Spin pumping and non-uniform magnetic excitation in spin-torque FMR studies of the spin Hall effect

Early on, spin-torque ferromagnetic resonance (ST-FMR) was used to establish an initially surprisingly strong spin Hall effect (SHE) in certain heavy metals (HM), and has since been widely deployed in the study of spin-orbit torques in HM/FM bilayers. However, there are questions as to whether ST-FMR always provides accurate, quantitative measures of the dampinglike spin-torque efficiency ξ_DL, principally because of the unsettled role of spin-pumping and the inverse SHE in ST-FMR, but also because of the assumption that only the uniform mode is excited. Here we report on an extensive ST-FMR study of Pt/FM and β-W/FM bilayers and HM/spacer/FM trilayers chosen such that the spin pumping effect is both strong and variable. We show that spin pumping, when significant, subtracts from the antidamping torque signal, resulting in ξ_FMR<ξ_DL. In conjunction with the spin pumping model, the FMR studies also clearly indicate that there can be significant coupling of the incident spin current to non-uniform modes in the FM layer, which also contributes to a lower apparent ξ_DL. These results explain why ST-FMR often underestimates ξ_DL in comparison to quasi-static second harmonic results, the latter of which are generally confirmed by ST switching of MTJs.