Dynamical Mean Field Theory of Temperature and Field Dependent Band Shifts in Magnetically Coupled Semimetals: Applocation to EuB6

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.