weak “anisotropy” terms. In the undoped material, these anisotropies favor a simple paramagnetic triplet state. Doping introduces additional exchange energy contributions that modify the anisotropy, causing $\Delta_{\alpha\beta}$ to “flop” into a different orientation with a ferromagnetic moment. In the present model, the excitonic order in the ferromagnet is of non-collinear triplet type, in which $$\Delta_s = 0, \qquad \vec\Delta_t \wedge \vec\Delta_t^* \neq 0.$$ As shown in Sec. \[sec:discussion\], in addition to ferromagnetic magnetization, this state has additional spatially-varying local static moments and spin currents transverse to the axis of net magnetization. The transition to this state from the paramagnet is generally first order, and therefore coincides with a jump in the electronic density. Since experiments are performed at fixed charge density (dictated by the concentration of dopant ions), the intermediate “forbidden” range of dopings can be accommodated only by phase separation. With long-range Coulomb interactions included, macroscopic phase separation is impossible, and charge domain formation is expected, as pointed out already in Refs. [@BalentsVarma; @Barzykin].

The [*detailed*]{} demonstration of this behavior with doping is non-trivial. As for many other strongly correlated systems, the problem of doping is much more difficult than that of the stoichiometric Mott insulator. Indeed, as the 