  In this paper the domain wall solutions of a Ginzburg-Landau non-linear
$\mathbb{S}^2$-sigma hybrid model are exactly calculated. There exist two types
of basic domain walls and two families of composite domain walls. The domain
wall solutions have been identified by using a Bogomolny arrangement in a
system of sphero-conical coordinates on the sphere $\mathbb{S}^2$. The
stability of all the domain walls is also investigated.
