On the conservation of spin currents in spin-orbit coupled systems

TL;DR

This paper demonstrates that a conserved convective spin current can be derived in spin-orbit coupled systems using relativistic and nonrelativistic quantum mechanics, highlighting its invariance under external electromagnetic fields.

Contribution

It introduces a new conserved convective spin current in spin-orbit coupled systems, derived via Gordon decomposition and Foldy-Wouthuysen transformation, applicable in relativistic and nonrelativistic regimes.

Findings

Conserved convective spin current derived using Gordon decomposition.

Conservation of spin component along external electromagnetic fields.

First derivation of conserved CSC in nonrelativistic limit.

Abstract

Applying the Gordon-decomposition-like technique, the convective spin current (CSC) is extracted from the total angular-momentum current. The CSC describes the transport properties of the electron spin and is conserved in the relativistic quantum mechanics approach where the spin-orbit coupling has been intrinsically taken into account. Arrestingly, in the presence of external electromagnetic field, the component of the convective spin along the field remain still conserved. This conserved CSC is also derived for the first time in the nonrelativistic limit using the Foldy-Wouthuysen transformation.