Orbital-order melting in rare-earth manganites: the role of super-exchange

We study the mechanism of orbital-order melting observed at temperature T_OO in the series of rare-earth manganites. We find that many-body super-exchange 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 the experimentally observed trends, play a minor role for the melting of orbital ordering in rare-earth manganites.