Spin current through a tunnel junction

TL;DR

This paper derives a comprehensive expression for spin current through a tunnel junction, accounting for charge transfer and exchange interactions, enhancing understanding of spin transport in magnetic nanostructures.

Contribution

It introduces a new Green's function-based formula for spin current that includes both charge transfer and magnetic exchange effects.

Findings

Derived a Green's function expression for spin current

Identified two contributions: charge transfer and exchange coupling

Provides a framework for analyzing spin transport in magnetic tunnel junctions

Abstract

We derive an expression for the spin-current through a tunnel barrier in terms of many-body Green's functions. The spin current has two contributions. One can be associated with angular-momentum transfer by spin-polarized charge currents crossing the junction. If there are magnetic moments on both sides of the tunnel junction, due to spin accumulation or ferromagnetic ordering, then there is a second contribution related to the exchange coupling between the moments.