Pseudospectral interpretation of solitons in magnetic materials

A pseudospectral interpretation of the Landau-Lifshitz equation has been recently introduced [1] to achieve a grid-independent model of magnetization dynamics. The model relies on a spectral representation of the exchange interaction, i.e., a convolution kernel. This kernel can represent exchange dominated spin waves [1], magnetostatic waves [2], and generally any nonlocal interaction. However, solitons are also impacted because their spectral content can span the full Brillioun zone. Here, we demonstrate the emergence of solitons within the pseudospectral model. In addition to skyrmions [3], we show a Peregrine rogue wave established from several initial conditions, in agreement with other dispersive systems [4]. This work highlights the importance of considering the dispersion relation across the first Brillouin zone as well as its role to probe the nonlinear interactions that are relevant for nonlinear structures.

[1] K. Rockwell et al., Phys. Rev. B 109, L180404 (2024)

[2] A. Roxburgh et al., npj Computational Materials 11, 369 (2025)

[3] M. Copus and E. Iacocca, arXiv:2507.14365

[4] M. Onorato et al., Phys. Rep. 528, 47-84 (2013)