Determination of the spin Hall angle by the inverse spin Hall effect, device level ferromagnetic resonance, and spin torque ferromagnetic resonance: a comparison of methods

TL;DR

This paper compares three methods for measuring the spin Hall angle, highlighting the robustness of spin torque ferromagnetic resonance (STFMR) despite measurement complexities, and aims to improve accuracy in spin Hall angle determination for spintronic applications.

Contribution

The study systematically compares STFMR, device-level FMR, and ISHE methods, identifying artefacts and errors, and demonstrates STFMR as the most reliable technique for accurate SHA measurement.

Findings

STFMR is the most robust method among the three.

Measurement artefacts are caused by instrumentation noise floor.

Neglecting magnetic anisotropies can lead to 10% error in SHA.

Abstract

The spin torque ferromagnetic resonance (STFMR) is one of the popular methods for measurement of the spin Hall angle (SHA). However, in order to accurately determine SHA from STFMR measurements, the acquired data must be carefully analyzed: The resonance linewidth should be determined to an accuracy of a fraction of an Oe, while the dynamical interaction leading to the measured response consists of the conventional field-induced ferromagnetic resonance (FMR), spin-torque induced FMR, and of the inverse spin Hall effect (ISHE). Additionally, the signal often deteriorates when DC current is passed through the device. In this work we compare the STFMR method with two other FMR-based methods that are used to extract SHA. The first is a device-level FMR and the second is based on the ISHE. We identify artefacts that are caused by the noise floor of the instrumentation that make the measurement of SHA illusive even when the signal to noise ratio seems to be reasonable. Additionally, we estimate a 10% error in SHA that results from neglecting the magnetic anisotropies as in conventional measurements. Overall, we find the STFMR to be the most robust of the three methods despite the complexity of the interaction taking place therein. The conclusions of our work lead to a more accurate determination of SHA and will assist in the search of novel materials for energy efficient spin-based applications.