Abstract
Doped divalent hexaborides such as ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{B}}_{6}$ exhibit a high ${T}_{c}$ ferromagnetism. We isolate a degenerate pair of $2p$ orbitals of boron with two valence electrons, invoke electron correlation and Hund coupling, to suggest that the undoped state is better viewed as a spin-1 Mott insulator; it is predicted to be a type of $3d$ Haldane gap phase with a spin gap $\ensuremath{\sim}0.1\mathrm{eV},$ much smaller than the charge gap of $>1.0\mathrm{eV}$ seen in angle-resolved photoemission spectroscopy. The experimentally seen high ${T}_{c}$ ``ferromagnetism'' is argued to be a complex magnetic order in disguise---either a canted six-sublattice antiferromagnetic $(\ensuremath{\approx}120\ifmmode^\circ\else\textdegree\fi{})$ order or its quantum melted version, a chiral spin liquid state, arising from a type of double-exchange mechanism.
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