The positive muon and the positron as probes of defects

Conclusions A brief but hopefully general comparison has been made between muons and positrons as probes for the study of defects in metals. Since muon experiments are not only more demanding in manpower, cost and availability than positron experiments, they should be carefully designed in light of the knowledge that the muon is extremely sensitive to both intrinsic and extrinsic defects. Initial experiments should provide estimates of the muon diffusion coefficients as a function of sample temperature. High temperature hydrogen diffusion measurements do provide quidelines, although so far most of the observations of muon trapping have been made at low sample temperatures where hydrogen diffusion data do not exist. Given that the diffusion constant is known as a function of temperature, high-purity Fe²⁶ after low temperature electron irradiation is therefore a good candidate to study with muons. Since the defect type and concentration can be controlled in electron irradiated samples, such investigations could confirm the stated values of the diffusion constants in Fe thereby providing a new method for evaluating diffusion coefficients below Stage III in different metals.All the samples should be initially characterized by other less costly techniques to obtain, where possible, the concentration and type of extrinsic and intrinsic defects. Both transverse and longitudinal measurements should be made to unravel the question of different diffusion mechanisms versus defect-, impurity- or self-trapping.Provided that the full capabilities of the muon are utilized and coupled with complementary techniques, i.e., positron annihilation, the muon will constitute a useful new probe in deepening our understanding or defects in metals.Work supported by the US Dept. of Energy under contract DE-AC02-76CH00016.     

Low temperature diffusion and trapping of muons in aluminium: New experiments and comparison with theory

The low-temperature diffusion experiments in aluminium have been extended to measurements onAlSi,AlGe andAlGa. The systematic study of Al with various impurities now shows that the trapping rate at temperatures below 2 K (described by a T^−0.7 law) is directly related to the elastic distortion caused by each specific doping element. The overall diffusion behaviour in Al from 0.05 to 200 K can be described by the Kondo theory, only by assuming a low Debye frequency parameter, and if an additional T¹ diffusion rate is included in the intermediate temperature range.     

Dynamics of muons in the ferroelectric material KDP

Muon spin relaxation in zero field and longitudinal field was measured in single crystal samples of KH₂PO₄ (KDP) and KD₂PO₄ (DKDP) over a temperature range of 5 K to 300 K. At low temperatures, diamagnetic muons and muon substituted radicals with nuclear hyperfine coupling can be observed. For both KDP and DKDP, a minor change was observed in the dynamics of the muon below 140 K. Above 140 K, the mobility of the muon appears to increase and the diffusion rate becomes faster with increasing temperature. Only a small increase in the relaxation rate is observed in KDP due to the presence of theH ⁺, suggesting that the relaxation effects probably originate from the³¹P.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

Muon diffusion in Nb−H systems

We have studied the muon diffusion in various Nb−H_X systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ⁺ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.     

Inhomogeneous quantum diffusion of muons in solids

This article deals with the problems raised when a muon(muonium) quantum diffusion in a crystal is highly inhomogeneous. It is shown how static disorder arising from the crystal doping influence the diffusion process and drastically changes both the time decay of the polarization function and the temperature dependence of the depolarization rate. The spin depolarization of muons moving in a spatially inhomogeneous defect potential and trapping of particles by the long-ranged traps is studied in detail. Most attention is given to the particle localization and delocalization phenomena resulting in the two-component behavior of muon polarization at low temperature. Finally, the experimental data on muon depolarization in insulators KCl, GaAs, N₂ and superconducting metals Al, V are analyzed.     

Positive muon diffusion in helicoidally-ordered antiferromagnets

A method for measuring the time scale for positive muon diffusion in helicoidally ordered antiferromagnets is proposed. The experiment shows that the muon diffusion in dusprosium over the temperature interval 100–175 K is a tunneling process.     

Comparison of the paramagnetic fluctuations in GdM2 and DyM2 (M=Al,Ni)

The muon spin relaxation in the paramagnetic states of GdNi₂ and DyNi₂ compounds has been measured, as a complement to earlier studies of the rare earth dialuminides (REAl₂). In addition, improved data have been taken on a GdAl₂-sample, up to a temperature of 4T_c. At high temperatures the Moriya molecular field model predicts a rare earth spin fluctuation rate proportional to the Curie temperature of the compund, which would lead to a T _c ⁻¹ dependence of the muon relaxation rate. This relation is fulfilled for the pair GdNi₂/GdAl₂, but not for the DyNi₂/DyAl₂ ratios. Possible reasons for this discrepancy are discussed.     

Quantum diffusion of the positive muon in the superconducting state of Al

We report low temperature studies of muon diffusion and trapping in Al doped with Li impurities. The trapping rate at Li and the deduced muon diffusion rate increase more rapidly with decreasing temperature in the superconducting state compared with the normal state. The temperature dependence of the quantum diffusion rate in the superconducting state is close to that predicted by the Kondo theory.     

The motion of light interstitials in metals: Recent experiments

Recent theoretical considerations suggest, that at low temperatures the transport properties of light interstitials in metals are dominated by the interaction with the conduction electrons. After briefly surveying the state of the theory, experimental examples for the low and high temperature cases are presented. We begin with the low T regime and display first neutron scattering experiments on H trapped at O-impurities in Nb where a coherent tunneling state is observed. Its dependence on temperature and its properties in normal and superconducting Nb are discussed. Thereafter muon diffusion results in Al are examined. In Al, muon diffusion is observed via diffusion limited trapping and local properties of the impurity as well as long range diffusion are playing a role. Using a large variety of impurities it was possible to evaluate the diffusion coefficient over a large T-range. Muon motion in Al at accessible temperatures falls entirely in the hopping regime and constitutes an example for the high T regime of the theory.     

