  Context. Excess microwave emission, commonly known as anomalous microwave
emission (AME), is now routinely detected in the Milky Way. Although its link
with the rotation of interstellar (carbonaceous) nano-grains seems to be
relatively well established at cloud scales, large-scale observations show a
lack of correlation between the different tracers of nano-carbons and AME,
which has led the community to question the viability of this link. Aims. Using
ancillary data and spinning dust models for nano-carbons and nano-silicates, we
explore the extent to which the AME that come out of the Galactic Plane might
originate with one or another carrier. Methods. In contrast to previous
large-scale studies, our method is not built on comparing the correlations of
the different dust tracers with each other, but rather on comparing the poor
correlations predicted by the models with observed correlations. This is based
on estimates that are as realistic as possible of the gas ionisation state and
grain charge as a function of the local radiation field and gas density.
Results. First, nano-carbon dust can explain all the observations for medium
properties, in agreement with the latest findings about the separation of cold
and warm neutral medium in the diffuse interstellar medium. The dispersion in
the observations can be accounted for with little variations in the dust size
distribution, abundance, or electric dipole moment. Second, regardless of the
properties and abundance of the nano-silicate dust we considered, spinning
nano-silicates are excluded as the sole source of the AME. Third, the best
agreement with the observations is obtained when the emission of spinning
nano-carbons alone is taken into account. However, a marginal participation of
nano-silicates in AME production cannot be excluded as long as their abundance
does not exceed $Y_{\rm Si} \sim 1\%$.
