Theory of Orbital Excitation and Resonant Inelastic X-ray Scattering in Manganites

We study theoretically the collective orbital excitation named orbital wave in the orbital ordered manganites.The dispersion relation of the orbital wave is affected by the static spin structure through the coupling between spin and orbital degrees of freedom. As a probe to detect the dispersion relation, we propose two possible methods by utilizing resonant inelastic x-ray scattering. The transition probability of the orbital wave scattering is formulated, and the momentum and polarization dependences of the structure factor are calculated in several types of the orbital and spin structures. The elastic x-ray scattering in the L-edge case to observe the orbital ordering is also discussed.