Nonlinear Interaction and Topological Selection Rules in two Skyrmion Merging: Emergence of Skyrmionium Textures
Abstract
The nonlinear interaction of closely spaced magnetic skyrmions remains poorly understood, particularly the conditions governing their merger into a single skyrmion or a stable skyrmionium. Here, we investigate the merging dynamics of two Néel skyrmions using analytical modelling and micromagnetic simulations based on Landau-Lifshitz-Gilbert dynamics. We examine the effects of exchange, Dzyaloshinskii-Moriya interaction, anisotropy, and magnetostatic energies by varying the initial separation, polarity, winding number, and skyrmion size. Our results reveal a topological selection rule: skyrmions with identical polarity and opposite winding numbers form a stable skyrmionium at intermediate overlap, while all other configurations relax into a single skyrmion. We also identify a critical radius below which the skyrmionium collapses, showing that its formation requires both the appropriate topology and a minimum size. Energy analysis reveals that the transition involves cooperative relaxation of exchange frustration and redistribution of Dzyaloshinskii-Moriya and magnetostatic energies, leading to a double-domain-wall structure. The resulting skyrmionium exhibits persistent breathing oscillations around an equilibrium radius, confirming its dynamical stability as a metastable state. These findings establish a predictive framework for controlling skyrmion merging and provide design guidelines for engineering skyrmionium textures in chiral magnetic nanostructures.
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BibTeX
@misc{busaidi2026nonlinear,
title = {{Nonlinear Interaction and Topological Selection Rules in two Skyrmion Merging: Emergence of Skyrmionium Textures}},
author = {M. Al Busaidi and T. Hakioglu and R. Sbiaa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07807},
eprint = {2611.07807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07807},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonlinear Interaction and Topological Selection Rules in two Skyrmion Merging: Emergence of Skyrmionium Textures
AU - M. Al Busaidi
AU - T. Hakioglu
AU - R. Sbiaa
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07807
UR - https://arxiv.org/abs/2611.07807
AB - The nonlinear interaction of closely spaced magnetic skyrmions remains poorly understood, particularly the conditions governing their merger into a single skyrmion or a stable skyrmionium. Here, we investigate the merging dynamics of two Néel skyrmions using analytical modelling and micromagnetic simulations based on Landau-Lifshitz-Gilbert dynamics. We examine the effects of exchange, Dzyaloshinskii-Moriya interaction, anisotropy, and magnetostatic energies by varying the initial separation, polarity, winding number, and skyrmion size. Our results reveal a topological selection rule: skyrmions with identical polarity and opposite winding numbers form a stable skyrmionium at intermediate overlap, while all other configurations relax into a single skyrmion. We also identify a critical radius below which the skyrmionium collapses, showing that its formation requires both the appropriate topology and a minimum size. Energy analysis reveals that the transition involves cooperative relaxation of exchange frustration and redistribution of Dzyaloshinskii-Moriya and magnetostatic energies, leading to a double-domain-wall structure. The resulting skyrmionium exhibits persistent breathing oscillations around an equilibrium radius, confirming its dynamical stability as a metastable state. These findings establish a predictive framework for controlling skyrmion merging and provide design guidelines for engineering skyrmionium textures in chiral magnetic nanostructures.
ER -