  Nesting in a semimetal can lead to an excitonic insulator state with
spontaneous coherence between conduction and valence bands and a gap for
charged excitations. In this paper we present a theory of the ferromagnetic
state that occurs when the density of electrons in the conduction band and
holes in the valence band differ. We find an unexpectedly rich doping-field
phase diagram and an unusual collective excitation spectrum that includes two
gapless collective modes. We predict regions of doping and external field in
which phase-separated condensates of electrons and holes with parallel spins
and opposing spins coexist.
