PreprintCC BY 4.0arXiv
Uniqueness and radial symmetry of magnetic skyrmions
Abstract
This paper establishes radial symmetry and uniqueness of magnetic skyrmions as global minimizers of the simplest local micromagnetic energy. The strategy is to show that any radial critical point with strictly decreasing out-of-plane component is the unique minimizer in the class of general degree-one maps with the prescribed limit at infinity. To this end, we identify a class of null Lagrangians that is sufficiently flexible to contain a calibration, giving a uniform lower bound for the energy that is uniquely saturated on the critical point. Our arguments provide a blueprint for proofs of symmetry and uniqueness of minimizers in vectorial variational problems under topological constraints.
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BibTeX
@misc{fratta2026uniqueness,
title = {{Uniqueness and radial symmetry of magnetic skyrmions}},
author = {Giovanni Di Fratta and Cyrill B. Muratov and Theresa M. Simon and Valeriy V. Slastikov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02141},
eprint = {2611.02141},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02141},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniqueness and radial symmetry of magnetic skyrmions
AU - Giovanni Di Fratta
AU - Cyrill B. Muratov
AU - Theresa M. Simon
AU - Valeriy V. Slastikov
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02141
UR - https://arxiv.org/abs/2611.02141
AB - This paper establishes radial symmetry and uniqueness of magnetic skyrmions as global minimizers of the simplest local micromagnetic energy. The strategy is to show that any radial critical point with strictly decreasing out-of-plane component is the unique minimizer in the class of general degree-one maps with the prescribed limit at infinity. To this end, we identify a class of null Lagrangians that is sufficiently flexible to contain a calibration, giving a uniform lower bound for the energy that is uniquely saturated on the critical point. Our arguments provide a blueprint for proofs of symmetry and uniqueness of minimizers in vectorial variational problems under topological constraints.
ER -