We propose a generalization of the theory of magnetic Skyrmions in chiral magnets in two dimensions to a higher-dimensional theory with magnetic Skyrmions in three dimensions and an S3 target space, requiring a 4-dimensional magnetization vector. A physical realization of our theory could be made using a synthetic dimension, recently promoted and realized in condensed matter physics. In the simplest incarnation of the theory, we find a Skyrmion and a sphaleron - the latter being an unstable soliton. Including also the Skyrme term in the theory enriches the spectrum to a small metastable Skyrmion, an unstable sphaleron and a large stable Skyrmion.
@article{arxiv.2411.12190,
title = {Higher-dimensional magnetic Skyrmions},
author = {Sven Bjarke Gudnason and Stefano Bolognesi and Roberto Menta},
journal= {arXiv preprint arXiv:2411.12190},
year = {2025}
}