### A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called “domain walls” – in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors ${m}_{\alpha}^{\pm}\in {\mathbb{S}}^{2}$ that differ by an angle $2\alpha $. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The...