Modeling of a magnetic field sensor based on spin Hall magnetoresistance

TL;DR

This paper develops a comprehensive model for a magnetic field sensor based on Spin Hall Magnetoresistance, validated experimentally, providing design insights to optimize sensitivity and power efficiency in spintronic sensors.

Contribution

It introduces a multiphysics modeling framework that incorporates magnetic domains and spintronic effects, validated with experimental data, advancing the design of SMR-based magnetic sensors.

Findings

Model accurately predicts sensor behavior across different materials.

Design guidelines for minimizing power and maximizing sensitivity.

Experimental validation confirms model reliability.

Abstract

Next-generation spintronic sensors aim to overcome the limitations of traditional tunneling-magnetoresistance (TMR) devices, such as complex manufacturing, high $1/f$ noise, and significant offsets. This work presents a comprehensive modeling and experimental validation of a magnetic field sensor based on Spin Hall Magnetoresistance (SMR) in a Wheatstone bridge configuration. Utilizing a multiphysics approach, we simulate the interplay between SMR, Anisotropic Magnetoresistance (AMR), and Spin-Orbit Torque (SOT) using a Stoner-Wohlfarth model complemented by a Fuchs-Sondheimer analysis of current distribution. To account for the presence of magnetic domains, we incorporate a modified Stoner-Wohlfarth framework that considers non-uniform magnetization and domain wall motion through a "truncated astroid" approach, allowing for a statistical distribution of single-domain particles. The model is validated against experimental measurements of Pt/$\text{Fe}_{60}\text{Co}_{20}\text{B}_{20}$ and Ta/$\text{Fe}_{60}\text{Co}_{20}\text{B}_{20}$ bilayers patterned into Hall bars and Wheatstone bridges. The model provides critical design guidelines for optimizing material properties, layer thickness, and device layout to minimize power consumption and maximize sensitivity in SMR-based sensing applications.