Research ArticlePHYSICS

Giant nonlinear damping in nanoscale ferromagnets

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Science Advances  25 Oct 2019:
Vol. 5, no. 10, eaav6943
DOI: 10.1126/sciadv.aav6943
  • Fig. 1 Spin wave spectra in a nanoscale MTJ.

    (A) Normalized ST-FMR spectra V˜mix (f) of spin wave eigenmodes in a perpendicular MTJ device (sample 1) measured as a function of out-of-plane magnetic field. Resonance peaks arising from three low frequency modes of the MTJ FL ∣0,0〉, ∣0,1〉, and ∣1,0〉 are observed. (B) Schematic of the three-magnon confluence process, denoted as ψ0,1, and the inverse process of three-magnon splitting, denoted as ψ0,1*. Mode profiles are shown. (C) Spectral linewidth of the quasi-uniform ∣0,0〉 spin wave mode as a function of out-of-plane magnetic field. Strong linewidth enhancement is observed in the three-magnon scattering regime at H1 and H2.

  • Fig. 2 Effect of spin torque on spin wave resonance lineshape.

    (A and B) Spin wave resonance lineshapes for different values of direct bias current Idc, far from three-magnon scattering regime H > H1. (C and D) Spin wave resonance lineshapes in the three-magnon regime at H = H1. (A and C) Measured ST-FMR spectra (sample 2). (B and D) Solutions of Eqs. 3 and 4. Identical current values Idc, displayed in (A), are used in all four figure panels.

  • Fig. 3 Effect of spin torque on linewidth.

    Linewidth of the quasi-uniform spin wave mode as a function of applied direct bias current (sample 3): red open circles—in the three-magnon scattering regime H = H1; blue open squares—far from the three-magnon scattering regime, HH1. Lines are numerical fits using Eqs. 3 and 4.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaav6943/DC1

    Note S1. Calculation of linewidth.

    Note S2. Micromagnetic simulations.

    Note S3. Solution of the equations of motion.

    Note S4. Effect of the drive amplitude and intrinsic nonlinearitites on the resonance lineshape.

    Note S5. Effective single-mode nonlinear oscillator approximation.

    Note S6. Mode coupling parameter.

    Fig. S1. Spatial profiles of spin wave eigenmodes.

    Fig. S2. Effect of intrinsic nonlinearities on the quasi-uniform spin wave resonance lineshape.

    Fig. S3. Effect of the drive amplitude on linewidth in the three-magnon regime.

    References (4147)

  • Supplementary Materials

    This PDF file includes:

    • Note S1. Calculation of linewidth.
    • Note S2. Micromagnetic simulations.
    • Note S3. Solution of the equations of motion.
    • Note S4. Effect of the drive amplitude and intrinsic nonlinearitites on the resonance lineshape.
    • Note S5. Effective single-mode nonlinear oscillator approximation.
    • Note S6. Mode coupling parameter.
    • Fig. S1. Spatial profiles of spin wave eigenmodes.
    • Fig. S2. Effect of intrinsic nonlinearities on the quasi-uniform spin wave resonance lineshape.
    • Fig. S3. Effect of the drive amplitude on linewidth in the three-magnon regime.
    • References (4147)

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