Anomalous Muonium Research Articles

First-principles calculation of anomalous muonium in silicon: origin of the negative Fermi contact interaction constant

We present the calculation of anomalous muonium in silicon which has been extensively studied but there still remains unresolved problems in the first-principles calculations. We perform calculations using spin-polarized density functional theory within the general gradient approximation or the local density approximation. We check the size effect of supercells and find that we need to use large sizes of supercells to obtain reliable results. Some quantitative disagreement between the experimental and theoretical values in previous studies may be due to the use of insufficient sizes of supercells. We clarify that the negative Fermi contact interaction constant (FCIC) is induced by the electron correlation effect. By using the Hubbard model, we find that the FCIC is zero when we neglect the correlation effect and the negative value of the FCIC is induced by the correlation effect.

MuSR method and tomographic-probability representation of spin states

Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and muon spin tomograms is established. Time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. Entanglement phenomenon of a bipartite muon-electron system is investigated via tomographic analogues of Bell number and positive partial transpose (PPT) criterion. Reconstruction of the muon-electron spin state as well as the total spin tomography of composed system is discussed.

Oxide muonics: A new compendium

A new survey of muonium states brings the total of binary non-magnetic oxides studied to 30, with normal muonium—the interstitially trapped atomic state—found in 15 of these. The number of shallow-donor states of the type known in ZnO now also totals 15, but there are hints of several others. Tantalizingly, the shallow-donor and deep-atomic states are found to coexist in several of the candidate high-permittivity dielectrics. Highly anisotropic states, resembling anomalous muonium in semiconductors and including examples of muonium trapped at oxygen vacancies, complete a spectrum of hyperfine parameters covering five powers of ten. Effective ionization temperatures range from 10 K for shallow to over 1000 K for deep states, with corresponding activation energies between several meV and several eV. The oxide band gap emerges as a parameter controlling the systematics of the deep-to-shallow transition for muonium and, by inference, monatomic hydrogen.

On the kinetics of anomalous muonium in silicon

The spin relaxation rate of anomalous muonium in a longitudinal magnetic field was measured in a silicon single crystal. The results are treated as the diffusion of anomalous muonium in a silicon crystal.

Short range electron transport in GaAs

We report direct evidence that the anomalous muonium (Mu BC 0) center in GaAs is formed via transport to the muon of excess electrons that are initially more than 3×10 −6 cm away.

The origin of anomalous muonium in semiconductors

The origin of muonium defect centers in semi-insulating GaAs has been studied using newly developed μSR techniques employing alternating electric fields. This technique prevents the accumulation of near-surface charges which may screen the external field. The screening effect was tested at ISIS by the measurements of the current induced by muon beam. Suppression of anomalous muonium signal with electric field suggests that muonium formation proceeds via transport of excess electrons from the ionization track to the muons.

First-principles study of the quantum states of muonium and hydrogen in crystalline silicon

We present a theoretical study of the quantum states of muonium and atomic hydrogen in crystalline silicon using the generalized gradient approximation to density-functional theory combined with the path-integral molecular-dynamics method. Normal muonium, one of the two stable states, is distributed around the tetrahedral site. The potential-energy surface is considerably modified in the presence of muonium by distorting silicon cage and stabilizes the state. The other state of muonium, anomalous muonium, is located around the bond center site with significant quantum vibration in a steep potential well. The relative stabilities and dynamics of the two sites are discussed, and the essential roles of quantum effects are emphasized.

Evidence for a novel muon species in crystalline silicon

Investigations of positive muons ( μ +) in crystalline silicon employing the longitudinal field-quenching (LFQ) technique give strong evidence for the existence of a novel paramagnetic muon species with a small anisotropic hyperfine interaction. It adds to the list of known muon species, i.e., normal and anomalous muonium and the diamagnetic muon species. The signatures of the novel species are found in intrinsic but not in doped samples (dopant concentration about 10 16 cm −3). The novel species is not formed promptly but results from a reaction in which normal muonium transforms into the novel species. The reaction rate constant at 10 K was found to be about 10 6 s −1. The hyperfine coupling of the novel paramagnetic muon species corresponds, after rescaling, to that of a hydrogen center termed VH, which has been discovered recently by Bech Nielsen et al. ( Phys. Rev. Lett., 79, 1997, 1507) and which has been attributed to hydrogen trapped in vacancies. The LFQ data are tentatively interpreted in terms of trapping of normal muonium in vacancies that are created during the slowing-down of implanted muons close to the end of their stopping tracks.

Muonium Formation via Electron Transport in Silicon

We report muon spin rotation measurements in $n$-type silicon from 10 to 310 K in electric fields up to 5 kV/cm. These experiments reveal the nature of the partition of neutral muonium centers into normal muonium $({\mathrm{Mu}}_{T}^{0})$ and anomalous muonium $({\mathrm{Mu}}_{\mathrm{BC}}^{0})$: Formation of ${\mathrm{Mu}}_{T}^{0}$ is consistent with epithermal processes prior to thermalization, while ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$ is formed via electron transport to a thermalized positive muon. The spatial distribution of the excess electrons created in the ${\ensuremath{\mu}}^{+}$ ionization track is shown to be anisotropic with respect to the muon.

