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Emergent magnetic field and vector potential of the toroidal magnetic hopfions

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  • Guslienko, Konstantin Y.

Abstract

Magnetic hopfions are localized magnetic solitons with non-zero 3D topological charge (Hopf index). Here I present an analytical calculation of the toroidal magnetic hopfion vector potential, emergent magnetic field, the Hopf index, and the magnetization configuration. The calculation method is based on the concept of the spinor representation of the Hopf mapping. The hopfions with arbitrary values of the azimuthal and poloidal vorticities are considered. The special role of the toroidal coordinates and their connection with the emergent vector potential gauge are demonstrated. The hopfion magnetization field is found explicitly for the arbitrary Hopf indices. It is shown that the Hopf charge density can be represented as a Jacobian of the transformation from the toroidal to the cylindrical coordinates.

Suggested Citation

  • Guslienko, Konstantin Y., 2023. "Emergent magnetic field and vector potential of the toroidal magnetic hopfions," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007415
    DOI: 10.1016/j.chaos.2023.113840
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    References listed on IDEAS

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    3. I. Luk’yanchuk & Y. Tikhonov & A. Razumnaya & V. M. Vinokur, 2020. "Hopfions emerge in ferroelectrics," Nature Communications, Nature, vol. 11(1), pages 1-7, December.
    4. Noah Kent & Neal Reynolds & David Raftrey & Ian T. G. Campbell & Selven Virasawmy & Scott Dhuey & Rajesh V. Chopdekar & Aurelio Hierro-Rodriguez & Andrea Sorrentino & Eva Pereiro & Salvador Ferrer & F, 2021. "Creation and observation of Hopfions in magnetic multilayer systems," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
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