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arXiv · 2509.13902

Three-dimensional magnetization textures as quaternionic functions

Konstantin L. Metlov·Andrei B. Bogatyrëv
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Abstract

Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications. Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and reason about. Here we build analytical representation for such a textures (with arbitrary number of singularity-free hopfions and singular Bloch point pairs) as products of simple quaternionic functions. It can serve as a language for expressing theoretical models of 3D magnetization textures and specifying a variety of topologically non-trivial initial conditions for micromagnetic simulations. It also follows from the quaternion algebra properties that three dimensional magnetic states can potentially be useful for implementing topological quantum computation.

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Konstantin L. Metlov, Andrei B. Bogatyrëv. 2025-09-17. Three-dimensional magnetization textures as quaternionic functions. https://doi.org/10.1002/andp.70234

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