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High resolution resonant inelastic x-ray scattering (RIXS) has provenparticularly effective in the determination of crystal field and spinexcitations in cuprates. Its strength lies in the large Cu $L_{3}$ resonanceand in the fact that the scattering cross section follows quite closely thesingle-ion model predictions, both in the insulating parent compounds and inthe superconducting doped materials. However, the spectra become increasinglybroader with (hole) doping, hence resolving and assigning spectral features hasproven challenging even with the highest energy resolution experimentallyachievable. Here we have overcome this limitation by measuring the completepolarization dependence of the RIXS spectra as function of momentum transferand doping in thin films of NdBa$_{2}$Cu$_{3}$O$_{7-\delta}$. Besidesconfirming the previous assignment of $dd$ and spin excitations (magnon,bimagnon) in the antiferromagnetic insulating parent compound, we unequivocallysingle out the actual spin-flip contribution at all dopings. We alsodemonstrate that the softening of $dd$ excitations is mainly attributed to theshift of the $xy$ peak to lower energy loss. These results provide a definitiveassessment of the RIXS spectra of cuprates and demonstrate that RIXSmeasurements with full polarization control are practically feasible and highlyinformative.

Polarization resolved Cu $L_3$-edge resonant inelastic x-ray scattering of orbital and spin excitations in NdBa$_{2}$Cu$_{3}$O$_{7-\delta}$