  The desire to maximize the sensitivity of read/write heads and thus the
information density of magnetic storage devices has produced an intense
interest in the magnetoresistance (MR) of magnetic materials. Recent
discoveries include "colossal" MR of the manganites1-4 and the enhanced MR of
low carrier density ferromagnets4-6. In the low carrier density systems
investigated to date as well as the manganites, a key feature is that the
electrical conduction is due to a different set of electrons than the localized
electrons responsible for the magnetism. Here we propose a mechanism for
ferromagnetic MR originating from quantum interference effects, rather than
simple scattering. The new mechanism obtains in disordered low carrier density
magnets where the magnetism as well as the electrical conduction are due to the
same electrons. Here the MR is positive and only weakly temperature dependent
below the Curie point. This is very different from the MR seen when conduction
electrons and local moments can be treated separately, in which case the MR is
negative and strongly peaked at the Curie point.
