Theoretical Demonstration of How the Dispersion of Magnetic Excitations in Cuprate Compounds can be Determined Using Resonant Inelastic X-Ray Scattering

We show that in resonant inelastic x-ray scattering (RIXS) at the copper $L$ and $M$ edge direct spin-flip scattering is in principle allowed. We demonstrate how this possibility can be exploited to probe the dispersion of magnetic excitations, for instance magnons, of cuprates such as the high $T_c$ superconductors. We compute the relevant local and momentum dependent magnetic scattering amplitudes, which we compare to the elastic and $dd$-excitation scattering intensities. For cuprates these theoretical results put RIXS as a technique on the same footing as neutron scattering.