Hopfion

A hopfion is a topological soliton.[1][2][3] It is a stable three-dimensional localised configuration of a three-component field with a knotted topological structure. They are the three-dimensional counterparts of skyrmions, which exhibit similar topological properties in 2D.

Model of magnetic hopfion in a solid. Bem is emergent magnetic field (orange arrows); in a hopfion, it does not align to the external magnetic field (black arrow).

The soliton is mobile and stable: i.e. it is protected from a decay by an energy barrier. It can be deformed but always conserves an integer Hopf topological invariant. It is named after the German mathematician, Heinz Hopf.

A model that supports hopfions was proposed as follows[1]

The terms of higher-order derivatives are required to stabilize the hopfions.

Stable hopfions were predicted within various physical platforms, including Yang-Mills theory,[4] superconductivity[5][6] and magnetism.[7][8][9][3]

Experimental observation

Hopfions have been observed experimentally[10] in Ir/Co/Pt multilayers using X-ray magnetic circular dichroism[11] and in the polarization of free-space monochromatic light.[12][13]

In chiral magnets, the hopfion has been theoretically predicted to occur within the spiral magnetic phase, where it was called a "heliknoton".[14] In recent years, the concept of a "fractional hopfion" has also emerged where not all preimages of magnetisation have a nonzero linking.[15][16]

See also

References
  1. Faddeev L, Niemi AJ (1997). "Stable knot-like structures in classical field theory". Nature. 387 (6628): 58–61. arXiv:hep-th/9610193. Bibcode:1997Natur.387...58F. doi:10.1038/387058a0. S2CID 4256682.
  2. Manton N, Sutcliffe P (2004). Topological solitons. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511617034. ISBN 0-511-21141-4. OCLC 144618426.
  3. Kent N, Reynolds N, Raftrey D, Campbell IT, Virasawmy S, Dhuey S, et al. (March 2021). "Creation and observation of Hopfions in magnetic multilayer systems". Nature Communications. 12 (1): 1562. arXiv:2010.08674. Bibcode:2021NatCo..12.1562K. doi:10.1038/s41467-021-21846-5. PMC 7946913. PMID 33692363.
  4. Faddeev L, Niemi AJ (1999). "Partially Dual Variables in SU(2) Yang-Mills Theory". Physical Review Letters. 82 (8): 1624–1627. arXiv:hep-th/9807069. Bibcode:1999PhRvL..82.1624F. doi:10.1103/PhysRevLett.82.1624. S2CID 8281134.
  5. - Babaev E, Faddeev LD, Niemi AJ (2002). "Hidden symmetry and knot solitons in a charged two-condensate Bose system". Physical Review B. 65 (10): 100512. arXiv:cond-mat/0106152. Bibcode:2002PhRvB..65j0512B. doi:10.1103/PhysRevB.65.100512. S2CID 118910995.
  6. Rybakov FN, Garaud J, Babaev E (2019). "Stable Hopf-Skyrme topological excitations in the superconducting state". Physical Review B. 100 (9): 094515. arXiv:1807.02509. Bibcode:2019PhRvB.100i4515R. doi:10.1103/PhysRevB.100.094515. S2CID 118991170.
  7. Sutcliffe P (June 2017). "Skyrmion Knots in Frustrated Magnets". Physical Review Letters. 118 (24): 247203. arXiv:1705.10966. Bibcode:2017PhRvL.118x7203S. doi:10.1103/PhysRevLett.118.247203. PMID 28665663. S2CID 29890978.
  8. Rybakov FN, Kiselev NS, Borisov AB, Döring L, Melcher C, Blügel S (2019). "Magnetic hopfions in solids". arXiv:1904.00250 [cond-mat.str-el].
  9. Voinescu R, Tai JB, Smalyukh II (July 2020). "Hopf Solitons in Helical and Conical Backgrounds of Chiral Magnetic Solids". Physical Review Letters. 125 (5): 057201. arXiv:2004.10109. Bibcode:2020PhRvL.125e7201V. doi:10.1103/PhysRevLett.125.057201. PMID 32794865. S2CID 216036015.
  10. https://newscenter.lbl.gov/2021/04/08/spintronics-tech-a-hopfion-away/ The Spintronics Technology Revolution Could Be Just a Hopfion Away – ALS News
  11. Kent N, Reynolds N, Raftrey D, Campbell IT, Virasawmy S, Dhuey S, et al. (March 2021). "Creation and observation of Hopfions in magnetic multilayer systems". Nature Communications. 12 (1): 1562. arXiv:2010.08674. Bibcode:2021NatCo..12.1562K. doi:10.1038/s41467-021-21846-5. PMC 7946913. PMID 33692363.
  12. Sugic D, Droop R, Otte E, Ehrmanntraut D, Nori F, Ruostekoski J, et al. (November 2021). "Particle-like topologies in light". Nature Communications. 12 (1): 6785. doi:10.1038/s41467-021-26171-5. PMC 8608860. PMID 34811373.
  13. Ehrmanntraut, Daniel; Droop, Ramon; Sugic, Danica; Otte, Eileen; Dennis, Mark; Denz, Cornelia (June 2023). "Optical second-order skyrmionic hopfion". Optica. 10 (6): 725–731 – via Optica publishing group.
  14. Voinescu, Robert; Tai, Jung-Shen B.; Smalyukh, Ivan I. (27 July 2020). "Hopf Solitons in Helical and Conical Backgrounds of Chiral Magnetic Solids". Physical Review Letters. 125 (5): 057201. doi:10.1103/PhysRevLett.125.057201.
  15. Yu, Xiuzhen; Liu, Yizhou; Iakoubovskii, Konstantin V.; Nakajima, Kiyomi; Kanazawa, Naoya; Nagaosa, Naoto; Tokura, Yoshinori (May 2023). "Realization and Current‐Driven Dynamics of Fractional Hopfions and Their Ensembles in a Helimagnet FeGe". Advanced Materials. 35 (20). doi:10.1002/adma.202210646. ISSN 0935-9648.
  16. Azhar, Maria; Kravchuk, Volodymyr P.; Garst, Markus (12 April 2022). "Screw Dislocations in Chiral Magnets". Physical Review Letters. 128 (15): 157204. doi:10.1103/PhysRevLett.128.157204.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.