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  • The gyrovector G is defined as:

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    • γ: gyromagnetic ratio
    • Where: Q: Skyrmion topological charge, L: film thickness

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  • The Thiele Equation: G × v - α D v + F = 0
    • - α: Gilbert damping, D: dissipative tensor, F: external force

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  • The skyrmion Hall effect is due to Magnus force Gz × v.
  • SF: The current-induced skyrmion velocity barely exceeds 100 m/s

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SAF:

  • Increased velocity of current-induced motions over 1000 m/s
  • NO Hall effect

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Precision: microtesla (µT).

Lateral resolution: typically ~10–30 nm (limited by tip radius)

Magnetic Force Microscopy (MFM):

  • A sharp tip coated with a magnetic material (commonly Co, Fe, or Ni) is scanned close to the sample surface.
  • The tip experiences magnetic forces (attractive or repulsive) due to the stray fields from the sample.
  • These forces cause a shift in the oscillation phase or frequency of the cantilever, which is detected and mapped.

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  • The Pt/Co interfaces provide the PMA and DMI necessary to stabilize the skyrmions and the spin orbit torque to move them with current
  • The Ru thickness was optimized to achieve AF RKKY interlayer exchange coupling with a coupling field of m0H RKKY = 205 mT.
  • The thickness of the Co layers was adjusted such that they were perpendicularly magnetized but close to the in-plane/out-of-plane spin reorientation transition, leading to a linear and reversible hysteresis loop indicating a multidomain state (Fig. 2B)

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Summary

  • Velocity achieved 900 m/s
  • Almost no sign of Hall-effect
  • Lacks smooth dependence on current density
  • Simulation/Thiele equation can explains results only at higher current density
  • Role of deformation could be significant in future simulations.

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Different Skyrmion structures

  • Special solution:
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  • Helicity:
  • skyrmion : W = +1
  • antiskyrmion : W = −1

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w=+1 w=-1

Neel-type

Bloch-type

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Magnetic Skyrmion

  • Topologically protected and defined by skyrmon number
  • For 2D system:
  • Using

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  • With

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  • p: polarity, describes the magnetization direction at the origin, with p = +1 for Θ(r = 0) = π (center down) and p = −1 for Θ(r = 0) = 0(center up)
  • W :the winding number