Theory of structure and hyperfine properties of anomalous muonium in elemental semiconductors: Diamond, silicon, and germanium

A number of possible models for the anomalous muonium (${\mathrm{Mu}}^{\mathrm{*}}$) center in the elemental semiconductors diamond, silicon, and germanium are investigated in detail, both with respect to their stabilities and abilities to explain the extensive available experimental hyperfine-interaction data, the latter being the major focus of the present work. Using the unrestricted Hartree-Fock cluster procedure, the electronic structures and potential-energy curves associated with muon positions are obtained for the different models. The results are utilized to obtain hyperfine properties associated with the muon and its neighboring nuclei, including vibrational effects associated with the muon. Our results show that stability considerations favor both the vacancy-associated (VA) and bond-centered (BC) models for ${\mathrm{Mu}}^{\mathrm{*}}$. The VA model explains all the experimentally observed features of the muon hyperfine properties and provides reasonably good quantitative agreement with experiment. However, questions remain regarding its formation and ability to explain level-crossing resonance (LCR) data. On the other hand, although the BC model appears to explain the experimental features from LCR measurements, in its present form, it seriously overestimates the strengths of the muon hyperfine interactions as compared to experiment, by more than an order of magnitude in some cases. Additionally, it does not explain the trend from diamond through germanium. On the basis of the results in this paper for the VA and BC models, the direction for future investigations for understanding the nature of the ${\mathrm{Mu}}^{\mathrm{*}}$ center is commented on.