  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 $m^\pm \in \mathbb{S}^2$
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 minimal
energy splits into a contribution from an asymmetric, divergence-free core
which performs a partial rotation in $\mathbb{S}^2$ by an angle $2\theta$, and
a contribution from two symmetric, logarithmically decaying tails, each of
which completes the rotation from angle $\theta$ to $\alpha$ in $\mathbb{S}^1$.
The angle $\theta$ is chosen such that the total energy is minimal. The
contribution from the symmetric tails is known explicitly, while the
contribution from the asymmetric core is analyzed in [7]. Our reduced model is
the starting point for the analysis of a bifurcation phenomenon from symmetric
to asymmetric domain walls. Moreover, it allows for capturing asymmetric domain
walls including their extended tails (which were previously inaccessible to
brute-force numerical simulation).
