Nonlocal Anomalous Hall Effect

TL;DR

This paper introduces a theory for a nonlocal anomalous Hall effect observed in nonmagnetic metals like platinum when in contact with magnetic insulators, attributing it to spin-dependent scattering and the spin Hall effect.

Contribution

The paper proposes a novel first-order in spin-orbit coupling theory for the nonlocal anomalous Hall effect, differing from previous models by spatially separating spin-orbit interaction and magnetization.

Findings

The theory predicts the effect's sign depends on the spin Hall angle.

Calculated anomalous Hall conductivity matches experimental data.

Effect occurs without induced magnetization in the metal.

Abstract

The anomalous Hall effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator (yttrium iron garnet (YIG)), even when precautions are taken to ensure there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect -- the only difference being the spatial separation of the spin orbit interaction and the magnetization. For this reason we name this effect \textit{nonlocal anomalous Hall effect} and predict that its sign will be determined by the sign of the spin Hall angle in the metal. The AH conductivity that we calculate from our theory is in good agreement with the measured values in Pt/YIG structures.