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We study the Landau-Lifshitz model for the energy of multi-scale transitionlayers -- called "domain walls" -- in soft ferromagnetic films. Domain wallsseparate domains of constant magnetization vectors $m^\pm \in \mathbb{S}^2$that differ by an angle $2\alpha$. Assuming translation invariance tangentialto the wall, our main result is the rigorous derivation of a reduced model forthe energy of the optimal transition layer, which in a certain parameter regimeconfirms the experimental, numerical and physical predictions: The minimalenergy splits into a contribution from an asymmetric, divergence-free corewhich performs a partial rotation in $\mathbb{S}^2$ by an angle $2\theta$, anda contribution from two symmetric, logarithmically decaying tails, each ofwhich completes the rotation from angle $\theta$ to $\alpha$ in $\mathbb{S}^1$.The angle $\theta$ is chosen such that the total energy is minimal. Thecontribution from the symmetric tails is known explicitly, while thecontribution from the asymmetric core is analyzed in [7]. Our reduced model isthe starting point for the analysis of a bifurcation phenomenon from symmetricto asymmetric domain walls. Moreover, it allows for capturing asymmetric domainwalls including their extended tails (which were previously inaccessible tobrute-force numerical simulation).

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