  A model for semimetals such as $EuB_6$, in which band overlaps are controlled
by magnetic order, is presented and is solved in the dynamical mean field
approximation. First order phase boundaries are computed by evaluating free
energies of different states. The phase diagram is determined. A specific and
physically reasonable choice of parameters is found to approximately reproduce
the available data on $EuB_6$. For this material, predictions are made for the
location of a metamagnetic transition and its associated endpoint, and a change
in the order of the magnetic transition.
