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arXiv · 2509.12172

Many-body skyrmion interactions in helimagnets

N. P. Vizarim·J. C. Bellizotti Souza·Raí M. Menezes·Clécio C. de Souza Silva·P. A. Venegas·M. V. Milošević
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Abstract

Many-body interactions strongly influence the structure, stability, and dynamics of condensed-matter systems, from atomic lattices to interacting quasi-particles such as superconducting vortices. Here, we investigate theoretically the pairwise and many-body interaction terms among skyrmions in helimagnets, considering both the ferromagnetic and conical spin backgrounds. Using micromagnetic simulations, we separate the exchange, Dzyaloshinskii-Moriya, and Zeeman contributions to the skyrmion-skyrmion pair potential, and show that the binding energy of skyrmions within the conical phase depends strongly on the film thickness. For small skyrmion clusters in the conical phase, three-body interactions make a substantial contribution to the cohesive energy, comparable to that of pairwise terms, while four-body terms become relevant only at small magnetic fields. As the system approaches the ferromagnetic phase, these higher-order contributions vanish, and the interactions become essentially pairwise. Our results indicate that realistic models of skyrmion interactions in helimagnets in the conical phase must incorporate many-body terms to accurately capture the behavior of skyrmion crystals and guide strategies for controlling skyrmion phases and dynamics.

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N. P. Vizarim, J. C. Bellizotti Souza, Raí M. Menezes, Clécio C. de Souza Silva, P. A. Venegas, M. V. Milošević. 2025-09-15. Many-body skyrmion interactions in helimagnets. https://arxiv.org/abs/2509.12172

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