Observations on the resonant inelastic x-ray scattering cross section in copper oxide compounds

We report properties of the resonant inelastic x-ray scattering (RIXS) cross section in a number of cuprates. We find that the observed spectra have the periodicity of the underlying crystal lattice, that is, the excitations are a function of reduced momentum $\mathbf{q}$ and not the total momentum $\mathbf{Q}=\mathbf{G}+\mathbf{q}$, where $\mathbf{G}$ is a reciprocal lattice vector. Measurements with two different incident photon polarizations show that the line shape and momentum dependence of the observed spectra are independent of the particular state the $4p$ photoelectron resides in the intermediate state. These latter results support theoretical approaches in which the $4p$ is taken to be a spectator in the RIXS process. In addition, a discussion is presented of what might be expected to be generic features of the RIXS cross section with the aid of some crude models, and a comparison is made between RIXS and electron energy loss data for a number of cuprates both at $\mathbf{q}=0$ and at finite $\mathbf{q}$. Taken together, there is a suggestion in the data that RIXS measures an $S(\mathbf{q},\omega )$-like response.