Research ArticleSPINTRONICS

Dramatic influence of curvature of nanowire on chiral domain wall velocity

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Science Advances  05 May 2017:
Vol. 3, no. 5, e1602804
DOI: 10.1126/sciadv.1602804
  • Fig. 1 Dependence of the DW velocity on curvature for different structures.

    (A) Optical image of a typical U-shaped device with R = 7 μm and w = 2 μm. (B) v versus J shows faster or slower DW motion in a curved nanowire compared to a straight wire. (C) Representative Kerr images showing the expansion or contraction of a magnetic domain along the positive or negative curvature of a curved nanowire. The Kerr images are taken before and after the application of two 100-ns-long electrical pulses with a current density of 0.6 × 108 A/cm2. They are overlaid together, and the unedited picture is available in fig. S14. The yellow (gray) dots indicate the positions of ⊙ | ⊗ (⊗ | ⊙) DWs, and the arrows represent the trajectory of their motion. (D and E) v versus J showing the same relationship [as (B)] between the sign of the curvature on the increase or decrease in the DW velocity irrespective of the signs of DMI and SHE. (F) Truth table derived on the basis of (B), (D), and (E). Note that thicknesses of the layers in (B), (D), and (E) are in angstrom.

  • Fig. 2 Influence of curvature and width of the wire.

    DW motion as a function of the magnitude of the curvature (A to C) and width (D to F) for the film structure used in Fig. 1B. (C and F) The analytical model simulations for ⊗ | ⊙ (top) and ⊙ | ⊗ (bottom) DW displacements in their respective wires after a 40-ns current pulse with current density of 1.2 × 108 A/cm2 is applied. (C) shows images for representative wires with various R for a fixed w = 2 μm, and (F) shows images for various w for R = 16 μm. The DW’s initial position is at the center of each nanowire. (A) and (D) show ν versus J. (B) and (E) show the calculated ratio (Embedded Image of the ⊗ | ⊙ and ⊙ | ⊗ velocities for the same J.

  • Fig. 3 A quasi-2D model simulation of the CIDWM in curved nanowires.

    (A and B) Schematic illustration of the critical parameters, fields, and torques that describes the current-induced DW motion (CIDWM). (A) ⊙ | ⊗ with positive curvature (top) and ⊗ | ⊙ with negative curvature (bottom). (B) ⊗ | ⊙ with positive curvature at low J (top) and ⊗ | ⊙ with positive curvature at high J (bottom). Size of symbols ⊡ and ⊠ represent the magnitudes of their respective torques. (C and E) Calculated ν versus J for ⊙ | ⊗ and ⊗ | ⊙ configurations: (C) straight wire and curved wires with R= 4, 5, and 7 μm for a fixed w = 2 μm; (E) straight wire and curved wires with w = 2, 4, and 6 μm for a fixed R = 16 μm. (D and F) Calculated φ (main panels) and ζ (insets) versus J that correspond to (C) and (E), respectively, with the same corresponding colors and symbols. See fig. S11 for details about the parameters used in the calculations. Note that R and w in (C) to (F) are in micrometers.

  • Fig. 4 DW motion along a curved wire in a SAF structure.

    (A) Schematic illustration of the DW motion in a curved SAF nanowire showing the current-induced rotation of the Néel moments in the top (mU) and bottom (mL) layers by SHE from spin accumulation from the underlying Pt layer. (B) v versus J for ⊙ | ⊗ and ⊗ | ⊙ for positive and negative curvatures, respectively, for a device with R = 7 μm and w = 2 μm. The film stack is shown in the inset with thicknesses of layers in angstrom. (C) Representative Kerr images showing the motion of ⊙ | ⊗ | ⊙ and ⊗ | ⊙ | ⊗ DWs through a curved SAF nanowire.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/5/e1602804/DC1

    Supplementary Text

    fig. S1. Schematic illustration of basic parameters used in the Q2D model for current driven domain wall motion.

    fig. S2. Profile of anisotropy constant Keff(q) with Formula = 3.5 × 106 erg/cm3, η = 0.03, qs = 0 nm, and q0 = 10 nm.

