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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 𝑛 β†’ = ( 𝑛 π‘₯ , 𝑛 𝑦 , 𝑛 𝑧 ) 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] 𝐻 = ( βˆ‚ 𝑛 ) 2 + ( πœ– 𝑖 𝑗 π‘˜ 𝑛 β‹… βˆ‚ 𝑖 𝑛 Γ— βˆ‚ 𝑗 𝑛 ) 2 The terms of higher-order derivatives are required to stabilize the hopfions. Stable hopfions were predicted within various physical platforms, including Yang–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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