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The capability to probe the dispersion of elementary spin, charge, orbital,and lattice excitations has positioned resonant inelastic x-ray scattering(RIXS) at the forefront of photon science. In this work, we will investigatehow RIXS can contribute to a deeper understanding of the orbital properties andof the pairing mechanism in unconventional high-temperature superconductors. Inparticular, we will show how direct RIXS spectra of magnetic excitations canreveal long-range orbital correlations in transition metal compounds, bydiscriminating different kind of orbital order in magnetic andantiferromagnetic systems. Moreover, we will show how RIXS spectra ofquasiparticle excitations in superconductors can measure the superconductinggap magnitude, and reveal the presence of nodal points and phase differences ofthe superconducting order parameter on the Fermi surface. This can reveal theproperties of the underlying pairing mechanism in unconventionalsuperconductors, in particular cuprates and iron pnictides, discriminatingbetween different superconducting order parameter symmetries, such as $s$, $d$(singlet pairing) and $p$ wave (triplet pairing).

Theoretical approach to direct resonant inelastic x-ray scattering on magnets and superconductors