  We focus on a special type of domain walls appearing in the Landau-Lifshitz
theory for soft ferromagnetic films. These domain walls are divergence-free
$S^2$-valued transition layers that connect two directions in $S^2$ (differing
by an angle $2\theta$) and minimize the Dirichlet energy. Our main result is
the rigorous derivation of the asymptotic structure and energy of such
"asymmetric" domain walls in the limit $\theta \to 0$. As an application, we
deduce that a supercritical bifurcation causes the transition from symmetric to
asymmetric walls in the full micromagnetic model.
