Research ArticleCONDENSED MATTER PHYSICS

Multiple-q noncollinear magnetism in an itinerant hexagonal magnet

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Science Advances  16 Nov 2018:
Vol. 4, no. 11, eaau3402
DOI: 10.1126/sciadv.aau3402
  • Fig. 1 Structural/magnetic properties and temperature dependence of SANS patterns for Y3Co8Sn4.

    (A) Crystal structure of Y3Co8Sn4. (B) Magnetic field dependence of the magnetization measured under H || Embedded Image (red) and H || [001] (black) at 2 K. (C) Temperature dependence of magnetic susceptibility (M/H at μ0H = 0.02 T) for H || [001]. (D and E) The integrated scattering intensity and the magnitude of the wave number for the two types of magnetic reflection, qout and qin, as a function of temperature obtained from SANS profiles. (F) Schematic illustration of the experimental geometry for SANS measurement. kin and kout are the incident and scattered neutron wave vectors, respectively. (G to J) SANS patterns measured for the (001) plane at zero magnetic field at various temperatures. The color scale indicates the scattering intensity. The integrated intensities in (D) are taken from the boxed area shown in (J). a.u., arbitrary units; f.u., formula unit.

  • Fig. 2 Magnetic field dependence of SANS patterns for Y3Co8Sn4.

    (A to H) SANS patterns taken at 1.5 K with various magnitudes of magnetic field for H || [001] (A to D) and H || Embedded Image (E to H). The color scale indicates the scattering intensity. (I to L) The scattering intensity and the magnitude of the wave number for two magnetic reflections qout and qin as a function of magnetic field, measured for H || [001] (I and J) and H || Embedded Image (K and L).

  • Fig. 3 Polarized SANS study of the modulated magnetic states at zero field.

    (A and B) Polarized SANS patterns of (A) SF and (B) NSF channels measured at 1.5 K under zero magnetic field, which detects in-plane and out-of-plane spin components (Sxy and Sz), respectively. The color represents the scattering intensity. (C and D) Schematic illustration of (C) experimental setup and (D) the magnetic scattering selection rules. Only a local magnetization normal to q can give rise to magnetic neutron scattering. The additional selection rules provided by the longitudinal polarized beam geometry are that SF scattering arises due to Sxy spin components perpendicular to both q and kin (red arrow) and that NSF scattering arises due to Sz components || kin (blue arrow). Here, Sn represents the direction of the neutron polarization, which can be chosen experimentally to be either aligned or anti-aligned with kin. (E and F) Temperature variations of the scattering intensity of SF and NSF channels (corresponding to Sxy and Sz, respectively) for (E) qout and (F) qin. The data were integrated over the same detector regions, as shown in Fig. 1J.

  • Fig. 4 Magnetic phases in Y3Co8Sn4.

    (A and B) H-T magnetic phase diagrams derived from the field and the temperature dependence of the SANS intensity under (A) H || [001] and (B) H || Embedded Image. (C) Triple-q spin configuration obtained by simulated annealing based on the model described by eq. S5, with the parameters α = 0.4 and K = 1.5 (Embedded Image). Arrows represent the xy components of the magnetic moment. (D) Simulated SANS patterns corresponding to (C), with the color indicating the square root of the spin structure factor in arbitrary units. Hexagons in (C) and (D) represent the magnetic unit cell and first Brillouin zone, respectively.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau3402/DC1

    Section S1. SANS investigation of qin under in-plane magnetic field

    Section S2. Theoretical simulation of spin configuration

    Section S3. Crystal characterization

    Section S4. Band structure calculation

    Section S5. Neutron diffraction of ferromagnetic phase

    Fig. S1. Magnetic field dependence of SANS patterns for Y3Co8Sn4 under in-plane H.

    Fig. S2. Theoretical simulation for spin textures in the itinerant hexagonal magnet.

    Fig. S3. Directional preference of magnetic modulation vector under in-plane magnetic field.

    Fig. S4. Room temperature powder x-ray diffraction pattern of Y3Co8Sn4.

    Fig. S5. Band structure and electronic density of states for Y3Co8Sn4.

    Fig. S6. Temperature dependence of the magnetic contribution for the integrated (100) peak intensity at zero field.

    References (3739)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. SANS investigation of qin under in-plane magnetic field
    • Section S2. Theoretical simulation of spin configuration
    • Section S3. Crystal characterization
    • Section S4. Band structure calculation
    • Section S5. Neutron diffraction of ferromagnetic phase
    • Fig. S1. Magnetic field dependence of SANS patterns for Y3Co8Sn4 under in-plane H.
    • Fig. S2. Theoretical simulation for spin textures in the itinerant hexagonal magnet.
    • Fig. S3. Directional preference of magnetic modulation vector under in-plane magnetic field.
    • Fig. S4. Room temperature powder x-ray diffraction pattern of Y3Co8Sn4.
    • Fig. S5. Band structure and electronic density of states for Y3Co8Sn4.
    • Fig. S6. Temperature dependence of the magnetic contribution for the integrated (100) peak intensity at zero field.
    • References (3739)

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