The temperature effect in the muon flux of cosmic rays: Methods for considering and evaluating the parameters of earth’s atmosphere

Simplified approaches to adjusting the muon flux for the temperature effect (e.g., those of the effective level of muon generation and mass-averaged atmosphere temperature) are considered. The accuracy of adjustment is evaluated using data from the URAGAN muon hodoscope (Moscow, Russia). The difference between the adjusted data using temperature coefficients that are differential by altitude and the simplified methods does not exceed 1–1.5%. The considered methods can be used for a fast preliminary adjustment of experimental data, and for solving the inverse problem of evaluating atmospheric parameters according to the muon hodoscope data.     

Conformational studies of thiyl and selenenyl radicals

Muonium adds to the unsaturated bond in 1,3-dithiolane-2-thione or -2-selenone to form a chalcogen-centered radical. The muon hyperfine coupling constants (hfc) were measured for both compounds over a range of temperatures. In solution, the temperature dependence of the muon hfc indicates that for the thiyl radical the preferred conformation corresponds to the muon eclipsing the unpaired electronp _z-orbital, while there is practically free rotation in the case of the selenenyl radical in the temperature range studied. In pure thione the hfc values show a remarkable discontinuity at the melting point. The two radical signals seen in the solid are interpreted as due to the presence of two dominant crystal orientations in the samples studied. In pure selenone data were obtained only in the solid. For both systems, the solid phase results show that interaction between the muon and the unpaired electron spin is enhanced compared to the liquid phase and/or the solution.     

Palladium-iron: A giant-moment magnetic thermometer for the millikelvin temperature range

We have calibrated the temperature dependence of the susceptibility ofbar|Pb+2.2 at. ppm Fe and ofbar|Pd+11 at. ppm Fe with an NBS superconducting fixed point device and with a Pt NMR thermometer in the temperature range 4.5 mK to 208 mK. In this temperature range, the data follow a Curie law with deviations of less than 1%. Its properties seem to makebar|Pd–Fe the most attractive thermometric substance for the temperature range 0.3 mK to 500 mK. For example, ourbar|Pd–Fe thermometer has a time constant of 1 s at 10 mK and of 0.1 s atT>30 mK.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

Longitudinal muon spin relaxation in the organic metal polypyrrole

Longitudinal and zero field measurements of the muon spin relaxation function are reported for muons implanted in the conducting polymer polypyrrole. The observed muon relaxation can be accounted for by interaction with polaron excitations in the conducting polymer. Evidence is found for polaron localisation at temperatures below ∼ 50 K. The temperature dependence of the polaron mobility derived from the muon data is consistent with direct electrical conductivity measurements.     

Meteorological effects in the intensity of muon groups

The data of the experimental study of cosmic ray muon groups using the DEKOR setup for the period of 2004–2007, during which significant changes in the intensity of groups at the Earth’s surface were detected, are analyzed. It was found that these variations are caused by variations of weather conditions (temperature and atmospheric pressure); barometric and temperature coefficients were determined. It turned out that magnitudes of these coefficients for muon groups are significantly higher than available values for singlemuons. Possible physicalmechanismof the effect is discussed. Since muon groups are formed at high altitudes (of the order of several kilometers), the detected effect can be used for monitoring air temperature variations in the upper troposphere.     

Diffusion,trapping and detrapping of positive muon in Al-0.047% Mg

Positive muon spin relaxation was measured in Al-0.047% Mg quenched from 873 K under zero external magnetic field from 6.3 K to 270 K. The observed spectra were analysed with the calculated muon spin relaxation function which included the static relaxation rates, the trapping rates, the detrapping rates and thet=0 initial trapping fractions. Due to the precise measurements and the realistic expression of spin relaxation function, above four parameters could be determined distinctly. The trapping rates and the distortions around a muon were determined from the values of static relaxation rates at a trapping site. The diffusion features were clearly described by the trapping and detrapping rates. The diffusion process was determined by the temperature dependence of these parameters.     

Limitations of the diffusion approximation for muon motion in metals

It is discussed that applicability of the diffusion approximation depends critically on the magnitude of the phonon-induced incoherency between muon levels in adjacent interstitial sites. By means of two examples it is demonstrated that the temperature below which the diffusion approach breaks down may be different for different physical situations.     

Muon diffusion in β-V2H

Hydrogen diffusion in the ordered hydride β-V₂H is mainly brought about by a minority fraction of interstitial atoms on antistructural sites. Recently, this mechanism was elucidated in a single crystal QNS study at temperatures close to the critical point (390 K≤T≤440 K) where already an appreciable amount of antistructural sites is occupied. Here we use the positive muon as a radioactive hydrogen tracer in order to show that the same diffusion mechanism is also valid at low temperatures (80 K≤T≤320 K) where the different jump processes are very slow and where the fraction of antistructural atoms is tiny but nevertheless dominates the long range diffusion.     

Transverse field μ+SR study of V3Si

We have studied by transverse field positive muon spectroscopy μ+SR, the muon diffusion in V₃Si. We found that the muon is static and localized at tetrahedral interstitial sites below 200 K. Above 200 K the muons diffuse with an activiation energy 2550 (220) K. The nature of this diffusion process is discussed.     

Muon level-crossing resonance in magnetically ordered materials

The positive muon is widely used as a microscopic probe of internal fields at interstitial sites in magnetically ordered materials. Recently, we have demonstrated that the hyperfine fields on the neighboring host nuclear spins can be measured using a novel muon level-crossing resonance technique, thus providing a more detailed picture of the electronic and magnetic environment around the muon. In this paper I will describe the fundamentals of muon level-crossing resonance as applied to magnetically ordered materials, and report an example in MnF₂.