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3D Magnetic Textures with Mixed Topology: Unlocking the Tunable Hopf Index

by Maria Azhar, Sandra C. Shaju, Ross Knapman, Alessandro Pignedoli, and Karin Everschor-Sitte

Submission summary

Authors (as registered SciPost users):

Maria Azhar

Abstract

Knots and links play a crucial role in understanding topology and discreteness in nature. In magnetic systems, twisted, knotted and braided vortex tubes manifest as Skyrmions, Hopfions, or screw dislocations. These complex textures are characterized by topologically non-trivial quantities, such as a Skyrmion number, a generalized Hopf index H, a Burgers vector (quantified by an integer ν), and linking numbers. In this work, we introduce a discrete geometric definition of H for periodic magnetic textures, which can be separated into contributions from the self-linking and inter-linking of flux tubes of the emergent magnetic field of non-coplanar textures. We show that fractional Hopfions or textures with non-integer values of H naturally arise and can be interpreted as states of “mixed topology” that are continuously transformable to one of the multiple possible topological sectors. Our findings demonstrate a solid physical foundation for the generalized Hopf index to take integer, non-integer, or specific fractional values, depending on the underlying topology of the flux tubes of the emergent magnetic field of the system.

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