Spin-transfer torque in ferromagnetic bilayers generated by anomalous Hall effect and anisotropic magnetoresistance

TL;DR

This paper introduces an experimental method to measure spin-transfer torque efficiency in ferromagnetic bilayers by analyzing longitudinal magnetoresistance influenced by spin-orbit interactions, providing an analytical approach for extraction.

Contribution

It presents a novel experimental scheme and analytical formula to determine spin-transfer torque efficiency from magnetoresistance measurements in ferromagnetic bilayers.

Findings

Derived an analytical formula for longitudinal charge current density.

Proposed a method to extract spin-transfer torque efficiency from resistivity measurements.

Demonstrated the dependence of the current on film thickness and spin diffusion length.

Abstract

We propose an experimental scheme to determine the spin-transfer torque efficiency excited by the spin-orbit interaction in ferromagnetic bilayers from the measurement of the longitudinal magnetoresistace. Solving a diffusive spin-transport theory with appropriate boundary conditions gives an analytical formula of the longitudinal charge current density. The longitudinal charge current has a term that is proportional to the square of the spin-transfer torque efficiency and that also depends on the ratio of the film thickness to the spin diffusion length of the ferromagnet. Extracting this contribution from measurements of the longitudinal resistivity as a function of the thickness can give the spin-transfer torque efficiency.