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. In this Letter 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 be useful as a language for expressing theoretical models of 3D magnetization textures and specifying a variety of topologically non-trivial initial conditions for micromagnetic simulations.
@article{arxiv.2509.13902,
title = {Three-dimensional magnetization textures as quaternionic functions},
author = {Konstantin L. Metlov and Andrei B. Bogatyrëv},
journal= {arXiv preprint arXiv:2509.13902},
year = {2025}
}