Elementary excitations probed by L-edge resonant inelastic x-ray scattering in systems with weak and intermediate electron correlations

We develop a formalism to calculate the L-edge resonant x-ray scattering (RIXS) spectra from transition-metal compounds. Using a multi-orbital tight-binding model, we derive useful formulas to calculate the spectra by collecting up the ladder diagrams on the basis of the Keldysh scheme, without relying on the fast collision approximation. They are feasible in the weak and intermediate coupling regimes of itinerant electron systems, where the charge and the magnetic excitations are mixed together. We examine the difference between the present formulas and those of the fast collision approximation. Finally, to demonstrate how our theory works, we employ the formulas to study the RIXS spectra on a simple model, the single-orbital Hubbard model on the square lattice at half-filling. The intensities originated from the magnon and from the continuous states are obtained on the equal footing in the antiferromagnetic ground state.