Английская Википедия:Hopfion

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

A hopfion is a topological soliton. 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

<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, superconductivity and magnetism.

Experimental observation

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

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

See also

• Skyrmion
• Hopf fibration

External links

• Шаблон:Cite web