IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923007415.html
   My bibliography  Save this article

Emergent magnetic field and vector potential of the toroidal magnetic hopfions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923007415
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113840?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. L. Faddeev & Antti J. Niemi, 1997. "Stable knot-like structures in classical field theory," Nature, Nature, vol. 387(6628), pages 58-61, May.
    2. Danica Sugic & Ramon Droop & Eileen Otte & Daniel Ehrmanntraut & Franco Nori & Janne Ruostekoski & Cornelia Denz & Mark R. Dennis, 2021. "Particle-like topologies in light," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hanqing Zhao & Boris A. Malomed & Ivan I. Smalyukh, 2023. "Topological solitonic macromolecules," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    2. Cisternas, Jaime & Concha, Andrés, 2024. "Searching nontrivial magnetic equilibria using the deflated Newton method," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Rahul, O.R. & Murugesh, S., 2019. "Rogue breather modes: Topological sectors, and the ‘belt-trick’, in a one-dimensional ferromagnetic spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 262-269.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007415. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.