Conservation of spin current

TL;DR

This paper demonstrates that including self-consistent spin-spin interactions in models restores the conservation of spin current, which is otherwise not conserved due to spin-orbit interactions, and derives a related spin-conductance formula.

Contribution

It introduces a self-consistent spin-spin interaction framework that resolves the non-conservation of spin current and provides a new spin-conductance formula for multi-lead systems.

Findings

Spin current conservation is restored with spin-spin interactions.

A new spin-conductance formula for multi-lead conductors is derived.

Spin current non-conservation due to spin-orbit interaction is addressed.

Abstract

The conventional definition of spin-current, namely spin density multiplied by the group velocity, is not a conserved quantity due to possible spin rotations caused by spin-orbit (SO) interaction. However, in a model with spin-spin interactions, rotation of a spin causes a dynamic response of surrounding spins that opposes the rotation. Such a many-body effect restores the spin-current conservation. Here we prove that the non-conservation problem of spin-current can be resolved if a self-consistent spin-spin interaction is included in the analysis. We further derive a spin-conductance formula which partitions spin-current into different leads of a multi-lead conductor.