Muonium states in zincblende-structured compounds

The authors present a list of results of μSR experiments in materials with the diamond and zincblende structure. Besides the muonium hyperfine parameters, additional information is tabulated: the formation probability for the different muon states, the highest temperatures at which muonium states have been observed and the types of transitions found to occur between these states. The muonium hyperfine parameters show a linear rise as a function of host ionicity from Ge to GaAs to ZnSe followed by a sharp drop to CuBr.     

Charge exchange of muons in gases: Experimental implications from rate theory

The effects of the charge exchange process on muon spin dynamics have been investigated using a density operator formalism with special interest placed upon the diamagnetic muon and paramagnetic muonium signals observed after thermalization. In the charge exchange region the dynamics of the spin density operator is assumed to be determined by the muonium hyperfine interaction and by electron capture and loss processes for muons. Analytical expressions are obtained for the amplitudes and phases of the diamagnetic muon and paramagnetic muonium signals as a function of the duration of the charge exchange region,t _c, which is inversely proportional to the number density of the moderating gas. The theoretical signals exhibit three features which have, as yet, to be experimentally observed, namely: (i) that the amplitudes associated with the muonium Larmor frequency and with the hyperfine frequency are not, in general, equal, (ii) that all the amplitudes are, in general, damped oscillatory functions oft _c (temperature/pressure) and (iii) that phase jumps occur when an amplitude decreases to zero and then increases with falling pressure. Fits to the experimental argon data are discussed in light of the above points.     

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.     

Powder Pattern Hyperfine Spectroscopy of Shallow- Donor Muonium Centres

The hyperfine spectroscopy of muonium in II–VI semiconductors is reviewed, suggesting that whereas hydrogen is a deep-level defect in ZnS, ZnSe and ZnTe, it constitutes a shallow donor in ZnO, CdS, CdSe and CdTe. Shallow and deep states coexist in CdTe. Using new data for ZnO, it is shown that the principal values of the muonium hyperfine tensor may be obtained with equal facility from measurements in longitudinal or in transverse magnetic field, and from samples that are polycrystalline powders or single crystals. Spin density on the central muon in the shallow states correlates with the electron binding energy or donor depth. This revised version was published online in September 2006 with corrections to the Cover Date.     

Quantum diffusion of muonium in insulators

In this paper we review our recent experiments conducted at TRIUMF on muonium diffusion in alkali halides. First, the technique of longitudinal-field muonium spin relaxation (T ₁) due to nuclear hyperfine interaction, an indispensabletour de force for the present work. is described. It is demonstrated in KCl that the technique provides spectacular sensitivity for muonium diffusion as well as determining the average nuclear hyperfine coupling constant. The muonium hop rate shows a minimum (T ^*≃80 K) and steep increase with decreasing temperature. The result is compared with the current theory of quantum diffusion in non-metallic crystals. A few more sets of new data may be presented for other alkali halides. In addition, we show that muonium forms a delocalized state in NaCl as evidenced by a large change of the average nuclear hyperfine parameter. Related topics of local tunneling system may be briefly reviewed.     

Muonium acoustic resonance

Theoretical consideration is given to the effect of ultrasonic oscillations on the spin polarization of the positive muon of muonium present in matter. The resonant action of the periodic acoustic perturbation on the muonium hyperfine structure levels is shown to result in characteristic oscillations and to modify the muon spin precession pattern considerably. The possibilities for experimental detection of the muonium acoustic resonance are discussed     

Novel behavior of bond-centered muonium in heavily doped n-type silicon: Curie-like spin susceptibility and charge screening

Bond-centered muonium ( Mu(0)(BC)) has been observed in very heavily doped n-type Si:P. It exhibits a Curie-like electronic spin susceptibility which leads to a giant negative shift in the muon spin precession frequency. At high dopant levels, the Mu(0)(BC) hyperfine parameters, deduced from a model involving spin exchange with free carriers, are significantly reduced from those in intrinsic Si. This indicates that the spin density distribution for Mu(0)(BC) in metallic Si:P is altered significantly by charge screening effects, likely a general phenomenon for deep impurities in materials with high carrier concentrations.     

