  In this paper, starting from the classical 3D non-convex and nonlocal
micromagnetic energy for ferromagnetic materials, we determine, via an
asymptotic analysis, the free energy of a multi-structure consisting of a
nano-wire in junction with a thin film and of a multi-structure consisting of
two joined nano-wires. We assume that the volumes of the two parts composing
each multi-structure vanish with same rate. In the first case, we obtain a 1D
limit problem on the nano-wire and a 2D limit problem on the thin film, and the
two limit problems are uncoupled. In the second case, we obtain two 1D limit
problems coupled by a junction condition on the magnetization. In both cases,
the limit problem remains non-convex, but now it becomes completely local.
