Figure 1: Similarities between RIXS and the spin dynamical structure factor S(q, ω).

(a) Schematic diagram of a spin-flip excitation produced during the RIXS process at the Cu L₃-edge. The highlighted (darkened) orbitals represent holes. A spin-flip excitation is created when an electron with up spin is photoexcited from a Cu 2p core-level into the partially filled orbital. Subsequent de-excitation through the decay of an electron with down spin into the core produces a RIXS cross-section with a single spin-flip excitation. Such a single spin-flip channel can only be enabled when the outgoing photon polarization is (or has non-zero component) perpendicular to the incoming photon polarization. (b) A schematic picture of the area of the Brillouin zone accessible to RIXS at the Cu L-edge, as well as a line denoting the antiferromagnetic zone boundary (AFZB). The RIXS cross-section and the spin dynamical structure factor S(q, ω) have been evaluated in momentum space at the points marked by dots in the Brillouin zone (see also panel (c) below). (c) The RIXS cross-section for select points in momentum space at the Cu L₃-edge (top and middle panels) compared against S(q, ω) (bottom panels). Each has been calculated using exact diagonalization for the Hubbard model on a finite-size cluster for three different electron concentrations n. The top panels show RIXS spectra calculated for an in-coming polarization π and a sum over the outgoing polarizations. The middle panels show the results with out-going polarization discrimination, here chosen in the cross-polarized geometry to emphasize the spin excitations. The results were obtained for the Hubbard model parameters U=8t, t′=−0.3t with t=0.4 eV, a Lorentzian broadening with half width at half maximum (HWHM)=0.025t and a Gaussian broadening with HWHM=0.118t on the energy transfer (see Methods).