Abstract: Resonant X-ray scattering (RXS) has become one of the prime techniques to study charge and spin order in reciprocal space, owing to its high sensitivity to electronic states near the Fermi energy.

We have applied resonant X-ray methods to explore the emergent organization of the electronic degrees of freedom into periodically modulated patterns — a hallmark of strongly correlated quantum solids. The consequent breaking of translational symmetry is often manifested in the form of charge- or spin-density wave, two phenomena that are essential to the physics of two families of compounds, in particular cuprates and nickelates.

For copper oxide high-temperature superconductors, I will review the latest efforts to broadly chart out charge order across the extended doping-temperature phase diagram using RXS, as well as discuss recent implementations to extract symmetry information from the tensorial nature of the resonant scattering process.

For the rare earth nickelates (RENiO₃), I will focus on some of our recent efforts to use RXS at high spatial resolutions (50-75 nm) to visualize the nanoscale texture of spin-density waves across the Neel and metal-insulator transition. I will discuss the experimental trends observed both in pristine NdNiO₃ thin films and in electron-doped SmNiO₃, where control of the oxygen stoichiometry leads to dramatic changes in the electronic transport.

I will conclude with a few ideas and prospects on the use of coherent soft X-ray scattering methods (coherent diffractive imaging and ptychography) to map out the texture of electronic orders at even higher spatial resolutions, and with orders of magnitude improvements in imaging efficiency.