Muonium Centers Research Articles

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.

Self-consistent field cluster study of hyperfine properties of normal and anomalous muonium in elemental semiconductors

Using the Unrestricted Hartree Fock (UHF) Cluster Procedure, it is shown that for the normal muonium (Mu) center, the tetrahedral site is the most favorable in the two systems diamond and silicon investigated, while for the anomalous muonium (Mu*) center, a site displaced in the direction with respect to a vacancy in a double-positively charged environment is the appropriate one for all three elemental semiconductors. Using our calculated electronic wave-functions, one is able to explain all features of the observed hyperfine properties of both centers and, in a number of cases, obtain good quantitative agreement with experiment.

Muonium states in silicon carbide

Implanted muons in samples of silicon carbide have been observed to form paramagnetic muonium centers (μ+ e−). Muonium precession signals in low applied magnetic fields have been observed at 22 K in a granular sample of cubic β-SiC, however it was not possible to determine the hyperfine frequency. In a single crystal sample of hexagonal 6H-SiC, three apparently isotropic muonium states were observed at 20 K and two at 300 K, all with hyperfine frequencies intermediate between those of the isotropic muonium centers in diamond and silicon. No evidence was seen of an anisotropic muonium state analogous to the Mu* state in diamond and silicon.

Muonium defect centers in semiconductors

After a brief summary of the properties of the muonium defect centers observed in the elemental group IV semiconductors, the status of studies of muonium centers in semiconductors at the time of the last μSR conference in 1983 will be compared with what is currently known. With the introduction of new experimental techniques, such as high-transverse-field μSR and level-crossing spectroscopy, many new results are or soon will be available on muonium centers. These, combined with new theoretical studies, should lead to rapidly increased insight into a subject which has been both puzzling and resistant to clarification.

Atomic hydrogen and muonium in alkali halides

Atomic hydrogen can be trapped at interstitial and substitutional cation and anion sites in alkali halides. The geometrical structure of these defects was established by electron nuclear double resonance (ENDOR). From the analysis of the ENDOR spectra also detailed information was obtained on the electronic structure. In this article the major experimental and theoretical results for atomic hydrogen in several alkali halides are briefly reviewed. Special emphasis is given to the isotope effects upon replacing hydrogen by deuterium. The nature of the dynamical hyperfine and superhyperfine interactions is discussed. Its magnitude to be expected for muonium is estimated. Recent results on muonium centres are discussed on the basis of the knowledge about the hydrogen centres.

Muonium centers in the alkali halides

Muonium centers (Mu) in single crystals and powdered alkali halides have been studied using the high-timing-resolution transverse field μSR technique. Mu has been observed and its hyperfine parameter (HF) determined inevery alkali halide. For the rocksalt alkali halides, the HF parameter Aμ shows a systematic dependence on the host lattice constant. A comparison of the Mu HF parameter with hydrogen ESR data suggests that the Mu center is the muonic analogue of the interstitial hydrogenHi0-center. The rate of Mu diffusion can be deduced from the motional narrowing of the nuclear hyperfine interaction. KBr shows two different Mu states, a low-temperatureMuI-state and a high-temperatureMuII-state.

Muonium centers in the cuprous halides.

Muon-spin-rotation measurements in the group I-VII semiconductors CuCl, CuBr, and CuI reveal muonium centers with weak isotropic hyperfine (hf) parameters which range between 0.2716 and 0.3744 times the hf parameter for muonium in vacuum. The observed centers display several unusual characteristics when compared with muonium in other tetrahedrally coordinated materials. In particular the hf parameters in the copper halides are much smaller than expected on the basis of their ionicity. Also, in CuCl and CuBr two distinct muonium centers (${\mathrm{Mu}}^{\mathrm{I}}$ and ${\mathrm{Mu}}^{\mathrm{II}}$) with almost identical isotropic hf parameters are observed for the first time. The ${\mathrm{Mu}}^{\mathrm{I}}$ center is populated preferentially at low temperature but makes a thermally activated transition to ${\mathrm{Mu}}^{\mathrm{II}}$, indicating that ${\mathrm{Mu}}^{\mathrm{I}}$ is less stable than ${\mathrm{Mu}}^{\mathrm{II}}$. Measurements of the line broadening in the magnetic field region 0.2--1.2 T indicate that there is no motional averaging of the nuclear hyperfine interaction and therefore that the centers are close to being static.

