Green's function formalism for spin transport in metal-insulator-metal heterostructures

TL;DR

This paper introduces a Green's function approach to model spin transport in metal-insulator-metal heterostructures, accounting for magnonic interactions like Gilbert damping, and validates it against established equations.

Contribution

It develops a Green's function formalism specifically for spin transport in heterostructures with metallic and insulating magnetic layers, including disorder effects.

Findings

Disorder and Gilbert damping cause spin current fluctuations.

Spin current depends on ferromagnet thickness in clean systems.

Formalism agrees with stochastic Landau-Lifshitz-Gilbert equation in the continuum limit.

Abstract

We develop a Green's function formalism for spin transport through heterostructures that contain metallic leads and insulating ferromagnets. While this formalism in principle allows for the inclusion of various magnonic interactions, we focus on Gilbert damping. As an application, we consider ballistic spin transport by exchange magnons in a metal-insulator-metal heterostructure with and without disorder. For the former case, we show that the interplay between disorder and Gilbert damping leads to spin current fluctuations. For the case without disorder, we obtain the dependence of the transmitted spin current on the thickness of the ferromagnet. Moreover, we show that the results of the Green's function formalism agree in the clean and continuum limit with those obtained from the linearized stochastic Landau-Lifshitz-Gilbert equation. The developed Green's function formalism is a natural starting point for numerical studies of magnon transport in heterostructures that contain normal metals and magnetic insulators.