Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators

We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that in order to obtain the correct leading contributions to the Raman vertex operator R one must take into account the precise, photon-assisted microscopic hopping processes of the electrons. Hence in systems with multiple hopping paths, R might contain terms beyond those appearing in the traditional Loudon-Fleury theory. We apply the revised theory to the three-dimensional hyperhoneycomb Kitaev material β−Li2IrO3, and the results show a qualitative modification of the polarization dependence, including, e.g., the emergence of a sharp one-magnon peak at low energies, which is not expected in the traditional Loudon-Fleury theory. This peak is shown to arise from microscopic photon-assisted tunneling processes that are of similar type with the ones leading to the symmetric off-diagonal interaction Γ, but take the form of a bond-directional magnetic dipole term in the Raman vertex. These results are expected to apply across all Kitaev materials and mark a drastic change of paradigm for the understanding of Raman scattering in materials with strong spin-orbit coupling and multiple exchange paths.