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Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids

Nature Materials volume 16, pages 426–432 (2017)Cite this article

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Abstract

Three-dimensional (3D) topological solitons are continuous but topologically nontrivial field configurations localized in 3D space and embedded in a uniform far-field background, that behave like particles and cannot be transformed to a uniform state through smooth deformations. Many topologically nontrivial 3D solitonic fields have been proposed. Yet, according to the Hobart–Derrick theorem, physical systems cannot host them, except for nonlinear theories with higher-order derivatives such as the Skyrme–Faddeev model. Experimental discovery of such solitons is hindered by the need for spatial imaging of the 3D fields, which is difficult in high-energy physics and cosmology. Here we experimentally realize and numerically model stationary topological solitons in a fluid chiral ferromagnet formed by colloidal dispersions of magnetic nanoplates. Such solitons have closed-loop preimages—3D regions with a single orientation of the magnetization field. We discuss localized structures with different linking of preimages quantified by topological Hopf invariants. The chirality is found to help in overcoming the constraints of the Hobart–Derrick theorem, like in two-dimensional ferromagnetic solitons, dubbed ‘baby skyrmions’. Our experimental platform may lead to solitonic condensed matter phases and technological applications.

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Figure 1: 2D and 3D topological solitons.
Figure 2: 3D imaging of topological solitons using 3PEF-PM.
Figure 3: Topological solitons with Q = 1.
Figure 4: Comparison of Q = −1 and Q = 0 solitons.
Figure 5: Twist handedness, free energy density self-assembly and facile switching of hexagonal arrays for Q = 1 topological solitons.

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Acknowledgements

We thank Q. Liu for the assistance with synthesizing ferromagnetic nanoplates and H. O. Sohn and Q. Zhang for discussions. We acknowledge support of the National Science Foundation Grant DMR-1410735.

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Authors and Affiliations

  1. Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

    Paul J. Ackerman & Ivan I. Smalyukh

  2. Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA

    Paul J. Ackerman & Ivan I. Smalyukh

  3. Soft Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA

    Ivan I. Smalyukh

  4. Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA

    Ivan I. Smalyukh

Authors
  1. Paul J. Ackerman
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P.J.A. and I.I.S. contributed to all aspects of this work and wrote the manuscript. I.I.S. conceived and designed the project.

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Correspondence to Ivan I. Smalyukh.

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The authors declare no competing financial interests.

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Ackerman, P., Smalyukh, I. Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids. Nature Mater 16, 426–432 (2017). https://doi.org/10.1038/nmat4826

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