Theory of ferromagnetism in doped excitonic condensates

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. 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.