Enhancing the measurement of spin-orbit torque using the harmonic Hall method

Abstract

There is growing interest in discovering materials with strong spin-orbit torque (SOT). The harmonic Hall method is one of the most widely used for this measurement, but can lead to erroneous results due to invalid assumptions in analytical expressions, setup-related effects and neglecting thermoelectric effects. The primary objective of this research was to address gaps in current knowledge and enhance the measurement techniques for SOT in novel materials, particularly single-layer films. This research combines symmetry and microscopic approaches, deriving a magnetogalvanic tensor to model any material while respecting sample symmetry. A microscopic approach was employed to solve the balance of torques, including the SOT field.

A numerical simulation of harmonic Hall signals was developed. This model included parameters originating from both the sample and setup. An analysis of one million simulated harmonic Hall signals revealed high inaccuracies in published analytical methods for determining SOT. Highlighting the need for a numerical model to analyse the harmonic Hall signal when high accuracy is required.

The crystallographic origin of SOT in a single-layer Mn2 Rux Ga thin film was investigated. Symmetry analysis was used to determine the galvanomagnetic tensor and the numerical model to analyse the signal. A wide diversity of field directions and field strength were employed to ensure high accuracy. This method was benchmarked with two samples of CoPt (with and without structural inversion symmetry). The analysis of the single-layer Mn2 Rux Ga showed the absence of an SOT contribution from a crystallographic origin. However, a small interfacial contribution was present.

To eliminate the thermoelectric effect in the harmonic Hall measurement, a new device pattern was designed that allows for a rotational current. Analytical and finite element modelling, along with experimental testing, demonstrated the presence of SOT signals and the absence of thermoelectric contributions. A noise analysis and budget were carried out to quantify the impact of the new setup on signal accuracy. This study shows that this new design is widely applicable and independent of sample specificity.

In conclusion, this research developed accurate and precise measurement methods for SOT, addressing limitations in the existing analytical techniques and provides a robust framework for future spintronics research.