in a superconductor,[@Fulde; @LO] is present in the nested mean-field limit, there do not appear to be any general theoretical grounds mandating this behavior more generally. Moreover, the universality of the experimental results, now observed in a large number of different compounds (Ca$_{1-x}$La$_x$B$_6$, BaB$_6$, Ca$_{1-x}$Ce$_x$B$_6$, SrB$_6$,…)[@private], argues for the robustness of the phenomenon.

To determine whether excitonic ferromagnetism is indeed more general than its weak-coupling theoretical basis, we consider here the completely opposite [*strong-coupling*]{} regime. This is not expected to be directly applicable to the hexaborides, as these materials are most likely best described by an intermediate-coupling model. Nevertheless, many useful insights are gained from this complementary limit. As usual, the principle assumption of the strong-coupling limit is the dominance of potential over kinetic energy. This is achieved concretely using a tight-binding model (see Eqs. \[tb1\]-\[nnn\], in Sec. \[sec:model\]), in which the conduction and valence bands of the conventional continuum theories are replaced by localized $a$ and $b$ orbitals, respectively. The analog of band gap in the continuum model is the level splitting $E_G = E_a-E_b > 0$. The order parameter characterizing excitonic ordering is then a matrix in spin space: $$\Delta_{\alpha\beta} = a_\alpha^\dagger
  b_\beta^{\vphantom\dagger},
  \label{deldef}$$ where $a_\alpha^\dagger$ creates an 