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Hopfion - Wikipedia

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A hopfion is a topological soliton.[1][2][3][4] It is a stable three-dimensional localised configuration of a three-component field ๐‘› โ†’ = ( ๐‘› ๐‘ฅ , ๐‘› ๐‘ฆ , ๐‘› ๐‘ง ) with a knotted topological structure. They are the three-dimensional counterparts of 2D skyrmions, which exhibit similar topological properties in 2D. Hopfions are widely studied in many physical systems over the last half century, as summarized here http://hopfion.com 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] ๐ป = ( โˆ‚ ๐‘› ) 2 + ( ๐œ– ๐‘– ๐‘— ๐‘˜ ๐‘› โ‹… โˆ‚ ๐‘– ๐‘› ร— โˆ‚ ๐‘— ๐‘› ) 2 The terms of higher-order derivatives are required to stabilize the hopfions. Stable hopfions were predicted within various physical platforms, including Yangโ€“Mills theory,[5] superconductivity[6][7] and magnetism.[8][9][

Hopfion - Wikipedia Jump to content From Wikipedia, the free encyclopedia Topological soliton This article may be confusing or unclear to readers . Please help clarify the article . There might be a discussion about this on the talk page . ( November 2024 ) ( Learn how and when to remove this message ) 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 . [ 1 ] [ 2 ] [ 3 ] [ 4 ] It is a stable three-dimensional local

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