We derive a spin-orbital model for insulating LaMnO₃ which fulfills the SU(2) symmetry of $S=2$ spins at Mn³⁺ ions. It includes the complete eg and t2g superexchange which follows from a realistic Mn²⁺ multiplet structure in cubic site symmetry, and the Jahn-Teller-induced orbital interactions. We show that the magnetic ordering observed in LaMnO₃ is stabilized by a purely electronic mechanism due to the eg superexchange alone, and provides a unique and quantitatively correct explanation of the observed transition temperature and the anisotropic exchange interactions.
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Feiner et al. (1999) studied this question.