Toward a Theory of Orbiton Dispersion in LaMnO_3

TL;DR

This paper develops a minimal theoretical model to describe orbiton dispersion in LaMnO_3, accounting for electron-phonon interactions, orbital excitations, and Jahn-Teller distortions, revealing the emergence of a Goldstone mode.

Contribution

It introduces a simplified model capturing orbiton dispersion and phonon interactions in LaMnO_3, highlighting the role of oxygen displacements and Jahn-Teller symmetry breaking.

Findings

Orbiton excitations become dispersive with dynamic oxygen displacements.

A Goldstone mode appears at specific momentum due to Jahn-Teller symmetry breaking.

The model predicts a self-trapped exciton with energy half the Jahn-Teller gap.

Abstract

At 750K, LaMnO_3 has a cooperative Jahn-Teller (JT) distortion, with Mn atoms in distorted oxygen octahedra. This lifts the degeneracy of the singly-occupied $e_g$ orbitals of the Mn$^{3+}$ ions, which then become orbitally ordered. We use a minimal model to describe the ordered phase at T=0. The on-site Coulomb repulsion $U$ is set to infinity. There are two electronic orbitals and three oxygen vibrational coordinates per unit cell. In addition to spin excitations and phonons, the model has electronic excitations consisting of mis-orienting orbitals on Mn ions. Neglecting coupling to the oxygen displacements, the gap to such excitations is $2\Delta=16g^2/K$ where $g$ is the electron-phonon coupling and $K$ is the oxygen spring constant. When static oxygen displacements are coupled, this excitation becomes a self-trapped exciton with energy $\Delta$, half the JT gap. Adding dynamic oxygen displacements in one-phonon approximation introduces dispersion to both the (previously Einstein-like) phonons and the orbital excitons (``orbitons''). One of the phonon branches has zero frequency at $\vec{k}=(0,0,\pi)$. This is the Goldstone mode of the JT broken symmetry.