Abstract
We present a comprehensive quasiclassical approach for studying transport properties of superconducting diffusive hybrid structures in the presence of extrinsic spin-orbit coupling. We derive a generalized Usadel equation and boundary conditions that in the normal state reduce to the drift-diffusion theory governing the spin-Hall effect in inversion symmetric materials. These equations predict the non-dissipative spin-galvanic effect, that is the generation of supercurrents by a spin-splitting field, and its inverse -- the creation of magnetic moment by a supercurrent. These effects can be seen as counterparts of the spin-Hall, anomalous Hall and their inverse effects in the superconducting state. Our theory opens numerous possibilities for using superconducting structures in magnetoelectronics.
Highlights
We derive a generalized Usadel equation and boundary conditions that in the normal state reduce to the drift-diffusion theory governing the spin-Hall effect in inversion symmetric materials
The spin-orbit coupling (SOC) in normal systems is at the basis of striking magnetoelectric effects, such as the spin (SHE) [1] and anomalous (AHE) [2] Hall effects widely studied in normal systems [3]
This equation, Eq (5), generalizes the well known Usadel equation and contains the usual relaxation term due to the SOC, and a coupling between spin and charge degrees of freedom that lead to the SHE and AHE in the normal case
Summary
The spin-orbit coupling (SOC) in normal systems is at the basis of striking magnetoelectric effects, such as the spin (SHE) [1] and anomalous (AHE) [2] Hall effects widely studied in normal systems [3]. We derive a generalized Usadel equation and boundary conditions that in the normal state reduce to the drift-diffusion theory governing the spin-Hall effect in inversion symmetric materials. The SOC acts only as a relaxation term for the spin in the normal and for triplet correlations in the superconducting state.
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