Theory for electrical detection of the magnon Hall effect induced by dipolar interactions

TL;DR

This paper develops a theoretical framework for detecting the magnon Hall effect caused by dipolar interactions in magnetic insulators, proposing an electrical measurement method and predicting experimental signatures.

Contribution

It introduces a theoretical model linking dipolar interactions to the magnon Hall effect and suggests an experimental setup for electrical detection in YIG thin films.

Findings

Finite anomalous Hall conductivity in YIG films with perpendicular magnetic field

Predicted measurable Hall signals and coefficients at various temperatures and fields

Sign change of Hall coefficient with increasing film thickness

Abstract

We derive the anomalous Hall contributions arising from dipolar interactions to diffusive spin transport in magnetic insulators. Magnons, the carriers of angular momentum in these systems, are shown to have a non-zero Berry curvature, resulting in a measurable Hall effect. For yttrium iron garnet (YIG) thin films we calculate both the anomalous and magnon spin conductivities. We show that for a magnetic field perpendicular to the film the anomalous Hall conductivity is finite. This results in a non-zero Hall signal, which can be measured experimentally using Permalloy strips arranged like a Hall bar on top of the YIG thin film. We show that electrical detection and injection of spin is possible, by solving the resulting diffusion-relaxation equation for a Hall bar. We predict the experimentally measurable Hall coefficient for a range of temperatures and magnetic field strengths. Most strikingly, we show that there is a sign change of the Hall coefficient associated with increasing the thickness of the film.