UNDI: An open-source library to simulate muon-nuclear interactions in solids

We present UNDI, an open-source program to analyze the time dependent spin polarization of an isolated muon interacting with the surrounding nuclear magnetic dipoles in the context of standard muon spin rotation and relaxation spectroscopy experiments. The code can perform both exact and approximated estimates of the muon polarization function in presence of external fields and electric field gradients on the nuclei surrounding the muon. We show that this tool, combined to ab initio estimations of the electric field gradient at the nuclei interacting with the muon, can become a valuable complement to supercell based identifications of muon sites in crystals when large nuclear magnetic moments are present in the sample. In addition, it allows to properly investigate physical properties influenced by the presence of a non-negligible electric field gradient such as avoided level crossing resonance, nature of the ground state, disentanglement of electronic and nuclear magnetic moments or charge ordered states. The efficiency and effectiveness of this method is shown along the lines of three realistic examples.