Research ArticleMATERIALS SCIENCE

Skyrmion lattice structural transition in MnSi

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Science Advances  09 Jun 2017:
Vol. 3, no. 6, e1602562
DOI: 10.1126/sciadv.1602562
  • Fig. 1 SANS measurements on equilibrium magnetic phases and quenched SkL state under a magnetic field of 0.2 T.

    (A) H-T magnetic phase diagram of MnSi. The open symbols denote phase boundaries between helical, conical, SkL, and field-induced ferromagnetic phases determined by resistivity measurements using the identical sample used in the SANS measurements. Inset: Typical time profiles of an electric current pulse and the resulting temperature change. (B) Schematic showing the experimental setup, orientation of the crystal, and directions of neutron beam and magnetic field. (C to E) SANS patterns measured in the H || ki configuration (C) in the equilibrium SkL phase, at 12.5 K and 0.2 T before applying the current pulse (D), and after the application of the pulse (E). (F to H) Corresponding SANS patterns measured in the Hki configuration.

  • Fig. 2 Magnetic field induced transitions in the lowest temperature (1.5 K) after quenching.

    (A) Magnetic field dependence of integrated intensity of the magnetic reflections measured in the H || ki configuration after quenching at 0.2 T with increasing and decreasing fields and (B) measured with increasing magnetic field after reaching the square SkL state in zero field. (C) Field dependence of average values of peak position in q measured in the H || ki configuration at 1.5 K. Filled and open symbols denote data measured with increasing and decreasing field, respectively. Gray data points in (B) are the data shown in (A). (D) Hall resistivity data redrawn from fig. S3a in the Supplementary Materials of the study by Oike et al. (23). Expected square SkL contribution in Hall resistivity is highlighted in pink. Slight discrepancies in transition fields are due to differences in temperature and demagnetizing effect. (E to H) Azimuthal angle profiles of the annular-averaged intensities measured at (E) 0.2 T, (F) 0.08 T, and (G) 0 T with decreasing field and at (H) 0.2 T with increasing field from 0 T. (I to P) The SANS patterns measured in the H || ki and Hki configurations at the selected magnetic fields. In (K), (L), and (O), the intensities (I) are multiplied by factors of 3, 3, and 10, respectively, to enhance clarity.

  • Fig. 3 Metastable state diagram mapped on the H-T magnetic phase diagram.

    Metastable state diagram mapped on the H-T magnetic phase diagram. The filled circles denote the boundaries between the metastable triangular SkL, square SkL, and (equilibrium) conical and helical magnetic states.

  • Fig. 4 Triangular SkL and square lattice arrangements of particles with the same modulation period λ.

    (A) The triangular SkL described by superposition of three screw magnetic modulations of q1, q2, and q3 (|qi| = 2π/λ, i = 1 to 3) shown in its inset and a uniform magnetization component along the z direction. Colors and arrows denote out-of-plane and in-plane components of the magnetic moments, respectively. (B) Schematic showing square lattice arrangements of particles characterized by two wave vectors of q1 and q2 (|qi| = 2π/λ, i = 1, 2) shown in its inset.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/6/e1602562/DC1

    Cooling rate dependence of the volume fraction of the quenched SkL state

    Azimuthal angle profiles measured in the Hki configuration

    Magnetic field and temperature dependence of the quenched SkL states

    fig. S1. Cooling rate dependence of the integrated intensities corresponding to the SkL and conical orders.

    fig. S2. Field dependence of azimuthal angle profile measured in the Hki configuration.

    fig. S3. Magnetic field and temperature dependence of the metastable SkLs.

    Reference (32)

  • Supplementary Materials

    This PDF file includes:

    • Cooling rate dependence of the volume fraction of the quenched SkL state
    • Azimuthal angle profiles measured in the Hki configuration
    • Magnetic field and temperature dependence of the quenched SkL states
    • fig. S1. Cooling rate dependence of the integrated intensities corresponding to the SkL and conical orders.
    • fig. S2. Field dependence of azimuthal angle profile measured in the Hki configuration.
    • fig. S3. Magnetic field and temperature dependence of the metastable SkLs.
    • Reference (32)

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