A precision determination of the hyperfine splitting of muonium in quartz

We report a precise measurement of the hyperfine interval of muonium in single crystal quartz at room temperature, using the muon spin rotation technique. The measured value is about 1% larger than the vacuum value. Our results also confirm a small anisotropy previously reported.     

Observation of “decoupled” diamagnetic muon states in Alkali halides by muon spin resonance

The states of positive muons in KCl, NaCl and KI were studied with the muon spin resonance method under a 3 kG decoupling longitudinal field, revealing a considerably larger fraction of diamagnetic muon state than observed by the conventional spin rotation method. The origin of this fraction, which increases with temperature, is attributed to a muonium to muon transition in solids.     

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.     

MuSR method and tomographic-probability representation of spin states

The 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. The time evolution of muonium, anomalous muonium, and a muonium-like system is studied in the tomographic representation. The entanglement phenomenon of a bipartite muon–electron system is investigated, in view of the tomographic analogs of the Bell number and the positive partial transpose (PPT) criterion. Reconstruction of the muon–electron spin state as well as the total spin tomography of the composed system is discussed.     

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     

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.This work is partially supported by the National Sciences and Engineering Research Council of Canada.     

Missing fractions in heavy gases: Xe and CCl4?

The spin polarization of positive muons thermalized in Xe has been measured as a function of pressure up to 4660 Torr (6.1 atm) by the muon spin rotation (MSR) technique. At 4660 Torr, triplet muonium (F=1, M=1) accounts for about 40% of the initial muon polarization and no significant signal from diamagnetic muons has been observed. The unexpectedly slow recovery of the polarization in Xe at high pressures is discussed in conjunction with similar results seen in CCl₄ and CHCl₃ vapors.     

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.     

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.     

Local magnetic susceptibility of the positive muon in the quasi-one-dimensional S=1/2 antiferromagnet dichlorobis (pyridine) copper (II)

We report muon spin rotation measurements of the local magnetic susceptibility around a positive muon in the paramagnetic state of the quasi-one-dimensional spin 1/2 antiferromagnet dichlorobis (pyridine) copper (II). Signals from three distinct sites are resolved and have a temperature dependent frequency shift which is significantly different than the magnetic susceptibility. This difference is attributed to a muon induced perturbation of the spin 1/2 chain. The obtained frequency shifts are compared with transfer matrix density-matrix renormalization-group numerical simulations.     

Diffusion of muonium and hydrogen in diamond

Jump rates of muonium and hydrogen in diamond are calculated by quantum transition-state theory, based on the path-integral centroid formalism. This technique allows us to study the influence of vibrational mode quantization on the effective free-energy barriers DeltaF for impurity diffusion, which are renormalized with respect to the zero-temperature classical calculation. For the transition from a tetrahedral (T) site to a bond-center (BC) position, DeltaF is larger for hydrogen than for muonium, and the opposite happens for the transition BC-->T. The calculated effective barriers decrease for rising temperature, except for the muonium transition from T to BC sites. The calculated jump rates are in good agreement with available muon spin rotation data.     

Precise measurement of hfs constant of the muonium substituted radical in cis-polyacetylene

The state of the muon in cis-polyacetylene was studied by muon spin rotation method under high transverse magnetic field. The most of the muons are found to be in muonium substituted radical state. The hyperfine coupling constant was determined to be 91 MHz with a line width of 10 MHz.     

Spin relaxation studies of the muonium substituted ethyl radical in the gas phase

This short communication draws attention to the power of μSR and related measurements in providing an unusually complete characterisation of muonium substituted organic radicals in the gas phase. Spectroscopic information is available from muon spin rotation and muon level crossing resonance, giving all the nuclear hyperfine coupling constants, just as in the liquid phase. In addition, measurements of the relaxation time of the muon Zeeman energy become possible; these are potentially informative on the molecular collision dynamics. Demonstration results are presented in summary for the muonium substituted ethyl radical, ĊH₂CH₂Mu, in ethene gas.     

Quantum magnetism in the paratacamite family: towards an ideal kagomé lattice

We report muon spin rotation measurements on the S=1/2 (Cu2+) paratacamite ZnxCu4-x(OH)6Cl2 family. Despite a Weiss temperature of approximately -300 K, the x=1 compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around x=0.5. For x=1, we discuss the relevance to a singlet picture.     

Muonium to diamagnetic muon conversion in KCl and NaCl revealed by time-differential muon spin resonance

The conversion of muonium into a diamagnetic muon state in KCl and NaCl was directly observed by detecting a time-delayed appearance of diamagnetic muon states with muon spin resonance. The conversion rate, determined from the time-differential resonance signals, shows a thermal activation characteristic in temperature variation.     

Radio-frequency muon spin resonance studies of endohedral and exohedral muonium adducts of fullerenes

The radio-frequency muon spin resonance technique (RF-μSR) is described, with examples drawn from muon studies of fullerences. Two distinct species can be detected by RF-μSR when solid C₆₀ is irradiated with positive muons. Endohedral muonium (Mu@C₆₀) is characterized by a muon hyperfine constant (A _μ) close to the vacuum value. A remarkable feature of the RF-μSR spectrum is the double quantum transition, which appears when the allowed transitions are saturated. The exohedral muonium adduct (C₆₀Mu) is also detected, and has a much smaller value ofA _μ typical of a carbon-centred organic radical. It has been studied by RF-μSR in dilute solution, which is not possible for transverse field muon spin rotation (TF-μSR). There is a significant difference inA _μ of C₆₀Mu in the solid and in solution, a result of great import to the analysis of avoided-level crossing experiments on¹³C₆₀Mu.     

Radiofrequency muon depolarization in the muonium + nuclear spin system

The effect of a considerable strengthening of muon depolarization in ALC resonance experiments was predicted for the muonium + nuclear spin system in the presence of a radiofrequency field. A mathematical approach was developed for obtaining analytic solutions that described the muon spin dynamics in ALC experiments, including a particular exact solution that contained much information about the system studied in fairly low magnetic radiofrequency fields. An analysis of these solutions and numerical calculations allowed us to comprehensively analyze muon depolarization patterns in a radiofrequency field. The results reveal the potential of muon depolarization strengthening for considerably increasing the sensitivity of experimental studies of muonium interactions with neighboring nuclear spins and for obtaining new spectroscopic information.     

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.