Influence of the Hall-bar geometry on harmonic Hall voltage measurements of spin-orbit torques

TL;DR

This paper investigates how the geometry of Hall bars affects harmonic Hall voltage measurements of spin-orbit torques, revealing that aspect ratio influences the apparent spin Hall angle and emphasizing the importance of geometry in accurate measurements.

Contribution

It provides a detailed analysis and experimental validation of how Hall bar aspect ratio impacts the measurement of spin Hall effects, a factor previously not well quantified.

Findings

Aspect ratio significantly affects the apparent spin Hall angle.

Reduction of the apparent spin Hall angle observed at aspect ratio 1:1.

Finite-element simulations confirm experimental results.

Abstract

Harmonic Hall voltage measurements are a wide-spread quantitative technique for the measurement of spin-orbit induced effective fields in heavy-metal / ferromagnet heterostructures. In the vicinity of the voltage pickup lines in the Hall bar, the current is inhomogeneous, which leads to a hitherto not quantified reduction of the effective fields and derived quantities, such as the spin Hall angle or the spin Hall conductivity. Here we present a thorough analysis of the influence of the aspect ratio of the voltage pickup lines to current channel widths on the apparent spin Hall angle. Experiments were performed with Hall bars with a broad range of aspect ratios and a substantial reduction of the apparent spin Hall angle is already seen in Hall crosses with an aspect ratio of 1:1. Our experimental results are confirmed by finite-element simulations of the current flow.