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

Abstract

The spin torque ferromagnetic resonance (STFMR) is one of the popular methods for measurement of the spin Hall angle, θSH. However, in order to accurately determine θSH 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), the spin-torque induced FMR, and the inverse spin Hall effect (ISHE). Additionally, the signal often deteriorates when DC is passed through the device. In this work, we compare the STFMR method with two other FMR-based methods that are used to extract θSH. The first is a device-level FMR, and the second is based on the ISHE. We identify artifacts that are caused by the noise floor of the instrumentation that make the measurement of θSH illusive even when the signal to noise ratio seems to be reasonable. Additionally, we estimate a 10% error in θSH 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 θSH and will assist in the search of novel materials for energy efficient spin-based applications.