{
  "id": "1711.07654",
  "version": "v1",
  "published": "2017-11-21T07:22:43.000Z",
  "updated": "2017-11-21T07:22:43.000Z",
  "title": "Determination of spin Hall effect and spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements",
  "authors": [
    "Andrew J. Berger",
    "Eric R. J. Edwards",
    "Hans T. Nembach",
    "Olof Karis",
    "Mathias Weiler",
    "T. J. Silva"
  ],
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.mtrl-sci"
  ],
  "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 ($\\sigma_\\mathrm{SH} = (2.36 \\pm 0.04)\\times10^6 \\Omega^{-1} \\mathrm{m}^{-1}$) and bulk spin Hall angle ($\\theta_\\mathrm{SH}=0.387 \\pm0.008$) 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-21T07:22:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin diffusion length",
      "inverse spin-orbit torque measurements",
      "damping enhancement",
      "network analyzer ferromagnetic resonance",
      "self-consistent fitting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}