Research ArticleAPPLIED PHYSICS

Spin-orbit torque–driven propagating spin waves

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Science Advances  27 Sep 2019:
Vol. 5, no. 9, eaax8467
DOI: 10.1126/sciadv.aax8467
  • Fig. 1 Device schematic, magnetoresistance, and nonlinearity coefficient.

    (A) Schematic of a SHNO with nanoconstriction width w. (B) Contour plot displaying the analytically calculated nonlinearity coefficient (N) as a function of PMA strength and applied OOP (θ = 80°) field for a thin magnetic film with saturation magnetization, μ0MS = 0.93 T; dashed black line indicates N=0. (C) Anisotropic magnetoresistance (MR) measured with 0.05 mA on a 200-nm nanoconstriction under a rotating 70 mT in-plane (IP) field.

  • Fig. 2 ST-FMR measurements.

    (A) Resonance frequency versus IP field (blue dots) with a Kittel fit (red line) yielding an effective magnetization μ0Meff=μ0(MsHk) of 0.31 T. Inset: Illustration of the ST-FMR measurement on a microstrip with dimensions of 6 μm by 18 μm. (B) Extracted linewidth (HWHM) versus resonance frequency yielding a Gilbert damping constant of α = 0.023. Inset: Current-dependent ST-FMR linewidth for both positive (blue squares) and negative (red dots) field directions yielding an SHA of −0.41.

  • Fig. 3 Auto-oscillating propagating SWs versus OOP field strength.

    PSDs versus OOP field for a (A) 150-nm and (B) 200-nm nanoconstriction. Orange data points are the ST-FMR resonances obtained under identical conditions on a microstrip with dimensions of 4 μm by 14 μm with the solid line being a fit to the Kittel equation (Eq. 2 in Materials and Methods).

  • Fig. 4 Current tunability of SW auto-oscillations at different OOP applied field strengths.

    PSDs of the SW auto-oscillations versus current for a w = 150 nm SHNO (A to D) and a w = 200 nm SHNO (E to H) subject to four different OOP field strengths (0.4, 0.6, 0.8, and 1.0 T). Orange dashed lines indicate the FMR frequency.

  • Fig. 5 Micromagnetic simulations.

    (A to C) Micromagnetically simulated PSDs as a function of applied dc through a 150-nm nanoconstriction under field conditions used in the experiments. FFT, fast Fourier transform. (D) Snapshots of the instantaneous mz component at three different currents showing how the auto-oscillations transition from localized (0.15 mA) to propagating (0.4 and 0.7 mA) with a wave vector that increases with current. (E) Cuts through (D) along the y axis at the three different currents.

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