Orbital wave in the Raman scattering cross section of LaMnO3*

We calculated the polarization-dependent Raman scattering cross-section spectra of LaMnO3 below the A-type magnetic ordering temperature. Two strong peaks appear around the MnO6 octahedra stretching phonon frequency. One mode shows Ag symmetry, while the other mode shows Bg symmetry. We found that the Ag symmetry peak is a Jahn-Teller phonon coupled to the orbital wave and the Bg symmetry peak is an orbital wave mode coupled to a Q2 phonon mode via the Jahn-Teller electron-phonon coupling.