Diamagnetic muonium states in InP

Transverse and zero‐field muon spin relaxation reveal several diamagnetic muonium states in InP characterized by their static linewidths and diffusion properties. We tentatively associate low‐temperature diamagnetic states with Mu⁺ in the BC and T_P interstitial sites and a missing fraction with Mu⁰ rapidly diffusing through T_In interstices. Trapping peaks above 250 K imply static centers which depend on doping type, consistent with Mu^- at T_In for n‐type samples and Mu coupled with a dopant or other defect for p‐type. This revised version was published online in August 2006 with corrections to the Cover Date.     

A reply to arguments against a spur model for muonium formation

A clear distinction is made between the spur model for muonium formation in condensed matter and the alternative hot model. Arguments against the spur model are considered and found lacking. Some new data is presented for aqueous systems: the initial diamagnetic fraction increases with OH^– concentration, and unequivocal muonium inhibition is demonstrated for HClO₄ solutions.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

Muons and muonium in cryocrystals

We present a collection of measurements of the muon and muonium asymmetries and relaxation parameters in cryocrystals of N₂, CO, Xe,¹³⁶Xe and Ne as functions of temperature. Generally, the fractions of the two species can be attributed to a competition between the formation of muonium or a diamagnetic species, where processes involving transport of spur electrons are important.     

MuSR/μ+SR studies in KDP and DKDP

The temperature dependence of muon interactions has been studied in ferroelectric KDP ( H₂KPO₄) and DKDP ( D₂KPO₄) using conventional μSR and muon spin resonance spectroscopy. In longitudinal field measurements, a fast relaxing component and a slow relaxing component were observed. The slow relaxing component is attributed to diamagnetic muons. The muon spin resonance measurements indicate that the fast relaxing component results from some muonium like species: either normal or anomalous. In zero field and weak longitudinal field μSR (0–100 G), a remarkable peak in the fast relaxing component is observed around 220 K in both KDP and DKDP. An additional feature is also seen around 300 K. The amplitude of the resonance measurement has a broad minimum around 200 K which corresponds to the maximum in the relaxation rate in longitudinal field (100 G). The temperature dependence of the muonium relaxation rate in KDP is almost identical to that of DKDP. The diamagnetic fraction also shows almost no difference in relaxation rate or asymmetry for DKDP and KDP. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermally activated muonium formation in Al2O3 and BaF2

Direct evidence is presented for thermally activated muonium formation in Al₂O₃ and BaF₂. In each case the signature of the transition is a transverse field depolarization rate of the prompt diamagnetic component which is much too large to be attributable to muon-nuclear dipolar couplings. Longitudinal field decoupling measurements in Al₂O₃ support the interpretation that the initial diamagnetic fraction converts into a state with a stongly coupled electron —-i.e., muonium.     

Final states in Si and GaAs via RF μSR spectroscopy

The ionization of muonium centers in Si and GaAs have been studied using radio frequency (RF) resonant techniques. In Si all three muonic centers are detectable by RF. No evidence was found for delayed Mu and Mu^* states at any temperature. However, our results on the diamagnetic final state (μ _f ⁺ ) show that it is composed of prompt fractions (as seen by conventional μSR) and delayed fractions arising from the ionization of Mu^* and Mu. We observe a full μ _f ⁺ fraction at 317 K when the Mu relaxation rate is above 10 μs⁻¹. GaAs differs from the situation in Si in that we observed only a partial conversion of Mu^* and Mu to a μ⁺ final state up to 310 K in spite of the fact that the transverse field relaxation rates become very high at 150 and 250 K respectively.     

Evidence for muonium emission from an SiO2 layer on n-type Si and the positive muon state in Si

Evidence for the emission of slow muonium atoms from a 3.0-nm-thick SiO₂ layer covered on an n-type Si is reported. Also, upon applying an rf-resonance technique at the muon frequency, a time-differential observation of a delayed state-change from muonium to diamagnetic muon at room temperature was observed. Combining results obtained by use of longitudinal field decoupling and transverse spin rotation methods, the conversion rate was estimated to be 5 to 10 μs⁻¹. Both of the above results, namely the observation of the emission and state-change of muonium, suggest a process in which μ⁺ initially captures an electron from Si, then quickly converts to μ⁺ again during thermal diffusion in the Si towards the SiO₂ layer. Within the oxide layer, muonium is again formed and subsequently is emitted from the SiO₂ surface.     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Mu centers in crystalline Ge under illumination

A slow conversion to a diamagnetic state has been observed for muonium centers at the tetrahedral interstitial site (Mu⁰ _T) in dark Ge at low temperatures. While the conversion process is affected by illumination, no effect of illumination upon the initial (Mu⁰ _T) centers themselves was observed at 10 K. This is in marked contrast with the case of (Mu⁰ _T) centers in Si where strong interaction with photo‐induced carriers is observed, suggesting that the electronic level associated with (Mu⁰ _T) state in Ge is not located in the energy gap. This revised version was published online in August 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.     

