Spin-state transitions are the hallmark of rare-earth cobaltates. In order to understand them, it is essential to identify all relevant parameters which shift the energy balance between spin states, and determine their trends. We find that Delta, the
eg-t2g crystal-field splitting, increases by ~250 meV when increasing pressure to 8 GPa and by about 150 meV when cooling from 1000K to 5K. It changes, however, by less than 100 meV when La is substituted with another rare earth. Also the Hunds rule coupling J_avg is about the same in systems with very different spin-state transition temperature, like LaCoO3 and EuCoO3. Consequently, in addition to Delta and J_avg, the Coulomb-exchange anisotropy Delta J_ avg and the super-exchange energy-gain Delta E_SE play a crucial role, and are comparable with spin-state dependent relaxation effects due to covalency. We show that in the LnCoO3 series, with Ln=Y or a rare earth (RE), super-exchange progressively stabilizes a low-spin ground state as the Ln^{3+} ionic radius decreases. We give a simple model to describe spin-state transitions and show that, at low temperature, the formation of isolated high-spin/low-spin pairs is favored, while in the high-temperature phase, the most likely homogeneous state is high-spin, rather than intermediate spin. An orbital-selective Mott state could be a fingerprint of such a state.
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 incr
eases 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.
