Ab initio modelling of positive muon implantation sites in crystalline solids

In this thesis, a computationally efficient method for identifying interstitial muon sites in crystalline solids is presented. An accurate determination of muon embedding positions and effects is important for muon spin rotation and relaxation experiments since it can significantly widen the capabilities of this experimental technique. Indeed, these information are usually unknown to the experimenter and in most cases it is not possible to characterize the muon sites and the muon induced perturbation from experimental knowledge. The approach proposed in this thesis is based on ab initio Density Functional Theory (DFT) simulations and it was designed to provide a companion tool to assist muon spin rotation data analysis. The first principles determined muon stopping site(s) and the expected perturbation produced by the muon implantation have been compared to muon spin rotation and relaxation results in a series of textbook cases that have been extensively characterized experimentally. It is also highlighted that the estimation of the ground state energy of the muon (also referred to as zero point motion energy) is crucial in order to distinguish between trapping and non-trapping muon sites. In order to keep the computational load of the ab initio simulations within the bounds of standard computer clusters capacities, we approximate the total Hamiltonian of the system introducing a Born-Oppenheimer separation between the degrees of freedom of the muon and those of the nuclei and of the electrons. This approach has been referred to as double adiabatic approximation in literature. The method is found to be sufficiently accurate as well as computationally feasible when an algorithmic procedure to efficiently perform the simulations is introduced. The successful results obtained so far include the identification of muon sites in iron pnictide superconductors, the study of F-mu-F centres in fluorides, muon diffusion in Copper and the recent identification of muon sites in MnSi and T'-La2CuO4. All these cases confirm the validity of the DFT approach and emphasize the importance of accurate muon site predictions.