Orbital-order melting in rare-earth manganites: Role of superexchange

We study the mechanism of orbital-order melting observed at temperature T-OO in the series of rare-earth manganites. We find that the purely electronic many-body super-exchange mechanism yields a transition temperature T-KK that decreases with decreasing rare-earth radius and increases with pressure, opposite to the experimental T-OO. We show that the tetragonal crystal-field splitting reduces T-KK further increasing the discrepancies with experiments. This proves that super-exchange effects, although very efficient, in the light of experimentally observed trends play a minor role for the melting of orbital ordering in rare-earth manganites.