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Toggle-switch-like crossover between two types of isolated skyrmions within the conical phase of cubic helimagnets

A. O. Leonov, A. N. Bogdanov, and K. Inoue
Phys. Rev. B 98, 060411(R) – Published 23 August 2018
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    Abstract

    We investigate the field-induced crossover between two types of isolated skyrmions that exist within the conical phase of cubic helimagnets and orient themselves either along or perpendicular to the field. Such a crossover takes place for the same value of the field at which the closely packed skyrmion lattice was predicted to stabilize in the A-phase region. The clusters and a skyrmion lattice composed by the skyrmions perpendicular to the field, however, are unfavorable and lose their stability as compared with the skyrmions parallel to the field. We also followed the transformation of perpendicular skyrmions into pairs of merons that rupture the helical state. Attractive interactions between different types of isolated skyrmions make it feasible to construct complex cluster states with the cubic arrangement of skyrmions.

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    • Received 1 June 2018
    • Revised 19 July 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.060411

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    MicromagnetismSkyrmions
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    A. O. Leonov1,2,3,*, A. N. Bogdanov1,2,3, and K. Inoue1,2

    • 1Chirality Research Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan
    • 2Department of Chemistry, Faculty of Science, Hiroshima University Kagamiyama, Higashi Hiroshima, Hiroshima 739-8526, Japan
    • 3IFW Dresden, Postfach 270016, D-01171 Dresden, Germany

    • *leonov@hiroshima-u.ac.jp

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    Issue

    Vol. 98, Iss. 6 — 1 August 2018

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    Images

    • Figure 1
      Figure 1

      (a) The spin texture of two types of isolated skyrmions (ISs) oriented either along the field (IS-1) or perpendicular to it (IS-2). Whereas (b) IS-1 exhibits an axisymmetric shape, IS-2 acquires a nonaxisymmetric shape with the circular core section centered around point A and the antiskyrmionlike crescent centered around point B.

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    • Figure 2
      Figure 2

      Magnetic structure of IS-1 showing its evolution from the axisymmetric structure for h=0.6 (a), (d) to the non-axisymmetric one within the conical phase for h=0.3 (b), (e) and within the spiral state for zero magnetic field h=0 (c), (f). The color plots in the upper (lower) row indicate a z(y) component of the magnetization, and the black arrows are projections of the magnetization on to the xy(xz) plane. The conical phase has the wave vector co-aligned with the field h∥z.

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    • Figure 3
      Figure 3

      Magnetic structure of IS-2 showing the field-driven evolution for (a) h=0.6 (a pair of IS-2's surrounded by the homogeneous state), (d) h=0.3 (a pair of IS-2's surrounded by the conical phase), and (g) h=0 (a pair of IS-2's surrounded by the spiral state). Whereas one IS-2 for the same orientation of the field as in Fig. 2 transforms into a pair of merons that rupture the spiral state, a pair of IS-2's—transforms into two merons with Q=1/2 and a skyrmion with Q=1. The my component of the magnetization is shown as contour lines in the upper row for different values of the field, whereas the black arrows indicate projections of the magnetization onto the xz plane. Consequent rows (b), (e), and (h) and (c), (f), and (i) exhibit energy density (1) counted with respect to the surrounding phase and the topological charge density, respectively.

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    • Figure 4
      Figure 4

      Energy of IS-1 (red curves) and IS-2 (blue curves) plotted in dependence on the applied magnetic field for two configurations with (a) Q=1 and (b) Q=2. The crossover between two types of isolated skyrmions [point A in (a)] is shifted towards lower fields with adding more skyrmions into skyrmion clusters [point B in (b) for two skyrmions in a cluster]. The dashed and solid lines show the energies of remote skyrmions and coupled skyrmion pairs, correspondingly. (c) Energy densities of SkL-1 and SkL-2. Only SkL-1 can be stabilized by additional anisotropic interactions around the critical field h=0.2 (point C).

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