  We present a study of the proximity effect between a ferromagnet and a
paramagnetic metal of varying disorder. Thin beryllium films are deposited onto
a 5 nm-thick layer of the ferromagnetic insulator EuS. This bilayer arrangement
induces an exchange field, $H_{ex}$, of a few tesla in low resistance Be films
with sheet resistance $R\ll R_Q$, where $R_Q=h/e^2$ is the quantum resistance.
We show that $H_{ex}$ survives in very high resistance films and, in fact,
appears to be relatively insensitive to the Be disorder. We exploit this fact
to produce a giant low-field magnetoresistance in the correlated insulator
phase of Be films with $R\gg R_Q$.

Mesoscale and Nanoscale Physics