  We develop the formalism of the macroscopic monopolization -- that is the
monopole moment per unit volume -- in periodic solids, and discuss its
relationship to the diagonal magnetoelectric effect. For the series of lithium
transition metal phosphate compounds we use first-principles density functional
theory to calculate the contributions to the macroscopic monopolization from
the global distribution of magnetic moments within the unit cell, as well as
from the distribution of magnetization around the atomic sites. We find one
example within the series (LiMnPO$_4$) that shows a macroscopic monopolization
corresponding to a ferromonopolar ordering consistent with its diagonal
magnetoelectric response. The other members of the series (LiMPO$_4$, with M =
Co, Fe and Ni) have zero net monopolization but have antiferromonopolar
orderings that should lead to $q$-dependent diagonal magnetoelectric effects
