Skyrmion annihilation using a two-dimensional pseudospectral Landau-Lifshitz

A pseudospectral Landau-Lifshitz (PS-LL) description of magnetization dynamics was recently introduced to accurately describe the energy and momentum relation of magnons within a continuum model [1]. While this approach was originally envisaged for numerical studies of ultrafast magnetization dynamics, it can also be useful in effectively describing solitons with sizes approaching the material’s exchange length in one-dimension [2]. To investigate the applicability of this model in higher dimensions, we derive a two-dimensional PS-LL model with the addition of Dzyaloshinskii-Moriya interaction (DMI). DMI is implemented by including its contribution in the material’s magnon dispersion relation. With this approach, we investigate skyrmion annihilation using an external field with an atomic discretization as a test case. Within the PS-LL framework, the skyrmion annihilates at a finite field while a micromagnetic interpretation requires a much larger field because of its large exchange energy at the edge of the first Brillouin zone. Our results demonstrate that the PS-LL model can be extended to higher dimensions and can correctly describe solitons approaching the exchange length limit.

[1] Kyle Rockwell, Joel Hirst, Thomas A. Ostler, and Ezio Iacocca, Phys. Rev. B 109, L180404 (2024)

[2] M. Estiphanos and E. Iacocca, arXiv:2407.02628