  Nowadays, nonhomogeneous and periodic ferromagnetic materials are the subject
of a growing interest. Actually such periodic configurations often combine the
attributes of the constituent materials, while sometimes, their properties can
be strikingly different from the properties of the different constituents.
These periodic configurations can be therefore used to achieve physical and
chemical properties difficult to achieve with homogeneous materials. To predict
the magnetic behavior of such composite materials is of prime importance for
applications. The main objective of this paper is to perform, by means of
Gamma-convergence and two-scale convergence, a rigorous derivation of the
homogenized Gibbs-Landau free energy functional associated to a composite
periodic ferromagnetic material, i.e. a ferromagnetic material in which the
heterogeneities are periodically distributed inside the ferromagnetic media. We
thus describe the Gamma-limit of the Gibbs-Landau free energy functional, as
the period over which the heterogeneities are distributed inside the
ferromagnetic body shrinks to zero.
