Research ArticlePHYSICS

Disordered skyrmion phase stabilized by magnetic frustration in a chiral magnet

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Science Advances  14 Sep 2018:
Vol. 4, no. 9, eaar7043
DOI: 10.1126/sciadv.aar7043
  • Fig. 1 Temperature–Mn concentration phase diagram of (Co0.5Zn0.5)20−xMnx, schematic SANS patterns, and SANS images at 146 K in Co7Zn7Mn6.

    (A) The zero-field magnetic phase diagram of (Co0.5Zn0.5)20−xMnx (0 ≤ x ≤ 20) in the T (temperature) versus x (Mn composition) plane, as determined by magnetization measurements (see fig. S2A). The inset shows a schematic of a β-Mn–type structure (space group: P4132) as viewed along the [111] axis. (B) Schematic of magnetic structures in real space and the corresponding SANS patterns in the H (magnetic field) || neutron beam and H ⊥ neutron beam geometries. The direct-beam spot expected at the center of each pattern is masked out. (i) The helical (H) state forms three domains with single-q || [100], [010], or [001], respectively, resulting in four spots in both geometries. (ii) In the conical (C) state with q || H || [001], only two spots are observed in the H ⊥ beam geometry. (iii) The triangular-lattice SkX state forms two domains with one of the triple-q || [100] or [010] (degenerate preferred q-directions), respectively, resulting in 12 spots in the H || beam geometry and 2 spots in the H ⊥ beam geometry. (iv) In the disordered helical (DH) state, the spots are broadened compared with (i). (v) In the three-dimensionally disordered skyrmion (DSk) state, a spherical q distribution manifests itself as a ring in both geometries. (C) SANS images observed in Co7Zn7Mn6 at 146 K and at 0 T and 0.03 T in the H || beam and H ⊥ beam geometries, respectively. The 0 T and 0.03 T patterns represent (i) helical and (iii) SkX [plus (ii) conical] states, respectively. Twelve spots in the H || beam geometry indicate that the SkX state consists of two kinds of domains with one of the triple-q || [100] or [010]. Note that the intensity scale of the color plots varies between each panel. arb. units, arbitrary units.

  • Fig. 2 Temperature-field phase diagrams in Co7Zn7Mn6.

    T-H phase diagrams in Co7Zn7Mn6 determined by ac susceptibility and SANS measurements (see figs. S3B, S4, D and E, and S8) (A) in the field-increasing runs after ZFC and (B) in the field-decreasing runs from the induced ferrimagnetic (higher H) region. The helical-conical and conical-ferrimagnetic phase boundaries are indicated by black diamonds and squares, respectively. The phase boundaries of the conventional SkX phase are indicated by green circles. The crossover region around 90 K, below which the helical state becomes disordered, is indicated by gray hatching. Spin glass transition temperatures around 30 K are indicated by black triangles. Pink circles show the magnetic fields where either 12-spot or ring-like SANS patterns are observed. The equilibrium phase (plus metastable state in the case of field-decreasing processes) of DSks is indicated by a red color region. Note that the SkX and conical states and conical and DSk states coexist in broad regions, and only the majority phase is indicated in the phase diagrams.

  • Fig. 3 Field dependence of the SANS patterns at 50 K in Co7Zn7Mn6.

    (A) Schematic of the measurement process. The field-increasing run from 0 T to 0.3 T after ZFC and the subsequent field-decreasing run from 0.3 T to 0 T are denoted by pink and light blue arrows, respectively. In the schematic phase diagram, we use the following notations: P, paramagnetic; H, helical; C, conical; SkX, skyrmion crystal (green region); F, ferrimagnetic; DH, disordered helical; DSk, disordered skyrmion (red region); and SG, spin glass. (B) SANS images at selected fields in the H || beam geometry. Note that the intensity scale of the color plots varies between each panel. (C) Field dependence of integrated SANS intensities. The intensities for directions close to 〈100〉 over the regions at θ = 0° ± 15°, 90° ± 15°, 180° ± 15°, and 270° ± 15° (red region in the inset) are indicated by red squares. The intensities for directions close to 〈110〉 over the regions at θ = 45° ± 15°, 135° ± 15°, 225° ± 15°, and 315° ± 15° (blue region in the inset) are indicated by blue circles. Here, θ is defined as the clockwise azimuthal angle from the vertical [010] direction. The field-increasing and field-decreasing runs are indicated by closed and open symbols with the same colors, respectively. (D and E) SANS images (D) at 0.1 T in the field-increasing run and (E) at 0 T after the field-decreasing run in both geometries, respectively. In (D) and (E), the data for H ⊥ beam geometry were collected within the same field-sweeping process [shown schematically in (A)], as used for collecting the data shown in (B). Note that the intensity scale of the color plots varies between each panel.

