Zero field muon spin depolarization revisited

We consider the zero field depolarization of stationary muons at various sites in fcc and bcc crystals. Significant derivations from the classic Kubo-Toyabe treatment are explained as due to violations of some fundamental assumptions underlying this theory.     

Positive muon spin depolarization in quenched aluminium dilute alloys

Aluminum dilute alloys (Al-0.047 at% Mg, Al-0.052 at% Cu and Al-0.051 at% Si) were quenched from 600 and 450C. The positive muon behavior in the quenched alloys has been studied. Three peaks (Peak I, II and III) are found. Peak I is due to the trapping and detrapping of positive muons at single impurity atoms. The muon spin depolarization rate at the trap in Peak I was found to be 0.36sec^–1. Peak II is connected to impurity clusters. Peak III is the trapping of muons at quenched-in vacancies. The depolarization rate at the trapping site was found to be 0.2sec^–1. The activation energy of the trapping rate was found to be 25 meV. As the quenched-in vacancies annealed out, the trapping rates decreased to near zero.     

Theory of muon spin depolarization in condensed phases of hydrogen isotopes

A theory of muon spin depolarization in the molecular ion ( H₂μ)⁺(( D_2μ)) formed in a crystalline phase of hydrogen isotopes is presented. It is shown that the molecular ion ( H_2μ)⁺ has no time to thermalize during the muon lifetime, but after \tau\ll \tau_μ has time to transit to the lowest energy levels of the vibration‐rotation spectrum. The depolarization of the muon spin is determined by the interaction of the ion’s electric dipole moment with the lattice and by spin‐rotation interactions V_LS in the ion. This mechanism is analogous to that of “muonium”, replacing the hyperfine interaction by V_LS. The results can explain the experimental data and in particular the absence of a strong isotopic effect. This revised version was published online in August 2006 with corrections to the Cover Date.     

Theory of muon spin depolarization in crystalline phases of 3He

As is obvious from the energetic point of view, positive muons must form the molecular ion ( He_2μ)⁺ in condensed phases of helium. A theory of positive muon spin depolarization in crystalline phase of ³He in this model is devised. The theory explains experimental results. It is shown that the abrupt temperature dependence of the muon spin depolarization rate at T < 2 K which is observed in experiments is explained by spin–phonon interaction. This interaction mechanism arises due to a modulation of the exchange interaction between host atoms of the ³He‐lattice. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

On the mechanism of muon spin depolarization in the Spur model for Mu formation

The Mu formation mechanism due to Coulomb interaction of a muon with track electrons is considered. It is shown that taking into account the external electric field must essentially change the spin polarization behavior in liquid helium. The theory developed is consistent with experiments.     

Resolved nuclear hyperfine structure of muonium in CuCl by means of muon level-crossing resonance

Datailed muon level-crossing resonance measurements of Mu¹ and Mu¹¹ centres in single crystals of CuCl are presented. The hyperfine and nuclear hyperfine parameters of the closest two shells of nuclei are remarkably similar for the two centres, indicating that both are located at the same tetrahedral interstitial site with four Cu nearest neighbours and six Cl next-nearest neighbours. About 30% of the total unpaired-electron spin density is located on the muon, about 60% on the four nearest neighbours and the rest on the six next-nearest neighbours, with nothing observable for any other shell.     

Low-temperature muonium depolarization in Si and Ge

Measurements of the normal muonium depolarization rate in high purity silicon and germanium have been performed between 1.5 and 4.2 K. Two different Si samples and one Ge sample were investigated in a transverse field of 5 G, and in all cases, a temperature-independent depolarization rate was observed. The silicon results disagree with earlier work which showed a depolarization rate which decreased with increasing temperature in this temperature range. These results are compared with measurements of the direct muonium hyperfine transition.The authors wish to acknowledge the support of the N.S.F. grant DMR-79-09223.     

