  The low-temperature Hall resistivity \rho_{xy} of La_{2/3}A_{1/3}MnO_3 single
crystals (where A stands for Ca, Pb and Ca, or Sr) can be separated into
Ordinary and Anomalous contributions, giving rise to Ordinary and Anomalous
Hall effects, respectively. However, no such decomposition is possible near the
Curie temperature which, in these systems, is close to metal-to-insulator
transition. Rather, for all of these compounds and to a good approximation, the
\rho_{xy} data at various temperatures and magnetic fields collapse (up to an
overall scale), on to a single function of the reduced magnetization
m=M/M_{sat}, the extremum of this function lying at m~0.4. A new mechanism for
the Anomalous Hall Effect in the inelastic hopping regime, which reproduces
these scaling curves, is identified. This mechanism, which is an extension of
Holstein's model for the Ordinary Hall effect in the hopping regime, arises
from the combined effects of the double-exchange-induced quantal phase in
triads of Mn ions and spin-orbit interactions. We identify processes that lead
to the Anomalous Hall Effect for localized carriers and, along the way, analyze
issues of quantum interference in the presence of phonon-assisted hopping. Our
results suggest that, near the ferromagnet-to-paramagnet transition, it is
appropriate to describe transport in manganites in terms of carrier hopping
between states that are localized due to combined effect of magnetic and
non-magnetic disorder. We attribute the qualitative variations in resistivity
characteristics across manganite compounds to the differing strengths of their
carrier self-trapping, and conclude that both disorder-induced localization and
self-trapping effects are important for transport.
