Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8

Journal name:
Nature Materials
Volume:
14,
Pages:
1116–1122
Year published:
DOI:
doi:10.1038/nmat4402
Received
Accepted
Published online

Abstract

Following the early prediction of the skyrmion lattice (SkL)—a periodic array of spin vortices—it has been observed recently in various magnetic crystals mostly with chiral structure. Although non-chiral but polar crystals with Cnv symmetry were identified as ideal SkL hosts in pioneering theoretical studies, this archetype of SkL has remained experimentally unexplored. Here, we report the discovery of a SkL in the polar magnetic semiconductor GaV4S8 with rhombohedral (C3v) symmetry and easy axis anisotropy. The SkL exists over an unusually broad temperature range compared with other bulk crystals and the orientation of the vortices is not controlled by the external magnetic field, but instead confined to the magnetic easy axis. Supporting theory attributes these unique features to a new Néel-type of SkL describable as a superposition of spin cycloids in contrast to the Bloch-type SkL in chiral magnets described in terms of spin helices.

At a glance

Figures

  1. Comparison between Bloch- and Neel-type skyrmions following refs , .
    Figure 1: Comparison between Bloch- and Néel-type skyrmions following refs 4, 6.

    a, In a Bloch-type skyrmion, the spins rotate in the tangential planes—that is, perpendicular to the radial directions—when moving from the core to the periphery. b, In a Néel-type skyrmion, the spins rotate in the radial planes from the core to the periphery. The cross-section of the vortex is also depicted in both cases.

  2. Magnetic phases in the lacunar spinel GaV4S8.
    Figure 2: Magnetic phases in the lacunar spinel GaV4S8.

    a, Topographic image recorded by AFM on the (100) surface of the crystal at T = 11.6K. The colour scale corresponds to the altitude perpendicular to the image plane. Alternating blue and yellow stripes running along the cubic [001] direction are structural domains with different rhombohedral axes, whereas edges along the [010] axis are epilayer terraces. The yellow and white dashed lines highlight a domain boundary and a step between epilayer terraces, respectively. The magnetic patterns in Fig. 3 were recorded within the area of the red square. b, Magnetization curves measured at 12K in B [100], [110] and [111] (shifted vertically for clarity). Magnetization steps are observed at different field values, depending on the orientation. The inset shows the magnetization measured at T = 2K up to B = 1.2T. c, Phase boundaries from df, after projecting the magnetic field onto the easy axis of the corresponding domains. df, Magnetic phase diagrams derived from the field- and the temperature dependence of the magnetization. Circles and squares correspond to peaks in the field- and temperature-derivative of the magnetization curves, respectively. The insets show the orientation of the magnetic field relative to the easy axes of the four rhombohedral domains (cubic body diagonals). The easy axes of magnetically favoured/unfavoured domains are indicated by thick/thin green lines. For B [111], besides the cycloidal and the SkL states, there are two additional phases extending up to higher fields, labelled as the cycloidal and the SkL states.

  3. Real-space imaging of the magnetic patterns in GaV4S8.
    Figure 3: Real-space imaging of the magnetic patterns in GaV4S8.

    a, AFM image recorded at T = 11.2K and in B = 20mT on the (100) surface in the area indicated by the red square in Fig. 2a. Colour coding corresponds to the dissipated power due to magnetic interactions between the tip and the sample. A modulated structure with a single q-vector and a corresponding periodicity of acyc = 17.7 ± 0.4nm is observed on the left side of the domain boundary (yellow dashed line). The weak magnetic contrast does not allow the determination of the magnetic pattern on the other domain. b, Magnetic pattern measured in the same area at T = 11.6K and in B = 50mT. A distorted triangular lattice is observed on the right side of the domain boundary. (See the Supplementary Information for similar images taken at different temperatures and magnetic fields.) The area with red border is scaled by according to the red arrows—that is, perpendicular to the direction of the shortest lattice periodicity. The area, transformed to a square shape after this contraction, is shown in c. c, The green spots indicate a regular triangular SkL with a lattice constant of asky = 22.2 ± 1nm and vortex cores parallel to the [111] axis. For more details about the data analysis and the evolution of the magnetic pattern as a function of magnetic field, see the Supplementary Information. d, Two sections of a hexagonal array of vortex lines running along the [111] axis. The intersections of the vortices with the (111) and (100) planes form a regular and a distorted triangular lattice, respectively.

  4. Small-angle neutron scattering study of the magnetic states in GaV4S8.
    Figure 4: Small-angle neutron scattering study of the magnetic states in GaV4S8.

    ad, SANS images measured at T = 10.9K in various fields for B [111]. The images were recorded at field values representative of the different magnetic states assigned in Fig. 2d. e,f, SANS images taken at T = 10.9K in different magnetic fields for B [100]. Labels refer to the magnetic states assigned in Fig. 2f. The dashed circles having common diameter in all the images help in visualizing the change in the magnitude of the q-vectors. The two colour bars indicate the scattering intensity for the two field orientations.

