# Spin Hall Magnetoresistance in Metallic Bilayers with In-plane Magnetized Ferromagnets

## TL;DR

This paper analyzes spin Hall magnetoresistance in metallic bilayers with in-plane magnetized ferromagnets, explicitly including anisotropic magnetoresistance to distinguish contributions and optimize magnetic sensors.

## Contribution

It introduces a comprehensive model that explicitly incorporates AMR into SMR analysis in metallic bilayers, enabling precise separation of magnetoresistance contributions.

## Key findings

- Explicit inclusion of AMR improves accuracy of magnetoresistance analysis.
- Results enable better design of magnetic sensors.
- Provides insights into spin transport in metallic heterostructures.

## Abstract

We revisit the theory and experiment on spin Hall magnetoresistance (SMR) in bilayers consisting of a heavy metal (H) coupled to in-plane magnetized ferromagnetic metal (F), and determine contributions to the magnetoresistance due to SMR and anisotropic magnetoresistance (AMR) in four different bilayer systems: W/$\text{Co}_{20}\text{Fe}_{60}\text{B}_{20}$, W/Co, $\text{Co}_{20}\text{Fe}_{60}\text{B}_{20}$/Pt, and Co/Pt. To do this, the AMR is explicitly included in the diffusion transport equations in the ferromagnet. The results allow precise determination of different contributions to the magnetoresistance, which can play an important role in optimizing prospective magnetic stray field sensors. They also may be useful in the determination of spin transport properties of metallic magnetic heterostructures in other experiments based on magnetoresistance measurements.