Three‐Dimensional Magnetization Textures as Quaternionic Functions

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.