Orbital ordering in LaMnO$_3$: Electron-electron versus electron-lattice interactions

TL;DR

This study uses density functional theory to analyze the roles of electron-electron and electron-lattice interactions in orbital ordering in LaMnO$_3$, revealing that e-e interactions are crucial for stabilization and lattice distortion.

Contribution

It provides a systematic comparison of electron-electron and electron-lattice interactions in orbital ordering, highlighting the dominant role of e-e interactions in LaMnO$_3$.

Findings

Electron-lattice interaction alone is insufficient to stabilize orbital order.

Electron-electron interaction induces orbital ordering and enhances Jahn-Teller distortion.

Enhanced localization due to e-e interaction facilitates lattice distortions.

Abstract

The relative importance of electron-lattice (e-l) and electron-electron (e-e) interactions in ordering orbitals in LaMnO$_3$ is systematically examined within the LDA+$U$ approximation of density functional theory. A realistic effective Hamiltonian is derived from novel Wannier functions analysis of the electronic structure. Surprisingly, e-l interaction ($\simeq 0.9$ eV) alone is found insufficient to stabilize the orbital ordered state. On the other hand, e-e interaction ($\simeq 1.7$ eV) not only induces orbital ordering, but also greatly facilitates the Jahn-Teller distortion via enhanced localization. Further experimental means to quantify the competition between these two mechanisms are proposed.