Physics:Hopfion
A hopfion is a topological soliton.[1][2][3] It is a stable three-dimensional localised configuration of a three-component field [math]\displaystyle{ \vec{n}=(n_x,n_y,n_z) }[/math] with a knotted topological structure. They are the three-dimensional counterparts of skyrmions, which exhibit similar topological properties in 2D.
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]
[math]\displaystyle{ H= (\partial {\bf n})^2 + (\epsilon_{ijk}{\bf n}\cdot\partial_i {\bf n}\times \partial_j{\bf n})^2 }[/math]
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
- ↑ 1.0 1.1 "Stable knot-like structures in classical field theory". Nature 387 (6628): 58–61. 1997. doi:10.1038/387058a0. Bibcode: 1997Natur.387...58F.
- ↑ Topological solitons. Cambridge: Cambridge University Press. 2004. doi:10.1017/CBO9780511617034. ISBN 0-511-21141-4. OCLC 144618426.
- ↑ 3.0 3.1 "Creation and observation of Hopfions in magnetic multilayer systems". Nature Communications 12 (1): 1562. March 2021. doi:10.1038/s41467-021-21846-5. PMID 33692363. Bibcode: 2021NatCo..12.1562K.
- ↑ "Partially Dual Variables in SU(2) Yang-Mills Theory". Physical Review Letters 82 (8): 1624–1627. 1999. doi:10.1103/PhysRevLett.82.1624. Bibcode: 1999PhRvL..82.1624F.
- ↑ "Hidden symmetry and knot solitons in a charged two-condensate Bose system". Physical Review B 65 (10): 100512. 2002. doi:10.1103/PhysRevB.65.100512. Bibcode: 2002PhRvB..65j0512B.
- ↑ "Stable Hopf-Skyrme topological excitations in the superconducting state". Physical Review B 100 (9): 094515. 2019. doi:10.1103/PhysRevB.100.094515. Bibcode: 2019PhRvB.100i4515R.
- ↑ "Skyrmion Knots in Frustrated Magnets". Physical Review Letters 118 (24): 247203. June 2017. doi:10.1103/PhysRevLett.118.247203. PMID 28665663. Bibcode: 2017PhRvL.118x7203S.
- ↑ Rybakov FN, Kiselev NS, Borisov AB, Döring L, Melcher C, Blügel S (2019). "Magnetic hopfions in solids". arXiv:1904.00250 [cond-mat.str-el].
- ↑ "Hopf Solitons in Helical and Conical Backgrounds of Chiral Magnetic Solids". Physical Review Letters 125 (5): 057201. July 2020. doi:10.1103/PhysRevLett.125.057201. PMID 32794865. Bibcode: 2020PhRvL.125e7201V.
- ↑ https://newscenter.lbl.gov/2021/04/08/spintronics-tech-a-hopfion-away/ The Spintronics Technology Revolution Could Be Just a Hopfion Away – ALS News
- ↑ "Creation and observation of Hopfions in magnetic multilayer systems". Nature Communications 12 (1): 1562. March 2021. doi:10.1038/s41467-021-21846-5. PMID 33692363. Bibcode: 2021NatCo..12.1562K.
- ↑ "Particle-like topologies in light". Nature Communications 12 (1): 6785. November 2021. doi:10.1038/s41467-021-26171-5. PMID 34811373.
- ↑ Ehrmanntraut, Daniel; Droop, Ramon; Sugic, Danica; Otte, Eileen; Dennis, Mark; Denz, Cornelia (June 2023). "Optical second-order skyrmionic hopfion". Optica 10 (6): 725-731. https://doi.org/10.1364/OPTICA.487989.
- ↑ 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. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.057201.
- ↑ 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" (in en). Advanced Materials 35 (20). doi:10.1002/adma.202210646. ISSN 0935-9648. https://onlinelibrary.wiley.com/doi/full/10.1002/adma.202210646.
- ↑ 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. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.157204.
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