Model calculations of nuclear hyperfine structure for anomalous muonium and their implications

Calculations of the effects of resolved and unresolved nuclear hyperfine structure for anomalous muonium have been made for a range of axial nuclear hyperfine parameters and magnetic fields. Although the spectra arc complex, their moments allow predictions about line widths (or depolarization rates) from unresolved hyperfine structure. The increase of with decreasing field observed experimentally is obtained in these calculations. In addition we make predictions of for zero-field spectra, angular dependences of, and line shifts.The work of T.L. Estle and M.E. Warren was supported by N.S.F. grant DMR-79-09223. The help of Serge L. Rudaz is gratefully acknowledged.     

Calculations of the hyperfine parameters of bond-centered muonium in diamond

The electronic structure of hydrogen and muonium at the bond-centered site in diamond is investigated using ab initio cluster calculations. Correlation effects are accounted for by a configuration interaction expansion and by the local density approximation in the density functional approach. The hyperfine and superhyperfine parameters for anomalous muonium are determined by averaging over the spread of the muon wave function. Good agreement with experimental hyperfine parameters is found.This work has partially been supported by the Swiss National Science Foundation.     

Temperature dependence of the hyperfine parameters of anomalous muonium in germanium

The temperature variation of the anomalous muonium hyperfine interaction in germanium has been measured between 5 and 100 K. The results show that the component perpendicular to the defect axis decreases, while the parallel component increases with increasing temperature. These effects are a result of the interaction of anomalous muonium with the germanium host phonons.Work supported by National Science Foundation Grant DMR-79-09223.     

Hyperfine interactions of muonium and hydrogen in semiconductors: Cluster calculations

The electronic structure of muonium (Mu) located at different interstitial sites of the silicon crystal is calculated by the complete neglect of differential overlap (CNDO) and intermediate neglect of differential overlap (INDO) methods. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared with the experimental properties of both “normal” (Mu′) and “anomalous” (Mu^*) muonium centers. It is shown that the most likely dynamic model for Mu′ is that in which neutral Mu diffuses rapidly in the silicon lattice, whereas for Mu^* it is the model wherein interstitial Mu is located at the bond-center site. A correlation is made between the characteristics of the hydrogen-bearing Si-AA9 center, recently observed by EPR in a silicon crystal, and those of Mu^*. The Si-AA9 center is shown to be a hydrogen-bearing paramagnetic analogue of the Mu^* center.     

Quadrupole moment of muonium and hyperfine structure of muonium levels in silicon

It is shown that experimental data on Mu¹ in silicon are most satisfactorily described by the uniaxial symmetric spin hamiltonian which means muonium displacement from the octa-cell center.     

First-principles calculations of hydrogen in bulk GaAs

We present the results of first-principles calculations of the properties of neutral (H⁰) and charged (H⁺ and H^-) hydrogen in bulk GaAs. The equilibrium sites are determined, and the electronic properties for the equilibrium positions are studied. H⁺ behaves as a deep donor and prefers to stay in a high valence charge region which includes the bond center. H^- behaves as a deep acceptor and prefers the low valence charge region near a tetrahedral site. H⁰ has an amphoteric behaviour depending on the site it occupies. We compare our results with the results of calculations for H in Si.     

Location of muonium and hydrogen in C60 fullerene and associated electronic structure and hyperfine properties

The unrestricted Hartree-Fock (UHF) procedure is used to investigate the locations, associated electronic structures and hyperfine interactions for muonium and hydrogen in C₆₀ fullerene. Our results indicate that from total energy considerations, in keeping with earlier investigations, the exohedral model has the lowest energy. However, the energies of the endohedral model involving the muonium (hydrogen) inside the fullerene and bonded to one of the carbon atoms, and of the muon at the center are found to be almost equal, contrary to earlier results. The hyperfine interaction constant for the endohedral site is in good agreement with that required to explain the lower observed muon spin-rotation (SR) frequency in the C₆₀-muonium system. The same appears to be the case for the exohedral model. However, there seems to be some uncertainty about the theoretical result in the latter case due to significant admixtures of higher spin states in the UHF wave-function. Additionally, in solid fullerene, the calculated location of the muonium for the exohedral model is such that it could be bonded to two fullerene molecules and therefore a muonium attached to a simple fullerene may not be representative of the exohedral state. This feature as well as the difficulty for the exohedral model of explaining the observed equality of the correlation times for relaxation effects associated with both SR and¹³C relaxation times in nuclear magnetic resonance (NMR) experiments suggests that the endohedral model for muonium cannot at present be ruled out as a viable model in favor of the exohedral model. Possible avenues for future investigations to resolve some of the problems for both exohedral and endohedral models are discussed. Results obtained for muonium at the center of fullerene are presented and compared to the features of the observed high frequency SR signal, and possible improvements in theory are discussed.     

Resolved nuclear hyperfine structure of muonium centres in CuCl and GaAs by means of the avoided-level-crossing technique

Avoided-level-crossing resonances from isotropic muonium centres interacting with neighbouring nuclear spins in powdered CuCl are reported. The prominent resonances have a complex multiline structure and are strongly temperature-dependent. In addition, previously unobserved resonances in single-crystal GaAs from anomalous muonium interacting with a ⁷¹Ga neighbour are presented.     

Hyperfine interactions of muonium and hydrogen in silicon and diamond: Quantum chemical calculations

The electronic structure of a hydrogen-like atom located at interstitial sites of the silicon and diamond crystals is calculated by the intermediate neglect of differential overlap (INDO) method. Calculations of the electronic g- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared with the experimental properties of both “anomalous” muonium and hydrogen centers. It is shown that the most likely model for these centers in silicon and diamond is that in which interstitial neutral hydrogen-like atom locates at the bond-center site.     

Electronic structure and hyperfine interaction of muonium in semi-conductors

The Unrestricted Hartree-Fock self-consistent field cluster procedure is being utilized for first-principle investigations of the electronic structures and hyperfine interactions in normal and anomalous muonium states in semi-conductors. Our results for the total energy for the normal muonium state for a twenty-seven atom cluster in diamond, including the muonium and its neighboring atoms, show a minimum at the tetrahedral site and a maximum at the hexagonal site indicating that normal muonium is located in the tetrahedral region and avoids the hexagonal region. Using the calculated spin-density as a function of the position of muonium and carrying out averaging over the vibrational motion of the muon governed by the total energy curve obtained from our work, we have derived a muon hyperfine constant which is about 75% of that in free muonium, in good agreement with experiment. The natures of the total energy and spindensity curves permit us to draw conclusions regarding the origin of the observed trend in the hyperfine constants for normal muonium in diamond, silicon and germanium. The UHF cluster procedure is also applied to study a model of a muon in a positively charged environment for the anomalous muonium center in diamond. This model leads to a hyperfine interaction tensor with the observed feature of strong anisotropy but significantly weaker than experiment. The results obtained for this model indicate the importance for the anomalous muonium state with its relatively weak hyperfine interaction, of exchange polarization effects inherent in the UHF procedure.     

Quantum diffusion of muonium in GaAs

The diffusion rate of muonium in the III–V compound semiconductor GaAs has been determined from measurements of muon spinT ₁ relaxation induced by motion in the presence of nuclear hyperfine interactions. It is shown for the first time in a semiconductor that (a) there is a crossover of the transport mechanism at about 90 K from stochastic to zero-phonon hopping, as evidenced by a steep rise in the hop rate at lower temperatures, and that (b) the muonium diffuses at the hop rate of 10¹⁰ s⁻¹ (corresponding diffusion constantD≈10⁻⁶ cm²s⁻¹) at lower temperatures as well as at room temperature.