Electronic origin of magnetic and orbital ordering in insulating LaMnO₃

We derive a spin-orbital model for insulating LaMnO_3 which fulfills the SU(2) symmetry of S=2 spins at Mn^{3+} ions. It includes the complete e_g and t_{2g} superexchange which follows from a realistic Mn^{2+} multiplet structure in cubic site symmetry, and the Jahn-Teller induced orbital interactions. We show that the magnetic ordering observed in LaMnO_3 is stabilized by a purely electronic mechanism due to the e_g-superexchange alone, and provide for the first time a quantitative explanation of the observed transition temperature and the anisotropic exchange interactions.