Research ArticlePHYSICS

Entropy-limited topological protection of skyrmions

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Science Advances  29 Sep 2017:
Vol. 3, no. 9, e1701704
DOI: 10.1126/sciadv.1701704
  • Fig. 1 Magnetic phases and skyrmion decay in Fe1-xCoxSi.

    (A) Magnetic phase diagram of Fe1−xCoxSi with x = 0.5 obtained by first cooling the system at a fixed magnetic field, B ≈ 23 mT, and then raising or lowering the field at fixed temperature T. The decrease in the applied field triggers the decay into a helical configuration, whereas either a conical or ferromagnetic state is reached for an increase of the field. (B) Typical LTEM images of helical and skyrmion lattice order, respectively. (C) Schematic image of an early state of the decay of the skyrmion lattice toward a ferromagnetic state. The skyrmion splits by the formation of a pair of Bloch points located at the end of the skyrmion strings, which move toward the surface. (D) Decay of skyrmion lattice order toward the helical state. Neighboring skyrmions merge, and a Bloch point at the merging points moves toward the surface.

  • Fig. 2 Key characteristics of the decay of skyrmions into a helical order.

    The sample was field-cooled (FC) from above the helical transition temperature (Tc ≈ 38 K) under an applied magnetic field B = 23 mT down to Tm, where the field was reduced to Bm and data recorded as a function of time t. (A to C) Typical LTEM patterns at Tm = 16.7 K after reaching Bm = −2.6 mT for t = 0.1 , 4.8, and 20.2 s, respectively. (D) Evolution of the intensity across the white box marked in (A), (B), and (C) as a function of time (vertical axis). (E) Typical time dependence of the number of skyrmions for Tm = 20.4 K and Bm = −2.6 mT. The blue curve represents an exponential fit.

  • Fig. 3 Key characteristics of the decay of skyrmions for increasing magnetic fields.

    The sample was field-cooled (FC) from above the helical transition temperature (Tc ≈ 38 K) under an applied magnetic field B = 23 mT down to Tm, where the field was increased to Bm and the data were recorded as a function of time t. (A to C) Typical LTEM patterns at Tm = 18.5 K after reaching Bm = 57 mT, for t = 6.8, 23.6, and 56.0 s, respectively. (D) Evolution of the intensity across the white box marked in (A), (B), and (C) as a function time (vertical axis). (E) Typical time dependence of the number of skyrmions for Tm = 20.4 K and Bm = 57 mT, fitted by an exponential (green line). (F) Time dependence of the intensity within the red dashed circle in (A), (B), and (C). For a small number of skyrmions, a two-step decay via an intermediate state with lower intensity is observed. (G) Statistics of the intermediate-state intensities.

  • Fig. 4 Key characteristics of the decay rates of supercooled skyrmions in Fe1−xCoxSi (x = 0.5).

    (A) Typical decay times τ after field cooling at B = 23 mT, followed by a decrease/increase to Bm. (B and C) Decay time τ as a function of thermal energy for increasing and decreasing magnetic fields, respectively, and various values of Bm. (D) Attempt time τ0 as a function of energy barrier ΔE inferred from the exponential time dependence of the skyrmion decay. The variation of more than 30 orders of magnitude of τ0 reflects the extreme enthalpy-entropy compensation.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/9/e1701704/DC1

    section 1. Image processing for the skyrmion decay measurements

    section 2. Evaluation of intermediate states

    section 3. Scaling analysis of activation energies

    fig. S1. Thickness determination of the FIB lamella.

    fig. S2. Illustration of the evaluation of the skyrmion decay to the conical phase.

    fig. S3. Illustration of the evaluation of the skyrmion decay to the helical phase.

    fig. S4. Reduction of the skyrmion order deduced from the Fourier transform of the real-space data.

    Reference (44)

  • Supplementary Materials

    This PDF file includes:

    • section 1. Image processing for the skyrmion decay measurements
    • section 2. Evaluation of intermediate states
    • section 3. Scaling analysis of activation energies
    • fig. S1. Thickness determination of the FIB lamella.
    • fig. S2. Illustration of the evaluation of the skyrmion decay to the conical phase.
    • fig. S3. Illustration of the evaluation of the skyrmion decay to the helical phase.
    • fig. S4. Reduction of the skyrmion order deduced from the Fourier transform of the real-space data.
    • Reference (44)

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