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

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 (≈ 4 nm), 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 Ni 80 Fe 20 /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 (σ SH = (2.36 ± 0.04) × 10 6 Ω −1 m −1 ) and bulk spin Hall angle (θ 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. * thomas.silva@nist.gov † Contribution of the National Institute of Standards and Technology; not subject to copyright.

FMR-related phenomena in spintronic devices

“…Moreover, we observed a similar θsh of ~0.01-0.015 in Py (20 nm)/Ta (6-25 nm) and CoFeB (15 nm)/Ta (15 nm) bilayers by spin pumping measurements at room temperature. This similar SOT efficiencies from both ST-FMR and spin pumping measurements suggest the Onsager reciprocity, which has been also demonstrated recently[82].…”

Effective Spin-Mixing Conductance of Heavy-Metal–Ferromagnet Interfaces

“…A signature for the TMS contribution to the damping (αTMS) is that, to the first approximation, it is a parabolic function of the interfacial perpendicular magnetic anisotropy field 2Ks/MstFM [29,30]. If αTMS is significant, the total damping is given approximately by α = αint + αSP + αTMS or where the second term is the combined contribution from spin pumping into the Pt layer and from SML at the interface, which for convenience we parameterize as an "effective SML conductance" GSML [16,27], and βTMS is a coefficient that depends on both (Ks/Ms) 2 and the density of magnetic defects at the FM surfaces [29,30](We provide further justification for the FM −2 dependence of the TMS term in [37]).…”

Disorder Dependence of Interface Spin Memory Loss

“…20,[28][29][30] Recent studies suggesting that measurements of the SHA may actually be dominated by interface effects 20,28,31,32 are stimulating attempts to tailor these. [33][34][35][36][37] This makes it crucial to have a way to independently determine interface parameters. We recently described a formalism to evaluate local charge and spin currents 8 from the solutions of fully relativistic quantum mechanical scattering calculations 38 that include temperatureinduced lattice and spin disorder.…”