  We generalize the formalism of the dynamical vertex approximation
(D$\Gamma$A) -- a diagrammatic extension of the dynamical mean-field theory
(DMFT)-- to treat magnetically ordered phases. To this aim, we start by
concisely illustrating the many-electron formalism for performing ladder
resummations of Feynman diagrams in systems with broken SU(2)-symmetry,
associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then
analyze the algorithmic simplifications introduced by taking the local
approximation of the two-particle irreducible vertex functions in the
Bethe-Salpeter equations, which defines the ladder implementation of D$\Gamma$A
for magnetic systems. The relation of this assumption with the DMFT limit of
large coordination-number/ high-dimensions is explicitly discussed. As a last
step, we derive the expression for the ladder D$\Gamma$A self-energy in the FM-
and AF-ordered phases of the Hubbard model. The physics emerging in the
AF-ordered case is explicitly illustrated by means of approximated calculations
based on a static mean-field input for the D$\Gamma$A equations. The results
obtained capture fundamental aspects of both metallic and insulating ground
states of two-dimensional antiferromagnets, providing a reliable compass for
future, more extensive applications of our approach. Possible routes to further
develop diagrammatic-based treatments of magnetic phases in correlated electron
systems are briefly outlined in the conclusions.
