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arXiv · 1711.07654

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

Andrew J. Berger·Eric R. J. Edwards·Hans T. Nembach·Olof Karis·Mathias Weiler·T. J. Silva
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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 Ni$_{80}$Fe$_{20}$/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 ($\approx$ 4 nm), 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 Ni$_{80}$Fe$_{20}$/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 ($σ_\mathrm{SH} = (2.36 \pm 0.04)\times10^6 Ω^{-1} \mathrm{m}^{-1}$) and bulk spin Hall angle ($θ_\mathrm{SH}=0.387 \pm0.008$) 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.

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Andrew J. Berger, Eric R. J. Edwards, Hans T. Nembach, Olof Karis, Mathias Weiler, T. J. Silva. 2018-03-21. Determination of spin Hall effect and spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements. https://doi.org/10.1103/physrevb.98.024402

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