  • Fig. 4 SANS patterns during the FW process in Co7Zn7Mn6.

    (A) Schematic of the measurement process. (B) SANS images at selected temperatures in the H ⊥ beam geometry for the FW process at 0.025 T after a field decrease at 60 K. The intensity scale of the color plots varies between each panel. It is noted that the SANS images for both the FW process and the ZFW process (fig. S9C) were obtained from two rocking scans covering the same scanning region where the cryomagnet is rotated from −5° to 5° around both the vertical and horizontal axes. Pink and yellow dotted circles highlight the SANS intensities allocated to the SkX state and conical state, respectively. (C) Temperature dependence of integrated SANS intensities. The intensities integrated over the regions nearly perpendicular to the field at φ = 0° ± 30° and 180° ± 30° (red region in the inset) are indicated by red squares [I(qH)]. The intensities integrated over the regions nearly parallel to the field at φ = 90° ± 30° and 270° ± 30° (yellow region in the inset) are indicated by yellow triangles [I(q || H)]. Here, φ is defined as the clockwise azimuthal angle from the vertical [010] direction. (D) Temperature dependence of the SANS intensity ratio, I(qH)/I(q || H). The intensity ratio becomes smaller than 1 at 146 K because the volume fraction of a conical state is larger than that of an equilibrium SkX state (see also fig. S4). For (C) and (D), the crossover region, above (below) which both helical and skyrmion states are ordered (disordered), is indicated with gray hatching.

  • Fig. 5 Field-swept ac susceptibility after several cooling/warming processes in Co7Zn7Mn6.

    (A) Schematic of measurement processes for (B). FC1 (blue line) is a FC process passing through the SkX phase: (i) ZFC to 146 K, (ii) field increase to 0.025 T, and (iii) FC to 110 K. FW1 (red line) is a FW process passing through the DSk phase: (i) ZFC to 60 K, (ii) field increase to 0.2 T, (iii) field decrease to 0.025 T, and (iv) FW to 110 K. (B) Field dependence of the real part of the ac susceptibility (χ′) at 110 K after FC1 (blue circles) and FW1 (red line). Black lines show the field-returning runs from high-field ferrimagnetic regions. (C) Schematic of measurement processes for (D). FC2 (yellow line) is a FC process bypassing the SkX phase: (i) ZFC to 120 K, (ii) field increase to 0.025 T, and (iii) FC to 110 K. FW2 (green line) is a FW process bypassing the DSk phase: (i) ZFC to 2 K, (ii) field increase to 0.2 T, (iii) field decrease to 0 T, (iv) ZFW to 100 K, (v) field increase to 0.025 T, and (vi) FW to 110 K. (D) Field dependence of χ′ at 110 K after FC2 (yellow squares) and FW2 (green line). Black lines show the field-returning runs from high-field ferrimagnetic regions. In (B) and (D), the black lines for FC1 and FW1 and for FC2 and FW2 completely overlap with each other.

  • Fig. 6 LTEM measurements on a (001) thin-plate sample of Co7Zn7Mn6.

