Hamiltonian parameter inference from resonant inelastic x-ray scattering with active learning

Identifying model Hamiltonians is a vital step toward creating predictive models of materials. Here, we combine Bayesian optimization with the EDRIXS numerical package to infer Hamiltonian parameters from resonant inelastic x-ray scattering (RIXS) spectra within the single atom approximation. To evaluate the efficacy of our method, we test it on experimental RIXS spectra of ${\mathrm{NiPS}}_{3}, {\mathrm{NiCl}}_{2}, {\mathrm{Ca}}_{3}{\mathrm{LiOsO}}_{6}$, and ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$, and demonstrate that it can reproduce results obtained from hand-fitted parameters to a precision similar to expert human analysis while providing a more systematic mapping of parameter space. Our work provides a key first step toward solving the inverse scattering problem to extract effective multi-orbital models from information-dense RIXS measurements, which can be applied to a host of quantum materials. We also propose atomic model parameter sets for two materials, ${\mathrm{Ca}}_{3}{\mathrm{LiOsO}}_{6}$ and ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$, that were previously missing from the literature.