Accepted Paper

Inserted: 18 jan 2024
Last Updated: 6 aug 2024

Journal: SIAM Journal on Mathematical Analysis (SIMA)
Year: 2024

Abstract:

The present study concerns the nonlocal-to-local convergence of a family of exchange energy functionals in the limit of very short-range interactions. The analysis accounts for both symmetric and antisymmetric exchange. Our result is twofold. First, we extend the Bourgain-Brezis-Mironescu formula to encompass the scenario where antisymmetric contributions are encoded into the energy. Second, we prove that, under physically relevant assumptions on the families of exchange kernels, the family of nonlocal functionals Gamma-converges to their local counterparts. As a byproduct of our analysis, we obtain a rigorous justification of Dzyaloshinskii–Moriya interactions in chiral magnets under the form commonly adopted in the variational theory of micromagnetism when modeling antisymmetric exchange interactions.

Keywords: Gamma-convergence, Micromagnetics, nonlocal energies, Bourgain-Brezis-Mironescu formula, Antisymmetric exchange interactions, Dzyaloshinskii–Moriya interaction (DMI), Magnetic Skyrmions

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• Nonlocal_DMI.pdf