The definition of the spin current: The angular spin current and its physical consequences

TL;DR

This paper introduces the concept of angular spin current alongside linear spin current to fully describe spin transport, revealing their physical properties and how they generate distinct electric fields.

Contribution

It defines the angular spin current, discusses its physical properties, and predicts its unique electric field effects, expanding the understanding of spin transport mechanisms.

Findings

Angular spin current describes spin precession.

Angular spin current induces an electric field scaling as 1/r^2.

Linear spin current induces an electric field scaling as 1/r^3.

Abstract

We find that in order to completely describe the spin transport, apart from spin current (or linear spin current), one has to introduce the angular spin current. The two spin currents respectively describe the translational and rotational motion (precession)of a spin. The definitions of these spin current densities are given and their physical properties are discussed. Both spin current densities appear naturally in the spin continuity equation. Moreover we predict that the angular spin current can also induce an electric field $\vec{E}$, and in particular $\vec{E}$ scales as $1/r^2$ at large distance $r$, whereas the $\vec{E}$ field generated from the linear spin current goes as $1/r^3$.