  The rare-earth based pyrochlore molybdates involve orbitally degenerate
electrons Hund's coupled to local moments. The large Hund's coupling promotes
ferromagnetism, the superexchange between the local moments prefers
antiferromagnetism, and Hubbard repulsion tries to open a Mott gap. The phase
competition is tuned by the rare-earth ionic radius, decreasing which leads to
change from a ferromagnetic metal to a spin disordered highly resistive ground
state, and ultimately an 'Anderson-Mott' insulator. We attempt a quantitative
theory of the molybdates by studying their minimal model on a pyrochlore
geometry, using a static auxiliary field based Monte Carlo. We establish a
thermal phase diagram that closely corresponds to the experiments, predict the
hitherto unexplored orbital correlations, quantify and explain the origin of
the anomalous resistivity, and present dynamical properties across the
metal-insulator transition.