Comparative calculations on the hyperfine parameters of bond-centered impurities in silicon using high-level ab initio techniques

The electronic structure of hydrogen and muonium at the bond‐centered site (anomalous muonium) in silicon is investigated using ab initio cluster calculations. Correlation effects are accounted for by the configuration interaction method and by density functional calculations. A detailed investigation of the different functionals is presented. The calculations using configuration interaction and the different gradient corrected density functionals are in good agreement with each other. The effect of the zero point motion was included in the investigation.

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (MuT) and the diamagnetic states (μd), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (MuBC) and μd. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond.

Anomalous muonium relaxation rates in quartz at high temperatures

Muonium spin relaxation measurements of the \alpha‐, \beta‐, and \gamma‐tridymite phases of quartz have been carried out over a temperature range from 300 to 1250 K. Anomalous relaxation rate increases are observed which may result either from resonance coupling between the other impurity ions and defects in the lattice and the diffusing muonium, or may result from phonon interactions with the muonium quadrupole moment.

Muon state dynamics in germanium and silicon

The dynamics of the various muon states (paramagnetic states muonium Mu and anomalous muonium Mu*, diamagnetic states μd) were studied by means of radio‐frequency μ+ spin resonance (RFμSR), longitudinal field‐quenching (LFQ), and transverse μ+ spin rotation (TFμSR) in an undoped high‐purity and a gallium‐doped germanium single crystal in the temperature range 3.5–320 K.

Level-crossing resonance spectra for bond-centred muonium in silicon

Abstract Previous avoided level-crossing experiments have revealed the microscopic structure of the paramagnetic anomalous muonium state in silicon: in addition to the axially symmetric hyperfine interaction along a (1, 1, 1) axis, distinct orientation-dependent superhyperfine interactions with first and second nearest neighbour 29Si nuclei have been observed. Here we report a theoretical study of the influence of further distant 29Si nuclei. Their contribution to the field dependence of the time-integrated longitudinal polarization function is investigated. The appearance of additional resonances is discussed and their locations as a function of field strength are calculated analytically by perturbation theory as well as numerically.

Investigation of muon-state dynamics in silicon by longitudinal field-quenching and radio-frequency μ+ spin resonance

The two paramagnetic muon states-normal and anomalous muonium-and the diamagnetic muon states have been investigated in different monocrystalline silicon samples (intrinsic, boron-, phosphorus-, or arsenic-doped, float-zone or Czochralski-grown) between 6K and 800K by means of longitudinal field-quenching (LFQ) and radio-frequency μ + spin resonance (RFμSR). The LFQ data can be described consistently by coupled equations of motion for the muonium spin systems if spin exchange processes as well as transitions between different muon states are taken into account. It is shown that the initial formation probabilities of the different muon states, the ionization rate of the anomalous muonium, and the electron spin exchange rates depend strongly on the charge carrier densities. These results are in agreement with the RFμSR data obtained on the same samples if the different time scales of RFμSR and LFQ experiments are taken into account. At temperatures above 300 K both RFμSR and longitudinal relaxation results appear to indicate reversible ionization of normal muonium.

Field dependence of the longitudinal muon polarization for anomalous muonium

The constant muon polarization for anomalous muonium exhibits a peculiar field dependence which represents an easily measurable signature of anomalous muonium centers even in polycrystalline materials. Furthermore it can be used to extract information on the dynamical destruction of the state upon temperature variations and it might also be useful to investigate muonium in amorphous materials.

Distinctive field dependence of the longitudinal muon polarization for Mu* in polycrystalline silicon

A distinctive longitudinal magnetic field dependence of the muon polarization for anomalous muonium in polycrystalline semiconductor targets has been predicted. The polarization exhibits a cusp,i.e., a discontinuous jump in the slope from negative to positive. Measurements of the longitudinal polarization for polycrystalline silicon in fields up to 0.5 T, and temperatures 53 and 200 K have been made at LAMPF. A cusp in the field dependence indeed occurs at 0.345 T, in excellent agreement with the prediction. No cusp is observed at 200 K because Mu* has been thermally ionized.

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.

Interaction of anomalous muonium with electronic excitations in Si studied by longitudinal field μSR

We report longitudinal muon spin relaxation measurements in Si doped with phosphorus below room temperature. The data can be described qualitatively in a model where bond-centered muonium is undergoing spin exchange interactions below 150 K. Above this temperature, charge state cycling becomes important.

Field dependence of the longitudinal muon polarization for anomalous muonium.

An unusual longitudinal-magnetic-field dependence of the muon polarization for anomalous muonium (${\mathrm{Mu}}^{\mathrm{*}}$) in polycrystalline semiconductor targets is predicted, and has been observed for Si. As a function of field, the experimentally measured muon polarization at 53 K exhibits a cusp, i.e., a discontinuous jump in the slope from negative to positive, at 340(5) mT, in good agreement with theory. This occurs because the effective field on the ${\mathrm{\ensuremath{\mu}}}^{+}$ vanishes at this external field as the angle between it and the ${\mathrm{Mu}}^{\mathrm{*}}$ symmetry axis approaches 90\ifmmode^\circ\else\textdegree\fi{}. At 200 K no cusp is seen because ${\mathrm{Mu}}^{\mathrm{*}}$ has been thermally annihilated. Fractional populations of the different muonium species are derived from the 53-K data. All ${\mathrm{Mu}}^{\mathrm{*}}$ and other anisotropic centers, including molecular radicals, should exhibit such a cusp, allowing the possibility of observing such species even in disordered or amorphous solids where spectroscopic detection might be impossible. Integral counting (and therefore very high data rates) can be used for these observations.