  High resolution resonant inelastic x-ray scattering (RIXS) has proven
particularly effective in the determination of crystal field and spin
excitations in cuprates. Its strength lies in the large Cu $L_{3}$ resonance
and in the fact that the scattering cross section follows quite closely the
single-ion model predictions, both in the insulating parent compounds and in
the superconducting doped materials. However, the spectra become increasingly
broader with (hole) doping, hence resolving and assigning spectral features has
proven challenging even with the highest energy resolution experimentally
achievable. Here we have overcome this limitation by measuring the complete
polarization dependence of the RIXS spectra as function of momentum transfer
and doping in thin films of NdBa$_{2}$Cu$_{3}$O$_{7-\delta}$. Besides
confirming the previous assignment of $dd$ and spin excitations (magnon,
bimagnon) in the antiferromagnetic insulating parent compound, we unequivocally
single out the actual spin-flip contribution at all dopings. We also
demonstrate that the softening of $dd$ excitations is mainly attributed to the
shift of the $xy$ peak to lower energy loss. These results provide a definitive
assessment of the RIXS spectra of cuprates and demonstrate that RIXS
measurements with full polarization control are practically feasible and highly
informative.
