Research ArticleELECTROMAGNETISM

Multiferroicity and skyrmions carrying electric polarization in GaV4S8

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Science Advances  13 Nov 2015:
Vol. 1, no. 10, e1500916
DOI: 10.1126/sciadv.1500916
  • Fig. 1 Characterization of dielectric properties.

    (A) Real part of the dielectric constant ε′ measured at frequencies between 1 MHz (open squares) and 2.5 GHz (open triangles down). The electric field E was applied parallel to the crystallographic 〈111〉 direction. (Inset) An enlarged view of the measurements at 2.5 GHz. (B) Electric polarization P versus temperature measured parallel to the 〈111〉 direction. The elongation of the V4 units along the 〈111〉 direction is schematically indicated and contrasted with the orbitally degenerate high-temperature phase. (Inset) Excess polarization at the onset of magnetic order on an enlarged scale.

  • Fig. 2 Magnetic field–versus–temperature phase diagram of GaV4S8 for magnetic fields applied along one of the cubic 〈111〉 axes.

    (A) Low-temperature region below T = 15 K. The magnetic phase boundaries correspond to the unique structural domain whose easy axis is parallel to the magnetic field (for details, see the text). The SkL phase (red area) and the cycloidal phase (green area) are embedded within the FM phase (yellow area). Above TC = 12.7 K, the material is PM. The phase boundaries, as determined from measurements of magnetization, polarization (pyrocurrent and magnetocurrent), and specific heat, are indicated by squares, circles, and triangles, respectively. Full symbols correspond to temperature scans, whereas open symbols represent magnetic field scans. The hatched area characterizes the regime between the PM phase and the cycloidal/SkL phase, where the exact spin structure is unknown. (B) Complete phase diagram extending beyond the Jahn-Teller transition. Below TJT, within the orbitally ordered (OO) phase, four different FE states (FE1 to FE4) are found, each characterized by well-distinguishable polarization.

  • Fig. 3 Anomalies in magnetization, specific heat, and FE polarization at the magnetic phase boundaries.

    (A, C, and E) Magnetic field dependence of magnetization (M) given per formula unit (fu), specific heat (C), and isothermal polarization (ΔP) with H||〈111〉. (B, D, and F) Temperature dependence of magnetization, specific heat, and zero-field polarization. Background colors represent the different magnetic phases (following the color code used in Fig. 2). fu, definition.

  • Fig. 4 FE polarization of GaV4S8 determined from pyrocurrent measurements.

    Polarization as a function of temperature measured in various magnetic fields between 0 and 100 mT. Only the excess polarization ΔP arising upon entry to the magnetic phases at TC = 12.7 K is shown.

  • Fig. 5 FE polarization of GaV4S8 determined from magnetocurrent measurements.

    Magnetic field dependence of isothermal polarization measured at various temperatures between 2 and 13 K. Only the excess polarization ΔP induced by magnetic ordering is shown. A step-like increase in polarization at the transition from the cycloidal phase to the SkL phase and from the SkL phase to the FM phase can be identified in the P(H) curves measured between 7 and 12.5 K. All of the P(H) curves are projected onto the H-P plane, and all phase boundaries are indicated on the H-T plane. The black lines on the H-T plane indicate the same magnetic phase boundaries as in Fig. 2A.

  • Fig. 6 Bond symmetry in the rhombohedrally distorted structure of GaV4S8.

    (A) V4 clusters (red spheres) form an fcc lattice that is stretched along one of the body diagonals (dashed line). Two types of bonds result from this distortion, as illustrated for four selected clusters: intraplane bonds (green lines) between nearest-neighbor V4 units within the (111) planes and interplane bonds (blue lines) connecting V4 units in neighboring (111) planes. (B) The four selected clusters viewed from the 〈111〉 direction. Each blue bond lies within a mirror plane of the tetrahedron (see dashed line for an example), whereas green bonds are perpendicular to them.

  • Fig. 7 Polar dressing of SkL in GaV4S8.

    (A) Spatial dependence of the z component of the S = ½ spins forming the skyrmion and (B) spatial dependence of the spin-driven polarization Pz, both on the xy plane perpendicular to the vortex core. The radius of the skyrmion core ξ sets the lateral length scale. The polarization reaches its maximum in a ring-like region around the skyrmion cores (red regions). The outer blue regions in the polarization indicate the FE polarization of the almost collinear spin arrangement at the outer rims of the skyrmion.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/10/e1500916/DC1

    Sample characterization

    Fig. S1. Sample characterization.

    Hysteresis at the Jahn-Teller transition

    Fig. S2. Hysteresis behavior of magnetic susceptibility.

    Fig. S3. Hysteresis behavior of dielectric constant.

    Maxwell-Wagner relaxation and intrinsic dielectric response

    Fig. S4. Dielectric constant up to 300 K.

    Determination of the ferroelectric polarization

    References (57, 58)

  • Supplementary Materials

    This PDF file includes:

    • Sample characterization
    • Fig. S1. Sample characterization.
    • Hysteresis at the Jahn-Teller transition
    • Fig. S2. Hysteresis behavior of magnetic susceptibility.
    • Fig. S3. Hysteresis behavior of dielectric constant.
    • Maxwell-Wagner relaxation and intrinsic dielectric response
    • Fig. S4. Dielectric constant up to 300 K.
    • Determination of the ferroelectric polarization
    • References (57, 58)

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