Theory for position of muonium in α-quartz and associated hyperfine interaction

The electronic structures and hyperfine interactions of muonium and hydrogen in -quartz are investigated by the unrestricted Hartree-Fock cluster procedure. The muonium is found to be trapped near the center of the line joining two silicon atoms. On including vibrational effects, the muon hyperfine constant comes out as 1.09 times that for free muonium, this ratio being larger than unity and smaller than for protons in trapped hydrogen, both features being in agreement with experiment.Briefly reported in Abstract at the American Physical Society meeting in New Orleans, March 1988. See Bull. Am. Phys. Soc. 33 (1988) 770.     

Electronic structure of the muonium center as a shallow donor in ZnO

The electronic structure and the location of muonium centers (Mu) in single-crystalline ZnO were determined for the first time. Two species of Mu centers with extremely small hyperfine parameters have been observed below 40 K. Both Mu centers have an axial-symmetric hyperfine structure along with a <0001> axis, indicating that they are located at the antibonding (AB(O, parallel )) and bond-center (BC( parallel )) sites. It is inferred from their small ionization energy ( approximately 6 and 50 meV) and hyperfine parameters ( approximately 10(-4) times the vacuum value) that these centers behave as shallow donors, strongly suggesting that hydrogen is one of the primary origins of n type conductivity in as-grown ZnO.     

O(alpha(3) lnalpha) corrections to muonium and positronium hyperfine splitting

We compute O(alpha(3)lnalpha) relative corrections to the ground-state hyperfine splitting of a QED two-body bound state with different masses of constituents. The general result is then applied to muonium and positronium. In particular, a new value of the muon-to-electron mass ratio is derived from the muonium ground-state hyperfine splitting.     

Theoretical study of the Cox-Symons model for normal muonium in silicon

A theoretical study of the Cox-Symons model for normal muonium in Si is presented. The calculations are performed using polarized basis set ab-initio Hartree Fock calculations followed by corrections for electron correlation. It is shown that, if lattice relaxations are included, the antibonding site becomes a minimum of the potential energy surface (PES) for neutral interstitial hydrogen. The energy at this minimum is lower than that at the undistorted tetrahedral interstitial site. The spin density changes from being almost entirely on the muon (for Mu at the T site) to being almost entirely on a three-fold coordinated Si atom (for Mu in the AB configuration). The mechanism required to explain the isotropy and magnitude of the observed hyperfine tensor of Mu in c-Si is complicated. Large displacements of some host atoms are needed, and the system must be dynamic. However, this model is the first able to produce a minimum of the PES together with an isotropic hyperfine interaction and a delocalized spin density.     

Study of condensed nitrogen by μSR method

The temperature dependences of parameters of the muon spin relaxation in liquid and crystalline nitrogen have been studied. It has been established that in condensed nitrogen there takes place a fast depolarization of muons. An anomalous behaviour of the amplitude and phase of muon precession is found in the vicinity of the orientation phase transition in solid nitrogen. It has been shown that muon spin relaxation parameters in nitrogen do not change at reduction of the oxygen impurity content from 0.7·10⁻⁴ to 10⁻⁶. The fast depolarization of muons in condensed nitrogen is apparently due to the formation of muonium atoms. To explain the phenomena observed, a model of the muonium chemical reaction is proposed. The initial phase of the muon precession has been measured as a function of the perpendicular magnetic field to determine the state of short-lived muonium in nitrogen. It has been determined that muonium in nitrogen is in an excited state. Consideration of the nuclear hyperfine interaction of muonium in condensed nitrogen makes it possible to give a qualitative explanation for the temperature dependence of the initial amplitude of the muon precession.     

