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Evidence for phonon skew scattering in the spin Hall effect of platinum

G. V. Karnad, C. Gorini, K. Lee, T. Schulz, R. Lo Conte, A. W. J. Wells, D.-S. Han, K. Shahbazi, J.-S. Kim, T. A. Moore, H. J. M. Swagten, U. Eckern, R. Raimondi, and M. Kläui
Phys. Rev. B 97, 100405(R) – Published 26 March 2018
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    Abstract

    We measure and analyze the effective spin Hall angle of platinum in the low-residual resistivity regime by second-harmonic measurements of the spin-orbit torques for a multilayer of Pt|Co|AlOx. An angular-dependent study of the torques allows us to extract the effective spin Hall angle responsible for the damping-like torque in the system. We observe a strikingly nonmonotonic and reproducible temperature dependence of the torques. This behavior is compatible with recent theoretical predictions which include both intrinsic and extrinsic (impurities and phonons) contributions to the spin Hall effect at finite temperatures.

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    • Received 6 February 2017
    • Revised 30 August 2017

    DOI:https://doi.org/10.1103/PhysRevB.97.100405

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Spin Hall effectSpin accumulationSpin currentSpin torque
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    G. V. Karnad1, C. Gorini2,*, K. Lee1, T. Schulz1, R. Lo Conte1,3, A. W. J. Wells4, D.-S. Han1,5, K. Shahbazi4, J.-S. Kim5,†, T. A. Moore4, H. J. M. Swagten5, U. Eckern6, R. Raimondi7, and M. Kläui1,3,‡

    • 1Institut für Physik, Johannes Gutenberg-Universität, Staudinger Weg 7, 55128 Mainz, Germany
    • 2Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
    • 3Graduate School of Excellence “Materials Science in Mainz” (MAINZ), Staudinger Weg 9, 55128 Mainz, Germany
    • 4School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
    • 5Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
    • 6Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany
    • 7Dipartimento di Matematica e Fisica, Roma Tre University, Via della Vasca Navale 84, 00146 Rome, Italy

    • *cosimo.gorini@physik.uni-regensburg.de
    • †Present address: DGIST Research Center for Emerging Materials, DIGST, Daegu 42988, Republic of Korea.
    • ‡klaeui@uni-mainz.de

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    Issue

    Vol. 97, Iss. 10 — 1 March 2018

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    Images

    • Figure 1
      Figure 1

      Schematics of the second-harmonic measurement setup. A charge current Iω is injected along x̂, generating damping-like and field-like effective spin-orbit fields which exert a torque on the magnetization m̂. The damping-like torque acts along σ̂×m̂, and the field-like one acts along σ̂. Here σ̂ is the direction of the current-induced nonequilibrium spin current (SHE) and density (ISGE).

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    • Figure 2
      Figure 2

      Temperature dependence of Keff and M.

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    • Figure 3
      Figure 3

      Temperature dependence of the efficiency of damping-like (μ0HDL) and field-like (μ0HFL) effective fields.

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    • Figure 4
      Figure 4

      Temperature dependence of the deduced spin Hall angle (blue dots, connected by a basis spline as a guide to the eye) derived from the damping-like effective field. Practically identical behavior is found in a control sample, see Fig. S4 in the Supplemental Material [28].

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    • Figure 5
      Figure 5

      Sketch of the temperature behavior of the SHA for an ultraclean sample (skew scattering dominated, left panel) and a dirty one (intrinsic dominated, right panel). The sketch is based on Eq. (4) and built from knowledge of the high- and low-T asymptotics, which imply the existence (absence) of a minimum in clean (dirty) systems (see the Supplemental Material [28]). The precise behavior in the intermediate temperature range is however not yet known, nor can accurate values for T1,T2 be given since both temperatures depend on various system parameters. An order-of-magnitude estimate for Pt yields T1≲TD≲T2 and suggests that T1 should be higher the cleaner the sample. In dirty samples the compensation between intrinsic (red) and skew scattering (blue) curves can give rise to an effectively constant SHA over a broad T range as observed in Ta (for the details see Fig. S4 in the Supplemental Material [28]).

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