Scaling laws and pattern formation in hellimagnets

This talk focuses on a variational approach to explain pattern formation in helimagnetic compounds. Such materials are often modelled in terms of (discrete) frustrated spin systems. We derive (in the sense of Gamma-convergence) a limiting continuum model at the helimagnetic/ferromagnetic transition point and discuss relations to models from the literature for other pattern forming systems. We focus on the case of incompatible boundary conditions for the spin field, and discuss in particular the scaling laws for the minimal energy. The latter indicate that the formation of complex spin patterns is expected in certain parameter regimes. This is based on joint work with Janusz Ginster and Melanie Koser (both Humboldt-Universität zu Berlin).