Investigation of expected location of muonium in normal state in III–V semiconductors and associated muon hyperfine interaction

The location and hyperfine properties of muonium in AlP is investigated by the unrestricted Hartree-Fock cluster procedure. Two minima are found, one at the aluminium tetrahedral interstitial site, and the other at the corresponding phosphorus site. The former is deeper by 0.25 eV and separated from the other minimum by a steep maximum of 0.63 eV in the hexagonal region. Using the calculated electronic wave functions, the muon hyperfine constant, after vibrational averaging, comes out smaller than the value for free muonium, the ratio being 0.93. This value is, however, significantly higher than the experimental results in GaP and GaAs.Briefly reported in Abstract at American Physical Society meeting in New Orleans, March 1988, see Bull. Am. Phys. Soc. 33 (1988) 1364.     

Constraints on proton structure from precision atomic-physics measurements

Ground-state hyperfine splittings in hydrogen and muonium are very well measured. Their difference, after correcting for magnetic moment and reduced mass effects, is due solely to proton structure-the large QED contributions for a pointlike nucleus essentially cancel. The rescaled hyperfine difference depends on the Zemach radius, a fundamental measure of the proton, computed as an integral over a product of electric and magnetic proton form factors. The determination of the Zemach radius, (1.019+/-0.016) fm, from atomic physics tightly constrains fits to accelerator measurements of proton form factors. Conversely, we can use muonium data to extract an experimental value for QED corrections to hydrogenic hyperfine data. There is a significant discrepancy between measurement and theory, in the same direction as a corresponding discrepancy in positronium.     

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.     

New value of m(mu)/m(e) from muonium hyperfine splitting

The complete contribution to the muonium hyperfine splitting of relative order alpha(3)(m(e)/m(mu))lnalpha is calculated. The result is much smaller than suggested by a previous estimate and leads to a 2sigma upward shift of the most precise value for the muon-electron mass ratio. Analogous contributions are calculated for the positronium hyperfine splitting, where a discrepancy with experiment remains.     

Muonium in ice

Muonium has been studied in single crystals of H₂O and D₂O. Two-frequency precession in low transverse fields and a single zero-field oscillation indicate a small anisotropy of axial symmetry in the muonium hyperfine interaction. The anisotropy is shown to be the cause of the hitherto unexplained temperature independent contribution to muonium spin relaxation in polycrystalline samples. Relaxation rates for 99 K–263 K are reported for muonium in a single crystal of H₂O. Relaxation is attributed to electron-nuclear dipolar coupling of muonium to lattice protons, modulated by translational diffusion of muonium alongc-axis channels of the ice lattice. A simple model for H and Mu diffusion in ice is investigated.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

Electronic structure, dynamics, and metastability of muonium in semiconductors

Muonium centers are light hydrogen-like centers formed when positive muons are stopped in crystalline semiconductors. Detailed information on the hyperfine structure, dynamics and metastability of muonium are obtained using a combination of muon spin rotation or relaxation, muon level-crossing resonance and related methods. The expected close similarity to hydrogen, especially with regard to electronic structure, is important since the equivalent information on isolated hydrogen is either less detailed or completely absent. There are also interesting differences between muonium and hydrogen. In particular muonium dynamics are expected to exhibit enhanced quantum mechanical effects since the muon has only 1/9th the proton mass. In this paper we review the current status of experiments.     

Muonium as a shallow center in GaN

A paramagnetic muonium (Mu) state with an extremely small hyperfine parameter was observed for the first time in single-crystalline GaN below 25 K. It has a highly anisotropic hyperfine structure with axial symmetry along the <0001> direction, suggesting that it is located either at a nitrogen-antibonding or a bond-centered site oriented parallel to the c axis. Its small ionization energy (相似文献   

Recent advances in positive muon spin rotation; muonium as a probe of fullerenes

In non-metallic solids the positive muon often forms paramagnetic muonium centers which are characterized by the hyperfine interactions of the unpaired electron with the positive muon and with the surrounding nuclear spins. The static and fluctuating components of these hyperfine interactions provide information on local molecular dynamics and local electronic structure. Some recent results on C₆₀ and related compounds are presented to illustrate this.