  Hall experiments in chiral magnets are often analyzed as the sum of an
anomalous Hall effect, dominated by momentum-space Berry curvature, and a
topological Hall effect, arising from the real-space Berry curvature in the
presence of skyrmions, in addition to the ordinary Hall resistivity. This
raises the questions of how one can incorporate, on an equal footing, the
effects of the anomalous velocity and the real space winding of the
magnetization, and when such a decomposition of the resistivity is justified.
We provide definitive answers to these questions by including the effects of
all phase-space Berry curvatures in a semi-classical approach and by solving
the Boltzmann equation in a weak spin-orbit coupling regime when the
magnetization texture varies slowly on the scale of the mean free path. We show
that the Hall resistivity is then just the sum of the anomalous and topological
contributions, with negligible corrections from Berry curvature-independent and
mixed curvature terms. We also use an exact Kubo formalism to numerically
investigate the opposite limit of infinite mean path, and show that the results
are similar to the semi-classical results.
