We report a Cu $K$edge resonant inelastic x-ray scattering (RIXS) study of the orbital excitations in the orbital-ordered Mott insulator KCuF${}_3$. By performing the polarization analysis of the scattered photons, the excitation between the $e_g$ orbitals is successfully distinguished from the excitations from $t_{2g}$ to $e_g$. The polarization dependence of the respective excitations is interpreted based on a phenomenological consideration of the symmetry of the RIXS process that yields a necessary condition for observing the excitations. Owing to our polarization analysis, we are able to measure the momentum dependence of the orbital excitation corresponding to the orbital degree of freedom over the whole Brillouin zone. The excitation is found to be dispersionless within our experimental resolution.

• Received 18 May 2011

DOI:https://doi.org/10.1103/PhysRevB.83.241101