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

We study the mechanism of orbital-order melting observed at temperature $T_{\mathrm{OO}}$ in the series of rare-earth manganites. We find that the purely electronic many-body super-exchange mechanism yields a transition temperature $T_{\mathrm{KK}}$ that decreases with decreasing rare-earth radius and increases with pressure, opposite to the experimental $T_{\mathrm{OO}}$. We show that the tetragonal crystal-field splitting reduces $T_{\mathrm{KK}}$ 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.

Figure 1

Orbital order in TbMnO${}_3$, as obtained by LDA+DMFT calculations. The pseudocubic axes pointing along Mn-Mn bonds are shown in the left corner.

Figure 2

Top: Energy gain per formula unit due to orbital polarization, $\Delta E\left[p\right(T\left)\right]=\Delta E\left(T\right)$, in the case of LaMnO${}_3$. Error bars are smaller than the symbols. Bottom: Order parameter (orbital polarization) $p\left(T\right)$ vs temperature.

Figure 3

Orbital-order transition temperature $T_{\mathrm{KK}}$[30] vs RE${}^{3+}$ radius in the REMnO${}_3$ series, with $\mathrm{RE}=\mathrm{Dy}$ (triangles), Tb (squares), Nd (pentagons), La (circles). Full (empty) symbols: $T_{\mathrm{KK}}$ from LDA $+$ DMFT total-energy (order parameter) calculations. Symbols of decreasing size: $P=0$, 5.4, and 9.87 GPa. Crosses: Experimental values (ambient pressure) from Refs. 10, 11, 12.

Figure 4

Rotation of the most occupied state $|\theta \rangle$ as a function of temperature in the presence of a 130 meV tetragonal crystal field. The orbitals are shown for TbMnO${}_3$. The most occupied orbital remains well defined in the full temperature range; the orbital polarization is merely reduced by $30\%$ at $\sim$800 K.

Figure 5

Evolution of the crystal field with the RE${}^{3+}$ radius (structural data from Refs. 11, 39, 40, 41). Filled circles of decreasing size: LaMnO${}_3$ for $P=0$, 5.4, and 9.87 GPa.[13] Inset: Calculated occupied orbital.