Three-dimensional magnetization textures as quaternionic functions

Annalen der Physik. 2026. Vol. 538. No. 6. Article e70234.

Metlov K., Andrei B. Bogatyrëv

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.

Keywords: topological solitons, Bloch points, hopfions, micromagnetics