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Abstract
A hedgehog or Bloch point is a point-like 3D magnetization configuration in a ferromagnet. Regardless of widely spread treatment of a Bloch point as a topological defect, its 3D topological charge has never been calculated. Here, applying the concepts of the emergent magnetic field and Dirac string, we calculate the 3D topological charge (Hopf index) of a Bloch point and show that due to the magnetostatic energy contribution it has a finite, non-integer value. Thus, Bloch points form a new class of hopfions—3D topological magnetization configurations. The calculated Bloch point non-zero gyrovector leads to important dynamical consequences such as the appearance of topological Hall effect.
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1 Instituto de Ciencia de Materiales de Madrid, Madrid, Spain (GRID:grid.452504.2) (ISNI:0000 0004 0625 9726)
2 Universidad Politécnica de Madrid, Departamento de Matemática Aplicada a las TIC, ETSIST, Madrid, Spain (GRID:grid.5690.a) (ISNI:0000 0001 2151 2978)
3 Universidad del País Vasco, UPV/EHU, Departamento de Polímeros y Materiales Avanzados, San Sebastián, Spain (GRID:grid.11480.3c) (ISNI:0000000121671098); Ikerbasque, the Basque Foundation for Science, Bilbao, Spain (GRID:grid.424810.b) (ISNI:0000 0004 0467 2314)