Many-body interactions strongly influence the structure, stability, and dynamics of condensed-matter systems, from atomic lattices to interacting quasiparticles such as superconducting vortices. Here, we theoretically investigate pairwise and many-body interaction terms among skyrmions in helimagnets, considering both the saturated ferromagnetic and conical spin backgrounds. Using micromagnetic simulations, we calculate the exchange, Dzyaloshinskii-Moriya, and Zeeman contributions to the skyrmion-skyrmion pair potential, thereby identifying the physical origin of the attractive and repulsive regimes. For small skyrmion clusters in the conical phase, three-body interactions provide a substantial contribution to the cohesive energy, comparable in magnitude to the pairwise term, whereas four-body contributions become relevant only at low magnetic fields. As the system approaches the saturated phase, higher-order terms vanish and the interaction becomes essentially pairwise. These results demonstrate that realistic descriptions of skyrmion interactions in helimagnets, especially in the conical phase, require explicit many-body terms in order to capture the behavior of skyrmion crystals and to guide strategies for controlling skyrmion phases and dynamics.

Close

PrevNext

View figure in article

• Magnetism
• Skyrmions
• Helimagnets