Magnetoresistance originated from charge-spin conversion in ferromagnet

TL;DR

This paper presents a theoretical analysis of transverse magnetoresistance in ferromagnetic trilayers, highlighting the role of charge-spin conversion via the anomalous Hall effect and deriving an analytical formula for the resistivity.

Contribution

It introduces a new analytical model linking charge-spin conversion to magnetoresistance, considering the anomalous Hall effect and magnetization angles.

Findings

Charge-spin conversion affects magnetoresistance proportionally to the square of the spin anomalous Hall angle.

The angular dependence resembles the planar Hall effect with an additional magnetization angle term.

An analytical formula for transverse resistivity in ferromagnetic trilayers is derived.

Abstract

Transverse magnetoresistance in a ferromagnetic/nonmagnetic/ferromagnetic trilayer originated from charge-spin conversion by anomalous Hall effect is investigated theoretically. Solving the spin diffusion equation in bulk and using the spin-dependent Landauer formula at the ferromagnetic/nonmagnetic interface, an analytical formula of the transverse resistivity is obtained. The charge-spin conversion by the anomalous Hall effect contributes to the magnetoresistance in a manner proportional to the square of the spin anomalous Hall angle. The angular dependence of the magnetoresistance is basically identical to that of planar Hall effect, but has an additional term which depends on the relative angle of the magnetizations in two ferromagnets.