Measurement of17O quadrupole interactions and identification of the diamagnetic fraction in ice by muon level crossing resonance

By means of Level Crossing Resonance in a sample of ice which is enriched in H₂ ¹⁷O, the final diamagnetic state of implanted positive muons is determined to be the muonium-substituted molecule HMuO, accommodated in the regular and fully relaxed Ih structure. The¹⁷O quadrupole coupling constant is measured to be 6.1 MHz at 200 K assuming an asymmetry parameter close to unity, a decrease of about 5% relative to that in normal ice Ih at 77 K. The isotope effect is attributed to a greater polarization in the vicinity of a muonium (as opposed to a normal hydrogen) bond. At 50 K, an additional resonance is observed which could correspond to a precursor state, so far not definitely identified. One possibility is a muon trapped at a Bjerrum L-defect, giving a {H₂O−Mu−OH₂}⁺ species with an,¹⁷O quadrupole coupling constant of 8.2 MHz and asymmetry parameter of 0.55. Above this temperature, the fall in the (Gaussian) line-width parameter is attributed to the increasing rate of proton or muon migration, the correlation time dropping from 4 μs at 80 K to 1 μs near the melting-point. The increase in the diamagnetic fraction with rise in temperature is attributed to the increasing proportion of trapping sites available for muon capture.     

Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

Relaxation of anomalous muonium in silicon

The relaxation rate ^* of anomalous muonium in silicon with different dopant concentrations was investigated as a function of temperature. Below 140 K, a close correlation between ^* and the concentration of conduction electrons was found. We conclude from this behavior that the relaxation of anomalous muonium in this temperature region is caused by the scattering of conduction electrons. A microscopic model is developed and the value of the exchange interactionJ _ex is derived.The financial support of the Bundesminister für Forschung und Technologie is gratefully acknowledged.     

Temperature dependence of muonium in hydrocarbons

The diamagnetic and muonium fractions and their decay constants were measured for cyclohexane, neopentane andn-hexane for the temperature region covering liquid, plastic and non-plastic crystals. The muon and muonium parameters were almost the same for liquids and plastic crystals, but they showed a marked change in non-plastic crystals; a rapid decay of Mu precession, relaxation of the diamagnetic muon component and an increase in the lost polarization have been found to be characteristic of non-plastic crystals.     

Inhomogeneous muonium diffusion in solid nitrogen

The spin dynamics of the muonium (Mu) atom diffusing quantum mechanically in solid nitrogen (s-¹⁴N₂) has been studied using the technique of Mu spin relaxation. A strong relationship between longitudinal (T ₁ ^–1 ) and transverse (T ₂ ^–1 ) relaxation rates (familiar in NMR) has been experimentally demonstrated for the first time for muonium relaxation. At low temperatures the results are inconsistent with diffusion models using a single correlation time _c; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate _c ^–1 gives clear evidence that Mu quantum diffusion ins-N₂ is governed by the two-phonon interaction.     

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 (Mu_T) and the diamagnetic states (μ^d), 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 (Mu_BC) and μ^d. 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. This revised version was published online in August 2006 with corrections to the Cover Date.     

Search for muonium states in BN,WS2 and carbon nanotubes

A sizable missing fraction was found for semiconductors (cubic) BN and (hexagonal) WS₂. A repolarization measurement at room temperature yielded a high hyperfine frequency for the dominant muonium signal in BN. The missing fraction in carbon nanotubes with average 20 nm outer diameter was less than 4% at temperatures above 5 K, with very small relaxation in transverse and longitudinal fields, indicating that such tubulenes are microscopically (semi-)metals or small-gap semiconductors, non-magnetic and non-superconducting.     

Low temperature quantum diffusion of muonium in KCl

T ₁ spin relaxation of muonium in KCl has been studied at low temperatures (20 mK to 2 K), where the motion is believed to be band-like, i.e. the mean free path is longer than the lattice constant. The Celio model, based on the assumption of stochastic hopping of muonium, accurately describes the field dependence ofT ₁ at higher temperatures but fails below 4 K. The measuredT ₁ spin relaxation rates vary weakly with temperature below 2 K even thoughk _BT at the lowest temperature is well below the estimated muonium bandwidth obtained from the data at higher temperatures. This is taken as evidence that muonium is not completely thermalized on the time-scale of the muon lifetime due to the weak interaction with phonons at low temperatures.     

Muon implantation in alkali metal hydrides

Zero, longitudinal and transverse field μSR measurements have been made on LiH, LiD and NaH. The primary motivation for the study was to elucidate the behaviour of the muons in the diamagnetic state and analysis of the time‐dependent zero field relaxation data suggests that negatively charged muonium, Mu^-, is formed and takes up a H^- vacancy site in these materials. Evidence is presented for a small (approximately 2%) reduction in the Mu^-–Li distance relative to the unperturbed nearest neighbour anion‐cation distances in the pure crystal lattices. This revised version was published online in August 2006 with corrections to the Cover Date.     

Diffusion and trapping of muonium on silica surfaces

The spin relaxation rate λ_Mu of muonium atoms on fine silica powder surfaces was measured as a function of temperature and of the surface concentration of hydroxyl groups. Results indicate two-dimensional diffusion, trapping and detrapping of the muonium atoms on the silica surface. At low temperatures λ_Mu decreases dramatically as the concentration of surface hydroxyls is reduced. A three-state model is used to extract the muonium adsorption energy and other physical parameters.