Title: Variational models for the formation of microstructures and vortices in helimagnetic compounds
Abstract: We consider variational models for pattern formation in magnetic compounds. We start from a specific discrete frustrated ferromagnetic/anti-ferromagnetic $S^1$-valued spin system, and first discuss a continuum limit model in the case that incompatible boundary conditions are assigned on the spin field. For the resulting singularly perturbed multiwell energy, we derive the scaling law for the minimum in terms of the problem parameters. The results indicate in particular that in certain parameter regimes the formation of various complex branching-type patterns is expected. Finally, we discuss the scaling behaviour of the minimal energy of the discrete spin model and show that in some parameter regimes, the formation of vortices is energetically favourable. Some extensions to vectorial problems will also be outlined.
This talk is based on joint work with Janusz Ginster, Melanie Koser, Angkana Rüland and Antonio Tribuzio.
(Host: Mathias Oster)