  5. Tracing the magnetic phase boundaries by SANS.
    Figure 5: Tracing the magnetic phase boundaries by SANS.

    a, Angular dependence of the SANS intensity in various magnetic fields. The sample is rotated together with the magnetic field by an angle ϕ around the horizontal axis (orthogonal to both the scattering vector and the incoming beam). The rocking curves, representing the angular dependence of the total intensity of the Bragg spot, are characterized by a central peak located between ±2° and a flat part. Error bars are determined by assuming Poissonian statistics. b, |q|-dependence of the SANS intensity along [ ] in B = 58mT measured at rotation angles in the central region (red line) and the flat part (black line) of the corresponding rocking curve. The inset shows the difference between the red and black curves. The blue curve is representative of fields larger than B = 60mT, for which the |q|-dependence of the intensity is uniform for all angles between ± 5°. Horizontal bars indicate the instrumental resolution. c,d, The scattering intensity (upper part) and the magnetic periodicity, a = 2π/ |q|, (lower part) as a function of field for the two magnetic field orientations. Vertical dashed lines indicate the phase boundaries according to Fig. 2d, f. For B [100], the total scattering intensity summed over the Bragg spots is shown. For B [111], the intensity of the [ ] Bragg spot is plotted for the central region (red line) and the flat part (black line) of the rocking curve. As exemplified in b for B = 58mT, the splitting of the Bragg spot into two peaks with different |q| was resolved in the field range B = 30–60mT, which arises from the coexistence of cycloidal and SkL states in different rhombohedral domains. This splitting is emphasized by using open symbols over the corresponding field range.

  6. Spin patterns in the magnetic phases of GaV4S8.
    Figure 6: Spin patterns in the magnetic phases of GaV4S8.

    a, FCC lattice of V4 units, each carrying a spin 1/2, and the orientation of the Dzyaloshinskii–Moriya vectors for bonds on the triangular lattice within the (111) plane (chosen as the xy plane in the calculation). b, Cycloidal spin state obtained for the spin model in equation (1) on the triangular lattice in zero magnetic field. The colour coding indicates the out-of-plane components of the spins. c, Magnified view of the magnetization configuration for the cycloidal state. The arrows correspond to the in-plane components of the spins at every second site of the triangular lattice. (The remainder of the sites are not shown to reduce the density of the arrows and preserve the clarity of the figure.) d, Bragg peaks (q-vectors) of the cycloidal state in b in reciprocal space. e, SkL state obtained for the spin model in equation (1) on the triangular lattice for B/J = 0.08 along the z axis. The colour coding is the same as in b. f, Magnified view of the magnetization configuration for the SkL state clearly shows the Néel-type domain wall alignment. Note that the magnetization points opposite to the magnetic field in the core region of the skyrmions. (Similarly to c, only every second spin is shown.) g, Bragg peaks of the SkL state in e. The q-vectors of first-order Bragg peaks are located along the left fence1 0right fence directions (white lines) in the hard plane, for both the cycloidal and SkL states.

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Author information

Affiliations

  1. Department of Physics, Budapest University of Technology and Economics and MTA-BME Lendület Magneto-optical Spectroscopy Research Group, 1111 Budapest, Hungary

    • I. Kézsmárki &
    • S. Bordács
  2. Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany

    • I. Kézsmárki,
    • D. Ehlers,
    • V. Tsurkan &
    • A. Loidl
  3. Institut für Angewandte Photophysik, TU Dresden, D-01069 Dresden, Germany

    • P. Milde,
    • E. Neuber &
    • L. M. Eng
  4. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen, Switzerland

    • J. S. White
  5. Laboratory for Quantum Magnetism, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

    • H. M. Rønnow
  6. Institut Laue-Langevin, 6 rue Jules Horowitz 38042 Grenoble, France

    • C. D. Dewhurst
  7. Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara, Kanagawa 229-8558, Japan

    • M. Mochizuki &
    • K. Yanai
  8. PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan

    • M. Mochizuki
  9. Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan

    • H. Nakamura
  10. Institute of Applied Physics, Academy of Sciences of Moldova, MD 2028, Chisinau, Republica Moldova

    • V. Tsurkan

Contributions

I.K., S.B., P.M., E.N., L.M.E., J.S.W., C.D.D., D.E. and V.T. performed the measurements; I.K., S.B., P.M., E.N., H.M.R., J.S.W. and A.L. analysed the data; V.T. and H.N. contributed to the sample preparation; M.M. and K.Y. developed the theory; I.K. wrote the manuscript and planned the project.

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