Probing Hidden Orders with Resonant Inelastic X-Ray Scattering

We propose a general scheme for the derivation of the signals resonant inelastic (and elastic) x-ray scattering (RIXS) gives access to. In particular, we find that RIXS should allow to directly detect many hidden orders, such as spin nematic, bond nematic, vector and scalar spin chiralities. To do so, we choose to take the point of view of effective operators, leaving microscopic details unspecified, but still keeping experimentally-controllable parameters explicit, like the incoming and outgoing polarizations of the x-rays. We ask not what microscopic processes can lead to a specific outcome, but, rather, what couplings are in principle possible. This approach allows to systematically enumerate all possible origins of contributions to a general RIXS signal. Although we mainly focus on magnetic insulators, for which we give a number of examples, our analysis carries over to systems with charge and other degrees of freedom, which we briefly address. We hope this work will help guide theorists and experimentalists alike in the design and interpretation of RIXS experiments.