Theory-restricted resonant x-ray reflectometry of quantum materials

The delicate interplay of competing phases in quantum materials is dominated by parameters such as the crystal field potential, the spin-orbit coupling, and, in particular, the electronic correlation strength. Whereas small quantitative variations of the parameter values can thus qualitatively change the material, these values can hitherto hardly be obtained with reasonable precision, be it theoretically or experimentally. Here we propose a solution combining resonant x-ray reflectivity (RXR) with multiplet ligand field theory (MLFT). We first perform ab initio DFT calculations within the MLFT framework to get initial parameter values, which we then use in a fit of the theoretical model to RXR. To validate our method, we apply it to NiO and ${\mathrm{SrTiO}}₃$ and obtain parameter values, which are amended by as much as $20%$ compared to the ab initio results. Our approach is particularly useful to investigate topologically trivial and nontrivial correlated insulators, staggered moments in magnetically or orbitally ordered materials, and reconstructed interfaces.