Quantum diffusion of muon and muonium in solids

The quantum tunneling diffusion of muon and muonium in crystalline solids is discussed with emphasis on the effects of disorder and superconductivity. The complex effect of disorder on muonium diffusion in inhomogeneous crystals is scrutinized. The enhanced muon diffusion in the superconducting state of high-purity tantalum establishes the predominant influence of conduction electrons on the quantum diffusion in metals.     

Spin dynamics of the muon in muonium in normal metals

The question of the charge state of the proton (the positive muon) in metals is of fundamental importance for the theory of metal hydrides. The theory developed here permits determination of the charge state of μ ⁺ in normal metals. The experimental possibilities of the observation of Mu atoms in metals at various strengths of the external magnetic field and various temperatures are analyzed. Zh. éksp. Teor. Fiz. 111, 730–736 (February 1997)     

Stochastic model of muon diffusion in the presence of traps: Nonsecular effects on spin depolarization

A stochastic model is presented for calculating the depolarization of the positive muon when the latter undergoes jump diffusion in a solid in the presence of trapping impurities. The theory, restricted to low concentration of traps, is applicable to relaxation studies in both transverse and zero magnetic fields. In the transverse geometry, the dipolar interaction between the μ⁺ and the surrounding nuclear spins can be treated classically, and the analysis is simpler. The results obtained are shown to be identical to those derived before in a ‘two-state’ model, widely used recently in interpreting various experimental studies on trap-limited diffusion of light interstitials (μ⁺,H, etc.) in solids. The zero field technique is more versatile but is also more complicated to analyze as it involves nonsecular terms in the dipolar interaction. Assuming that the local dipolar fields are isotropic with their magnitudes distributed in a Gaussian manner, tractable results can be obtained for the Laplace transform of the zero field relaxation function. The latter needs to be inverted in order to facilitate comparison with experimental data, which are normally recorded in the time space. A scheme to handle this numerical problem is described and results are presented using realistic parameters.     

Low-field anomalous muonium depolarization in isotopically enriched germanium

The depolarization rate of anomalous muonium, Mu^*, in germanium isotopically enriched in⁷⁴Ge (I=0) was measured as a function of field. The concentration of⁷³Ge (I=9/2) was about 9 times less than natural abundance. The depolarization rate at 10 K in this isotopically enriched crystal for both lines of those Mu^* centers whose symmetry axes make an angle of 90° to the field is less than 1sec^–1 at all fields down to the lowest one measured, 14.5 gauss. This is in sharp contrast to the wide lines reported at low field in germanium having natural isotopic abundance. The spectrum of Mu^* in the isotopically enriched Ge crystal was also seen at zero field. These results confirm that the increased depolarization rate for Mu^* at low fields arises from unresolved nuclear hyperfine structure. The depolarization rates observed were consistent with an average hyperfine interaction with a single⁷³Ge nucleus of 2.5 MHz, a value requiring nearly 1% of the spin density to be on a typical atom.     

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.This work has been partially supported by the Swiss National Science Foundation.     

The muon depolarization rate in β-palladium hydride

A depolarization rate σ = 0.1205 ± 0.0050 μsec^?1, due to the proton nuclear dipolar fields, was observed for polarized muons implanted in Pd-H_0.97 in the β phase, at temperatures below 50 K, independent of temperature and applied field. The results indicate that the muon substitutes for one of the protons, and that nearest-neighbor protons are at octahedral lattice sites. On comparing our results with recent NMR data, it appears that the mean muon-proton nearest neighbor distance is significantly larger than that between protons alone. Also, a search for muon local moment magnetism gave a null result.     

Negative muon spin rotation in solids

Experimental advances in solid state physics research using polarized negative muons (in the ground state of muonic atoms) are reviewed. The main subject is studies of ^– hyperfine interactions in magnetic materials. Basic principles and distinctive features of the ^–SR method are also presented, and possible future developments are briefly discussed.