Enhancing muon spin spectroscopy: from atomistic simulation of muon implantation site to hyperfine coupling calculation

This thesis consists mainly of density functional theory (DFT) calculations, complemented by specific theoretical developments, to determine the implantation site of the positive muon and its magnetic hyperfine coupling in a range of selected materials, whose intriguing properties attract current scientific interest. The study is mainly motivated considering that in muon spin spectroscopy (µSR), whereby matter is probed by means of implanted muons, the site of muon implantation and the value of the different contributions to their magnetic coupling with the host environment are not known a-priori. They are crucial towards understanding certain physical properties of the materials, since knowledge of the muon implantation sites, muon hyperfine coupling and extent of perturbation of the muon's local environment in the host allows important information, beyond the values of the best fit parameters, to be indirectly extracted from µSR spectra. Notable examples are the magnitude of total magnetic moments and even the spin structure of some magnetic materials. The strategy for assigning the muon site with the DFT method is discussed and used successfully in the following selected materials; NaFe1-xNixAs, Yb2Pd2In1-xSnx and Sr2RuO4. Evidence for the coexistence of magnetism and superconductivity in NaFe1-xNixAs is provided by µSR measurements and the moment size on Fe, crucial in the context of iron pnictides, is determined by means of dipole sum calculations at the muon sites identified by DFT. In Yb2Pd2In1-xSnx, the muon sites are first calculated by DFT and then validated comparing a dipolar simulation with measured local fields. Furthermore, a steep increase in the measured muon local field by application of hydrostatic pressure at intermediate Sn doping is accounted for by assuming a transition to a different symmetry-allowed spin order. Lastly, the calculated muon implantation site in the superconducting Sr2RuO4 allows investigation of the extent of the muon perturbation and its effect on the time reversal symmetry breaking mechanism, in relation to the observation of this phenomenon with µSR in a very highly cited paper. I then proceed to discuss a systematic analysis of the accuracy of the calculation of the ab initio estimation of muon hyperfine contact field on elemental transition metals, using the projector-augmented pseudopotential approach. This approach allows one to include the core state effects and this accounts for the success of the calculated contact hyperfine field in Fe, Ni, Co. The same method is also used to calculate the contact field in non-centrosymmetric metallic compounds, presently of topical interest for their spiral magnetic structure giving rise to skyrmion phases, such as MnSi and MnGe. To further improve the accuracy of the calculated contact hyperfine field, I addressed the zero point vibration of the muon, not captured in the DFT treatment within the Born-Oppenheimer approximation. A published stochastic self-consistent harmonic approximation method is further developed specifically for the very light muon and used to successfully average the effect of the muon zero point vibrations on the calculated contact hyperfine field, improving the accuracy of the results. The last part of this thesis is the study of the charged and neutral states of hydrogen, an analogue of the implanted positive muon if one ignores zero point vibrations, in MnO and NiO. Hydrogen defect states at the band gap are observed to exist in these materials. The stability of these defect states is also discussed together with the magnetic coupling of the muon in the antiferromagnetically ordered transition metal mono-oxides. This allows to determine the easy axis of magnetization in MnO and NiO, a very subtle property to gain experimental access to, and a very nice example of the enhanced scope of µSR when used in conjunction with atomistic simulation.