Determination of spin Hall effect and spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements
Andy Berger, Eric R. Edwards, Hans T. Nembach, Olof Karis, Mathias Weiler, Thomas J. Silva
Understanding the evolution of spin-orbit torque (SOT) with increasing heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical for the development of magnetic memory based on SOT. However, several experiments have revealed an apparent discrepancy between damping enhancement and damping-like SOT regarding their dependence on NM thickness. Here, using linewidth and phase-resolved amplitude analysis of vector network analyzer ferromagnetic resonance (VNA-FMR) measurements,we simultaneously extract damping enhancement and both field-like and damping-like inverse SOT in Ni80Fe20/Pt bilayers as a function of Pt thickness. By enforcing an interpretation of the data which satisfies Onsager reciprocity, we find that both the damping enhancement and damping-like inverse SOT can be described by a single spin diffusion length (≈ 4nm), and that we can separate the spin pumping and spin memory loss (SML) contributions to the total damping. This analysis indicates that less than 40% of the angular momentum pumped by FMR through the Ni80Fe20/Pt interface is transported as spin current into the Pt. On account of the SML and corresponding reduction in total spin current available for spin-charge transduction in the Pt, we determine the Pt spin Hall conductivity (σSH= (2.36+/-0.04)x 106Ω-1m-1) and bulk spin Hall angle(θSH= 0.387+/-0.008) to be larger than commonly-cited values. These results suggest that Pt can be an extremely useful source of SOT if the FM/NM interface can be engineered to minimize SML. Lastly, we find that self-consistent fitting of the damping and SOT data is best achieved by a model with Elliott-Yafet spin relaxation and extrinsic inverse spin Hall effect, such that both the spin diffusion length and spin Hall conductivity are proportional to the Pt charge conductivity.