Double electron-muon resonance of anomalous muonium in silicon.

Double electron-muon resonance (DEMUR) is reported on anomalous muonium centers in silicon. Resonance of EPR transitions otherwise non-observable is detected by characteristic structure in the muon-spin-rotation (\ensuremath{\mu}SR) spectra. In order to explain the nature of this structure, the theory of DEMUR is extended to include inhomogeneous broadening of the EPR and \ensuremath{\mu}SR transitions owing to nuclear hyperfine interactions with the $^{29}\mathrm{Si}$ nuclei present. The principal effect of this extension is that only one of the two \ensuremath{\mu}SR lines is split rather than both as predicted when nuclear hyperfine effects are neglected.

Molecular radical models for the muonium centres in solids

Molecular radical models are presented for the various muonium-related paramagnetic centres observed in the elemental and compound semiconductors, and for those which are currently being reported in other crystalline solids, notably halides. The measured coupling constants are shown to place tight constraints on the intrinsic geometries which need be considered, i.e. on the crystallographic sites and local relaxation of the lattice, as well as on the nature of the singly occupied molecular orbital. The role of tunnelling states is emphasized.

Self-consistent field cluster investigation of muonium-related paramagnetic centres in diamond

The unrestricted Hartree–Fock method has been used to study the muonium centres in diamond. The diamond lattice is represented by a cluster of carbon and hydrogen atoms with the formula C10H16. Only one site is found in the undistorted cluster, at the centre of the interstitial tetrahedral space. By extending one of the carbon–carbon bonds another more stable site is created at the middle of this extended bond. The calculated properties of these centres are consistent with the available experimental data.

Review of experimental studies of muonium centers in semiconductors

After a brief description of muon spin rotation and muonium, the observations on muonium defect centers in semiconductors are described. Two different muonium centers are seen. Normal muonium has an isotropic hyperfine interaction which is roughly one half of that for free muonium. Anomalous muonium has a contact hyperfine parameter varying from 1.5% to 4.6% of that for free muonium. In addition, the hyperfine interaction is highly anisotropic. Normal muonium is thought to be interstitial, whereas anomalous muonium is proposed to be substitutional.

Muonium centers in GaAs and GaP.

Muonium centers in GaAs and GaP.

Decoupling of Muonium in High Transverse Magnetic Fields

Depolarization of muonium due to superhyperfine interaction, which until now has severly impeded the study of muonium in solids, can be quenched in a high transverse magnetic field (1.2 T). We report the observation of muonium precession in single crystals of KCl, CaF/sub 2/, GaP, and Al/sub 2/O/sub 3/. The high-field frequencies are of order 2 GHz and provide a direct and accurate (60 ppm) measure of the hyperfine interval. Several novel features of the muonium centers are observed.

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.

Theory of double electron-muon resonance

The theory of double electron-muon resonance is developed and particularized to the case of muonium and of the anomalous muonium center observed in silicon, germanium, and diamond. The theory can be used to explain and analyze the coherence effects observed in muon-spin---rotation frequency spectra resulting from intense near-resonant rf fields. The technique can, in principle, be used to observe EPR transitions which are otherwise unobservable by muon-spin rotation.

Temperature dependence of the anomalous muonium hyperfine interaction and depolarization rate in silicon

The temperature dependence of the anomalous muonium hyperfine interaction has been measured in silicon between 5 K and 150/sup 0/K. The hyperfine parameters are observed to decrease with increasing temperature. This is argued to result from interaction of the anomalous muonium center with the silicon host phonons. Above 120/sup 0/K a rapid increase of the depolarization rate of the anomalous muonium with temperature is observed; these data are consistent with a Raman process causing the increased depolarization.

Mu in silicon: An interesting example in quantum mechanics

A quantum-mechanical example is presented which arose from experimental research with positive muons in solids. The anomalous muonium center in silicon apparently finds a necessary and sufficient description in terms of a spin Hamiltonian with interesting analytical solutions in various limits.