Origin of Jahn-Teller Distortion and Orbital Order in LaMnO₃

The origin of the cooperative Jahn-Teller distortion and orbital order in LaMnO₃ is central to the physics of the manganites. The question is complicated by the simultaneous presence of tetragonal and GdFeO₃-type distortions and the strong Hund’s rule coupling between e_g and t_2g electrons. To clarify the situation we calculate the transition temperature for the Kugel-Khomskii superexchange mechanism by using the local density approximation+dynamical mean-field method, and disentangle the effects of superexchange from those of lattice distortions. We find that superexchange alone would yield T_KK∼650  K. The tetragonal and GdFeO₃-type distortions, however, reduce T_KK to ∼550  K. Thus electron-phonon coupling is essential to explain the persistence of local Jahn-Teller distortions to ≳1150  K and to reproduce the occupied orbital deduced from neutron scattering.