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Durham University

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Publication details for Paul Sutcliffe

Sutcliffe, P.M. (2018). Hopfions. In Ludwig Faddeev Memorial Volume: A Life in Mathematical Physics. Ge, M., Niemi, A., Phua, K.K. & Takhtajan, L.A. New Jersey: World Scientific. 539-547.

Author(s) from Durham


More than 40 years ago, Faddeev proposed the existence of three-dimensional topological solitons classified by the integer-valued Hopf invariant. These solitons are now known as hopfions and have been investigated in a range of systems, including the original model suggested by Faddeev, where a variety of stable knot and link solutions have been computed numerically. Very recently, numerical computations have predicted the existence of nanoscale hopfions in frustrated magnets and experiments have realized micrometer-sized hopfions in chiral ferromagnetic fluids. All these examples of hopfions will be described and their similarities and differences discussed.