Excitonic order at strong coupling: Pseudospin, doping, and ferromagnetism

A tight-binding model is introduced to describe the strong interaction limit of excitonic ordering. At stoichiometry, the model reduces in the strong-coupling limit to a pseudospin model with approximate U(4) symmetry. Excitonic order appears in the pseudospin model as in-plane pseudomagnetism. The U(4) symmetry unifies all possible singlet and triplet order parameters describing such states. Superexchange, Hunds-rule coupling, and other perturbations act as anisotropies splitting the U(4) manifold, ultimately stabilizing a paramagnetic triplet state. The tendency to ferromagnetism with doping (observed experimentally in the hexaborides) is explained as a spin-flip transition to a different orientation of the U(4) order parameter. The physical mechanism favoring such a reorientation is the enhanced coherence (and hence lower kinetic energy) of the doped electrons in a ferromagnetic background relative to the paramagnet. A discussion of the physical meaning of various excitonic states and their experimental consequences is also provided.