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Effect of boundary-induced chirality on magnetic textures in thin films

Jeroen Mulkers, Kjetil M. D. Hals, Jonathan Leliaert, Milorad V. Milošević, Bartel Van Waeyenberge, and Karin Everschor-Sitte
Phys. Rev. B 98, 064429 – Published 31 August 2018
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  • INTRODUCTION
  • MODEL AND METHODS
  • QUASIUNIFORM STATE
  • EDGE CANTING
  • ISOLATED DOMAIN WALL
  • ISOLATED SKYRMION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    In the quest for miniaturizing magnetic devices, the effects of boundaries and surfaces become increasingly important. Here we show how the recently predicted boundary-induced Dzyaloshinskii-Moriya interaction (DMI) affects the magnetization of ferromagnetic films with a C∞v symmetry and a perpendicular magnetic anisotropy. For an otherwise uniformly magnetized film, we find a surface twist when the magnetization in the bulk is canted by an in-plane external field. This twist at the surfaces caused by the boundary-induced DMI differs from the common canting caused by internal DMI observed at the edges of a chiral magnet. Furthermore, we find that the surface twist due to the boundary-induced DMI strongly affects the width of the domain wall at the surfaces. We also find that the skyrmion radius increases in the depth of the film, with the average size of the skyrmion increasing with boundary-induced DMI. This increase suggests that the boundary-induced DMI contributes to the stability of the skyrmion.

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    • Received 30 May 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.064429

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Domain wallsMicromagnetismSkyrmions
    1. Physical Systems
    Chiral magnets
    1. Techniques
    Micromagnetic modeling
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Jeroen Mulkers1,2,*, Kjetil M. D. Hals3,4, Jonathan Leliaert2, Milorad V. Milošević1,†, Bartel Van Waeyenberge2, and Karin Everschor-Sitte3

    • 1Department of Physics, University of Antwerp, B-2020 Antwerp, Belgium
    • 2DyNaMat, Department of Solid State Sciences, Ghent University, B-9000 Ghent, Belgium
    • 3Institute of Physics, Johannes Gutenberg Universität, 55128 Mainz, Germany
    • 4Department of Engineering and Science, University of Agder, 4879 Grimstad, Norway

    • *jeroen.mulkers@uantwerpen.be
    • †milorad.milosevic@uantwerpen.be

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    Issue

    Vol. 98, Iss. 6 — 1 August 2018

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    Images

    • Figure 1
      Figure 1

      Cross section of a skyrmion in an extended film with boundary-induced DMI (DS≠0) at the top and bottom surface, and without boundary-induced DMI (DS=0). Both systems are shown on the same scale. The dark contours represent isomagnetizations.

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    • Figure 2
      Figure 2

      (a) Out-of-plane magnetization mz at the top surface (blue), the bottom surface (red), and in the bulk (black) of a very thick film as a function of an external in-plane field hêx for symmetric DMI parameter DS=0.5Dc (solid line) and DS=0.2Dc (dashed line). (b) The magnetization profile mz(z) near the top and near the bottom surface of a thick film for an external in-plane field h=0.6hc. The surface is positioned at z=0 in both cases. The same coloring and line style is used as in (a). The dots in two panels denote the same top and bottom surface magnetization.

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    • Figure 3
      Figure 3

      (a) The magnetization profile mz(z)=sinψ(z) in films of different thickness d, for symmetric DMI parameter DS=0.5Dc, and in-plane field h=0.6hc, obtained after a numerical minimization of the free energy. The inset shows a sketch of the magnetization exhibiting surface twists in a film with finite thickness d. (b) The magnetization at the top (bottom) surface as a function of the film thickness d. Dashed lines represent the asymptotic values for d→∞, which were calculated analytically.

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    • Figure 4
      Figure 4

      Exemplary cross sections of the magnetization in a thin film, for the three different cases in which surface twists occur. (a) Quasiuniform state in a laterally infinite film with an applied field Hext=0.5hcêx. (b) Canting at a sample edge without applied field. (c) Domain wall in a laterally infinite film without applied field. In all cases, the film has a thickness d=5ξ, a symmetric DMI parameter DS=0.6Dc, and an asymmetric DMI parameter DA=0.9Dc. The color represents the angular difference Δψ with the magnetization in absence of the boundary-induced DMI (DS=0). The distance between the indicated lines in (c) is the domain wall width W(z) for DS=0.6Dc (solid line) and for DS=0 (dotted line).

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    • Figure 5
      Figure 5

      The average domain wall width W and the domain wall width at the top Wt and bottom Wb of a thin film with symmetric DMI strength DS=0.5Dc (solid line) and DS=0.6Dc (dashed line), as a function of its thickness d.

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    • Figure 6
      Figure 6

      Skyrmion profile in a film with DMI strength DA=0.8Dc and thickness d=2ξ (a) without boundary-induced DMI, and (b) with boundary-induced DMI DS=0.5Dc, and (c) DS=−0.5Dc. A 3D representation of the deformed skyrmion is readily shown in Fig. 1.

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    • Figure 7
      Figure 7

      The radius R0(z) of an isolated skyrmion in a film with thickness d increases monotonically from the top (solid line) to the bottom surface (dashed line). The skyrmion size at the top and the bottom surface are shown as function of the boundary-induced DMI DS (horizontal axis) and the bulk DMI DA (color). The dotted reference line is the skyrmion size in absence of boundary-induced DMI (DS=0).

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