Toward a theory of orbiton dispersion in LaMnO₃

At 750 K, LaMnO₃ 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 Mn³⁺ 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. The degrees of freedom are oxygen vibrations and electronic excitations consisting of misoriented orbitals on Mn ions. Neglecting coupling to the oxygen displacements, the gap to such excitations is 2Δ = 16 g²/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 Δ, 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 k = (0, 0, π). This is the Goldstone mode of the JT broken symmetry.