Magnetoresistance generated from charge-spin conversion by anomalous Hall effect in metallic ferromagnetic/nonmagnetic bilayers

TL;DR

This paper presents a theoretical model for magnetoresistance in ferromagnetic/nonmagnetic bilayers caused by charge-spin conversion via the anomalous Hall effect, deriving analytical resistivity expressions.

Contribution

It provides analytical formulas for magnetoresistance due to the anomalous Hall effect and explores the mixing of spin Hall and anomalous Hall effects in bilayers.

Findings

Magnetoresistance from charge-spin conversion is proportional to the square of spin polarization.

Pure anomalous Hall effect-induced magnetoresistance has a fixed sign.

Mixing of spin Hall and anomalous Hall effects leads to additional, sign-dependent magnetoresistance.

Abstract

A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional magnetoresistances in both nonmagnet and ferromagnet arising from the mixing of the spin Hall and anomalous Hall effects. The sign of this mixing resistance depends on those of the spin Hall angle in the nonmagnet and the spin polarizations of the ferromagnet.