We study the origin of the cubic to tetragonal and tetragonal to monoclinic structural transitions in KCrF3, and the associated change in orbital order, paying particular attention to the relevance of super-exchange in both phases. We show that super
-exchange is not the main mechanism driving these transitions. Specifically, it is not strong enough to be responsible for the high-temperature cubic to tetragonal transition and does not yield the type of orbital order observed in the monoclinic phase. The energy difference between the tetragonal and the monoclinic structure is tiny, and most likely results from the interplay between volume, covalency, and localization effects. The transition is rather driven by Slater exchange than super-exchange. Nevertheless, once the monoclinic distortions are present, super-exchange helps in stabilizing the low symmetry structure. The orbital order we obtain for this monoclinic phase is consistent with the magnetic transition at 80 K.
Orbital and spin ordering phenomena in strongly correlated systems are commonly studied using the local-density approximation + dynamical mean-field theory approach. Typically, however, such simulations are restricted to simplified models (density-de
nsity Coulomb interactions, high symmetry couplings and few-band models). In this work we implement an efficient general hybridization-expansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) which allows us to investigate orbital and spin ordering in a more realistic setting, including interactions that are often neglected (e.g., spin-flip and pair-hopping terms), enlarged basis sets (full d versus eg), low-symmetry distortions, and reaching the very low-temperature (experimental) regime. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides: LaMnO3 and rare-earth manganites as well as the perovskites CaVO3 and YTiO3. We show that spin-flip and pair hopping terms do not affect the Kugel-Khomskii orbital-order melting transition in rare-earth manganites, or the suppression of orbital fluctuations driven by crystal field and Coulomb repulsion. For the Mott insulator YTiO3 we find a ferromagnetic transition temperature 50 K, in remarkably good agreement with experiments. For LaMnO3 we show that the classical t2g-spin approximation, commonly adopted for studying manganites, yields indeed an occupied eg orbital in very good agreement with that obtained for the full d 5-orbital Hubbard model, while the spin-spin e_g-t_{2g} correlation function calculated from the full d model is 0.74, very close to the value expected for aligned eg and t2g spins; the eg spectral function matrix is also well reproduced. Finally, we show that the t2g screening reduces the eg-eg Coulomb repulsion by about 10%
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.
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 Hunds 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 super-exchange from those of lattice distortions. We find that super-exchange 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 at least 1150 K and to reproduce the occupied orbital deduced from neutron scattering.
