superconducting current and spin-orbit scattering, showing it increases paramagnetic susceptibility beyond conventional predictions.

Findings

Interference coupling causes additional spin polarization in superconducting particles.

The effect's magnitude is proportional to the spin-orbit interaction amplitude.

Electron paramagnetic resonance frequency is shifted due to this coupling.

Abstract

The Knight shift of nuclear magnetic resonance is an experimental probe of the paramagnetic spin susceptibility in metals. Information about the electron pairing in superconductors can be extracted from the Knight shift in the small-sized particles. The finite zero-temperature magnitude of paramagnetic susceptibility observed in the superconducting particles has been associated with the spin-orbit scattering of conduction electrons. The conventional treatment has delivered the paramagnetic susceptibility magnitude proportional to the square of the spin-orbit interaction amplitude. Here we examine the coupling between the superconducting current and the spin-orbit scattering of conduction electrons in the small-sized particles. Such interference coupling, absent in the normal state, results in an additional spin polarization of the conduction electrons generating the superconducting current in the magnetic field. This anomalous effect delivers the noticeably larger contribution to the paramagnetic susceptibility. The magnitude of the effect as well as the contribution to the paramagnetic susceptibility prove to be proportional to the amplitude of spin-orbit interaction. The frequency of electron paramagnetic resonance is shifted as well.