The Triskyrmion

Skyrmions are topologically non-trivial solutions that emerge in magnetic solids, characterized by an integer called the topological charge, Q. Motivated by the discoveries in [1], we wish to study the Q=3 solution, i.e the “triskyrmion”, a bound state of three Q=1 skyrmions. We explore the properties of the triskyrmion using the explicit spin components, following the model of Belavin and Polyakov (BP model) [2]. We investigate the triskyrmion stability via the minimization of the energy using the routine from [3]. We also explore the properties of other Q=3 structures, which are distinct from the triskyrmion. In addition to studying the triskyrmion, which can potentially be used for the same computing applications as the skyrmion, this work outlines the analytical framework that serves as a starting point for the study of other exotic classes of solutions within the BP model.

1] D. Capic et al., Stability of biskyrmions in centrosymmetric magnetic films, Phys. Rev. B 100, 014432 (2019).

[2] A. A. Belavin and A. M. Polyakov, Metastable states of two-dimensional isotropic ferromagnets, Pis’ma Zh. Eksp. Teor. Fiz. 22, 10 (1975).

[3] D. A. Garanin et al., Random field xy model in three dimensions, Phys. Rev. B 88, 224418 (2013).