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

Published

March 22, 2018

Author(s)

Andy Berger, Eric R. Edwards, Hans T. Nembach, Olof Karis, Mathias Weiler, Thomas J. Silva

Abstract

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.

Citation

Physical Review Letters

Volume

98

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevB.98.024402

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Keywords

spin-orbit, SOT, spin current, ferromagnetic resonance, spin Hall, damping, diffusion, enhancement, heavy-metal thickness, ferromagnet/normal metal, vector network analyzer ferromagnetic resonance, Onsager reciprocity, Elliott-Yafet spin

Citation

Berger, A. , Edwards, E. , Nembach, H. , Karis, O. , Weiler, M. and Silva, T. (2018), Determination of spin Hall effect and spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements, Physical Review Letters, [online], https://doi.org/10.1103/PhysRevB.98.024402 (Accessed April 24, 2024)