Three-Dimensional Shankar Skyrmions in Frustrated Antiferromagnets
Abstract
We formulate a continuum theory for three-dimensional (3D) Shankar skyrmions in frustrated chiral antiferromagnets (AFs) and derive the conditions for metastable finite-size π3(SO(3)) solitons. A Derrick--Hobart scaling analysis shows that exchange, Dzyaloshinskii--Moriya interaction (DMI), anisotropy, and frustration can balance to set a finite equilibrium size. We identify two microscopic routes to this common topological and stabilization framework: intrinsic rotation-frame order in noncollinear AFs and an 𝕊3 extension of an amplitude-softened Néel field. In the latter, the smooth four-component texture projects onto a Néel field containing a spatially separated pair of oppositely charged Bloch points. Numerical minimization yields metastable monopole textures, while the effective dynamics identifies coherent breathing oscillations as their characteristic finite-frequency collective mode. Our results provide a microscopic framework for the statics and dynamics of Shankar skyrmions and identify frustrated chiral AFs as promising hosts of 3D non-Abelian topological textures.
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BibTeX
@misc{kuchkin2026threedimensional,
title = {{Three-Dimensional Shankar Skyrmions in Frustrated Antiferromagnets}},
author = {Vladyslav M. Kuchkin and Ricardo Rama-Eiroa and Carlos Saji and Alvaro S. Nunez and Roberto E. Troncoso},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38624},
eprint = {2609.38624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38624},
}
RIS
TY - UNPB
TI - Three-Dimensional Shankar Skyrmions in Frustrated Antiferromagnets
AU - Vladyslav M. Kuchkin
AU - Ricardo Rama-Eiroa
AU - Carlos Saji
AU - Alvaro S. Nunez
AU - Roberto E. Troncoso
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38624
UR - https://arxiv.org/abs/2609.38624
AB - We formulate a continuum theory for three-dimensional (3D) Shankar skyrmions in frustrated chiral antiferromagnets (AFs) and derive the conditions for metastable finite-size π_3(SO(3)) solitons. A Derrick--Hobart scaling analysis shows that exchange, Dzyaloshinskii--Moriya interaction (DMI), anisotropy, and frustration can balance to set a finite equilibrium size. We identify two microscopic routes to this common topological and stabilization framework: intrinsic rotation-frame order in noncollinear AFs and an 𝕊^3 extension of an amplitude-softened Néel field. In the latter, the smooth four-component texture projects onto a Néel field containing a spatially separated pair of oppositely charged Bloch points. Numerical minimization yields metastable monopole textures, while the effective dynamics identifies coherent breathing oscillations as their characteristic finite-frequency collective mode. Our results provide a microscopic framework for the statics and dynamics of Shankar skyrmions and identify frustrated chiral AFs as promising hosts of 3D non-Abelian topological textures.
ER -