    fig. S3. Modeling of thermal broadening.

    fig. S4. Schematic of current distribution in curved wire with width w and mid-radius R.

    fig. S5. Plots of Q2D model calculation results that take neither nonuniform current distribution nor pinning and thermal fluctuation into account.

    fig. S6. Radial dependence of DW velocities transverse to the curve wire direction.

    fig. S7. Plots of Q2D model calculation results that take pinning and thermal fluctuation but no nonuniform current distribution into account.

    fig. S8. Plots of time-resolved Q2D model calculation results that take pinning and thermal fluctuation but no nonuniform current distribution into account.

    fig. S9. Plots of Q2D model calculation results that take nonuniform current distribution and pinning but no thermal fluctuation into account.

    fig. S10. Plots of Q2D model calculation results that take nonuniform current distribution, pinning, and thermal fluctuation into account for various radii while width is fixed.

    fig. S11. Plots of Q2D model calculation results that take nonuniform current distribution, pinning, and thermal fluctuation into account for various widths while the radius is fixed.

    fig. S12. Plots of time-resolved Q2D model calculation results that take pinning and thermal fluctuation but no nonuniform current distribution into account.

    fig. S13. Comparison of micromagnetic simulations and Q2D model.

    fig. S14. Unabridged Kerr images corresponding to the main text.

    fig. S15. Schematic table outlines the relationship between the effect of curvature on the DW velocity (⊙ | ⊗ or ⊗ | ⊙), which is found to be independent of the sign of DMI or SHE.

    fig. S16. ν against J of the quasi-2D model calculation results that take nonuniform current distribution, pinning, and thermal fluctuation into account for R = 100, 150, and 175 nm while w is fixed at 50 nm.

    movie S1. Animation of Q2D calculation of time resolved DW motion in curved nanowires with positive curvatures for various radii and widths.

    Reference (3336)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Schematic illustration of basic parameters used in the Q2D model for current driven domain wall motion.
    • fig. S2. Profile of anisotropy constant Keff(q) with Keff0 = 3.5 × 106 erg/cm3, η = 0.03, qs = 0 nm, and q0 = 10 nm.
    • fig. S3. Modeling of thermal broadening.
    • fig. S4. Schematic of current distribution in curved wire with width w and mid-radius R.
    • fig. S5. Plots of Q2D model calculation results that take neither nonuniform current distribution nor pinning and thermal fluctuation into account.
    • fig. S6. Radial dependence of DW velocities transverse to the curve wire direction.
    • fig. S7. Plots of Q2D model calculation results that take pinning and thermal fluctuation but no nonuniform current distribution into account.
    • fig. S8. Plots of time-resolved Q2D model calculation results that take pinning and thermal fluctuation but no nonuniform current distribution into account.
    • fig. S9. Plots of Q2D model calculation results that take nonuniform current distribution and pinning, but no thermal fluctuation into account.
    • fig. S10. Plots of Q2D model calculation results that take nonuniform current distribution, pinning, and thermal fluctuation into account for various radii while
      width is fixed.
    • fig. S11. Plots of Q2D model calculation results that take nonuniform current distribution, pinning, and thermal fluctuation into account for various widths
      while the radius is fixed.
    • fig. S12. Plots of time-resolved Q2D model calculation results that take pinning and thermal fluctuation but no nonuniform current distribution into account.
    • fig. S13. Comparison of micromagnetic simulations and Q2D model.
    • fig. S14. Unabridged Kerr images corresponding to the main text.
    • fig. S15. Schematic table outlines the relationship between the effect of curvature on the DW velocity (⊙ | ⊗ or ⊗ | ⊙), which is found to be independent of the sign of DMI or SHE.
    • fig. S16. v against J of the quasi-2D model calculation results that take nonuniform current distribution, pinning, and thermal fluctuation into account for R = 100, 150, and 175 nm while w is fixed at 50 nm.
    • Legend for movie S1
    • References (33–36)

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.avi format). Animation of Q2D calculation of time resolved DW motion in curved nanowires with positive curvatures for various radii and widths.

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