arXiv subjects

Andrei B. Bogatyrëv

Publications and source records attributed to Andrei B. Bogatyrëv.

4 recordsLinked to original sources

arXiv2026

Three-dimensional magnetization textures as quaternionic functions

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.

cond-mat.mes-hall↗

arXiv2018

Metastable states of sub-micron scale ferromagnetic periodic antidot arrays

The magnetic textures on nanoscale possess topological features due to the continuity of the magnetization vector field and its boundary conditions. In thin planar nanoelements, where the dependence of the magnetization across the thickness is inessential, the textures can be represented as a soup of 2-d topological solitons, corresponding to magnetic vortices and antivortices, which are the solutions of Skyrme's model. Topology of the element (of the boundary conditions) then imposes the restrictions on properties and locations of these objects. Periodic arrays of magnetic antidots have topology with infinite connectivity. In this work we classify and build an approximate analytical representation of metastable magnetization textures in such arrays and prove the conservation of their topological charge.

cond-mat.mes-hall↗

arXiv2018

What makes magnetic skyrmions different from magnetic bubbles ?

A large enough piece of ferromagnet is usually not magnetized uniformly, but develops a magnetization texture. In thin films these textures can be doubly-periodic. Such are the well known magnetic bubble domains and the recently observed "skyrmion" magnetization textures in MnSi. In this paper we develop a theory of periodic magnetization textures, based on complex calculus to answer the question -- is there a difference between those two textures even if they seem to carry the same topological winding number (or topological charge) ? We find that such difference exists, facilitated by a different role played by the magnetization vector's in-plane phase. We separate classical-like and quantum-like features of magnetization textures and highlight the role of magnetic anisotropy in favouring either of these cases.

cond-mat.mes-hall↗

arXiv2016

Topological constraints on positions of magnetic solitons in multiply-connected planar magnetic nano-elements

Here we consider an interplay between the topology of the magnetization texture (which is a topological soliton, or Skyrmion) in a planar magnetic nano-element and the topology of the element itself (its connectivity). We establish the existence of a set of constraints, coupling these topologies, which are specific for multiply connected elements and are absent in simply-connected case. As an example, a specific constraint is derived for a case of planar ring magnet, relating the angular positions of magnetic vortices and antivortices inside. We analyze the recent experimental data on the vortex magnetic domain walls in the ring to validate our findings.

cond-mat.mes-hall↗