    (A) Schematic illustration of the measurement processes. The field-increasing runs at 135 and 50 K after ZFC from room temperature are denoted by pink arrows. The field-decreasing run from 0.4 T to 0 T at 50 K and the subsequent ZFW process are denoted by light blue and red arrows, respectively. (B) Underfocused LTEM images at 135 K and at 0 T and 0.05 T. (C) Underfocused LTEM images at selected fields at 50 K and at selected temperatures in the subsequent ZFW process. Only for the image at 50 K and 0.2 T, the corresponding overfocused image is also shown at right side. The assignment of the LTEM images on each panel is given such as H, SkX, DH, DSk, F, and DSk + DH (mixed state). (D) Color coding of in-plane magnetization (white arrows) deduced from a transport-of-intensity equation analysis for the areas marked with the red dashed square in the underfocused and overfocused images at 50 K and 0.02 T.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/9/eaar7043/DC1

    Section S1. Magnetic properties in (Co0.5Zn0.5)20−xMnx

    Section S2. ZFC process in Co7Zn7Mn6

    Section S3. Field-sweeping processes in Co7Zn7Mn6

    Section S4. FW and FC processes across the spin glass transition temperature in Co7Zn7Mn6

    Section S5. ZFW and FW processes after field sweepings at low temperatures in Co7Zn7Mn6

    Fig. S1. Information of single-crystalline bulk samples of Co7Zn7Mn6.

    Fig. S2. Mn concentration (x) dependence of polycrystalline samples of (Co0.5Zn0.5)20−xMnx.

    Fig. S3. SANS and ac susceptibility measurements in the ZFC process in Co7Zn7Mn6.

    Fig. S4. SANS and ac susceptibility measurements in the field-sweeping process at 146 and 130 K in Co7Zn7Mn6.

    Fig. S5. SANS and ac susceptibility measurements in the field-sweeping process at 100 K in Co7Zn7Mn6.

    Fig. S6. SANS and ac susceptibility measurements in the field-sweeping process at 50 K in Co7Zn7Mn6.

    Fig. S7. SANS and ac susceptibility measurements in the field-sweeping process at 20 K, and the subsequent temperature-sweeping process in Co7Zn7Mn6.

    Fig. S8. Field dependence of the SANS intensities in the H || beam geometry at all the measured temperatures.

    Fig. S9. SANS and ac susceptibility measurements in the ZFW process after the field-decreasing run at 50 K and a subsequent ZFC process in Co7Zn7Mn6.

    Fig. S10. Field-swept ac susceptibility measurements after several warming processes in Co7Zn7Mn6.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Magnetic properties in (Co0.5Zn0.5)20−xMnx
    • Section S2. ZFC process in Co7Zn7Mn6
    • Section S3. Field-sweeping processes in Co7Zn7Mn6
    • Section S4. FW and FC processes across the spin glass transition temperature in Co7Zn7Mn6
    • Section S5. ZFW and FW processes after field sweepings at low temperatures in Co7Zn7Mn6
    • Fig. S1. Information of single-crystalline bulk samples of Co7Zn7Mn6.
    • Fig. S2. Mn concentration (x) dependence of polycrystalline samples of (Co0.5Zn0.5)20−xMnx.
    • Fig. S3. SANS and ac susceptibility measurements in the ZFC process in Co7Zn7Mn6.
    • Fig. S4. SANS and ac susceptibility measurements in the field-sweeping process at 146 and 130 K in Co7Zn7Mn6.
    • Fig. S5. SANS and ac susceptibility measurements in the field-sweeping process at 100 K in Co7Zn7Mn6.
    • Fig. S6. SANS and ac susceptibility measurements in the field-sweeping process at 50 K in Co7Zn7Mn6.
    • Fig. S7. SANS and ac susceptibility measurements in the field-sweeping process at 20 K, and the subsequent temperature-sweeping process in Co7Zn7Mn6.
    • Fig. S8. Field dependence of the SANS intensities in the H || beam geometry at all the measured temperatures.
    • Fig. S9. SANS and ac susceptibility measurements in the ZFW process after the field-decreasing run at 50 K and a subsequent ZFC process in Co7Zn7Mn6.
    • Fig. S10. Field-swept ac susceptibility measurements after several warming processes in Co7Zn7Mn6.

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