Resolving ultrafast dynamics with a pseudo-spectral Landau-Lifshitz model

Ultrafast magnetism provides a platform to study far-from-equilibrium physics in solid-state materials. From a theoretical point of view, it represents a challenging problem because of the transition between an atomic scale to a continuum representation [1]. One of the main issues is the energy discrepancy in atomistic and micromagnetic approaches. Here, we propose a pseudo-spectral Landau-Lifshitz equation PS-LLE [2] that can be implemented within a continuum framework yet resolving the atomic-scale energies. In other words, we replace the Laplacian approximation of the Heisenberg exchange Hamiltonian with a convolution kernel that reproduces the quantum-mechanical magnon dispersion relation. This approach is similar to “dispersion engineering” used in fluid dynamics [3]. Our PS-LLE model is expected to enable seamless multiscale between atomistic spin dynamics and micromagnetic simulations as well as the development of multigrid expansions to resolve singularities, topological objects, and long-range dipole interactions on equal footing in magnetic materials. In addition, the use of a continuum framework enables some degree of analytical study, e.g. within the context of spin hydrodynamics [4].

References

[1] R. F. L. Evans et al., J. Phys.: Condens. Matter 26, 103202 (2014) ; Méndez et al., Phys. Rev. Research 2, 013093 (2020)

[2] K. Rockwell and E. Iacocca, in preparation.

[3] G. B. Whitham, “Linear and nonlinear waves”, John Wiley & Sons (1974)

[4] E. Iacocca and M. A. Hoefer, Phys. Lett. A 383, 125858 (2019)