Determination of the spin Hall effect and the spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements

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 dampinglike 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 fieldlike and dampinglike 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 dampinglike inverse SOT can be described by a single spin diffusion length (approximate to 4nm), and that we can separate the spin pumping and spin-memory loss 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 spin-memory loss and corresponding reduction in total spin current available for spin-charge transduction in the Pt, we determine the Pt spin Hall conductivity [sigma(SH) = (2.36 +/- 0.04) x 10(6) omega(-1) m(-1)] and bulk spin Hall angle (theta(SH) = 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 spin loss. 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.