Modeling of a magnetic field sensor based on spin Hall magnetoresistance

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.