Английская Википедия:Hopfion
A hopfion is a topological soliton.[1][2][3] It is a stable three-dimensional localised configuration of a three-component field <math>\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>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
External links
- ↑ 1,0 1,1 Шаблон:Cite journal
- ↑ Шаблон:Cite book
- ↑ 3,0 3,1 Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite arXiv
- ↑ Шаблон:Cite journal
- ↑ https://newscenter.lbl.gov/2021/04/08/spintronics-tech-a-hopfion-away/ The Spintronics Technology Revolution Could Be Just a Hopfion Away – ALS News
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal