The theory of indirect resonant inelastic X-ray scattering on magnons

Recent experiments reveal indirect resonant inelastic X-ray scattering (RIXS) to be a new probe of spin dynamics. Here I derive the cross-section for magnetic RIXS and determine the momentum-dependent four-spin correlation function that it measures. These results show that this technique offers information on spin dynamics that is complementary to, e.g., neutron scattering. As an example the RIXS spectrum of Heisenberg antiferromagnets is calculated by considering a half filled single band Hubbard model at strong coupling and zero temperature. It turns out that only scattering processes that involve at least two magnons are allowed. Other selection rules imply that the scattering intensity vanishes for specific transferred momenta q, in particular for q = 0. All results agree very well with recent experimental data. (author)