Incoherent tunnelling of positive muons and trapping by vacancies in electron-irradiated aluminium

We have measured the transverse spin relaxation of positive muons ⁺ in Al single crystals after irradiation at 150 K with 3 MeV electrons. The relaxation functions agree with those expected for diffusion-limited trapping of the ⁺ in monovacancies. Between 215 K and 60 K the ⁺ diffusivity is well described by the Flynn-Stoneham law (multi-phonon incoherent tunnelling between ground states) with an activation enthalpyH _a = (30±2) meV. At lower temperatures, few-phonon (in particular one-phonon) processes become important. The decrease of the vacancy concentration by a factor of 100 during annealing between 227 K and 267 K has been studied.     

The investigation of defects in metals with positive muons

It is shown that the trapping of positive muons by defects in metals attracting positively charged particles may be used to investigate such defects in considerable detail by spin relaxation of positive muons.     

Measurement of the depolarization rate of positive muons in copper and aluminum

Positive muon spin rotation experiments for polycrystalline Cu and Al from 19K to temperatures near the melting points are reported. At low temperatures, the depolarization associated with localization of the muons at octahedral interstitial sites is seen in Cu, while in A? only slight depolarization is observed below 250K. At high temperatures, no evidence for trapping of positive muons at vacancies in thermal equilibrium is found for either metal. It is concluded that the muons either diffuse too slowly to find vacancies or, if they do find vacancies, are bound too weakly to remain trapped.     

Antiferromagnetic solid oxygen studied by positive muons

We present a zero magnetic field muon spin rotation study of-O₂ (antiferromagnetic phase of solid oxygen) in the temperature range of 10–24 K. Static magnetic order has been observed below the- transition temperatureB =23.8 K. The temperature dependence of the muon precession frequency exhibits behavior characteristic of a two-dimensional Heisenberg spin-1 system with the anisotropy parameter 10^–2 quite similar to that of antiferromagnetic phase of the high-temperature superconductor parent compounds. A unique local field at the muon site has been determined to beB ₀=1.27(5) kG at low temperatures.     

Trapping of positive muons by vacancies in non-stoichiometric compounds

A direct evidence for trapping of positive muons by vacancies was found by using the longitudinal field method., 65.5 at. %Cu-34.5 at. %Al, 51at. %Al-49at. %Ni and 52 at. %Al-48at. %Ni polycrystalline samples were studied. The forward/backward asymmetry was measured as a function of time at room temperature changing the magnetic field from 0 to 70 Oe. At H=0, a relaxation function of Kubo-Toyabe type was found. Analysing the data, it was found that positive muons are trapped by vacancies in these materials.     

Quantum diffusion of positive muons

Recent studies of the diffusion of positive muons in metals, particularly aluminium, are reviewed. At low temperatures, quantum tunnelling is an important process for the mobility of the muons and experiments aimed at the study of tunnelling in the presence of phonons and conduction electrons are discussed. The concept of quantum diffusion is introduced and the conditions for quantum diffusion and quantum propagation (i.e. band-like motion) in normal and superconducting metals are compared.     

The spin turning in ferromagnetic Gd studied by positive muons

We have studied the muon precession frequency in a ferromagnetic single crystal of Gd metal. The overall features of our findings are compatible with earlier results on polycrystalline material. In the temperature region between 245 and 220 K where the Gd magnetization starts to turn away from the c-axis, we observe an increase in the muon depolarization rate, and a complex precession signal which can be separated into two frequency components meaning that spin turning does not occur simultaneously in different parts of the sample (domains). From these more detailed data follows that previously obtained values forB _fc andB _dip can not both be correct. Two explanations for our new result are possible: EitherB _fc undergoes a change around 230 K which is directly coupled to the spin turning angle, or the value of the dipolar field contribution used in the earlier evaluation is too low. This imposes some uncertainty as to the value of the angle at the onset of spin turning derived fromSR frequencies.     

Trapping by vacancies and mobility of positive muons in neutron-irradiated aluminium

By means of the muon spin rotation (µSR) technique the trapping at vacancies and the mobility of positive muons are investigated in the temperature range 2.5 K to 297 K in polycrystalline aluminium irradiated with fast neutrons at 4.6 K. The observed damping of the µSR signal at temperatures below 50 K is in good agreement with saturation trapping at monovacancies. The temperature dependence of the damping above 50 K indicates that the muon diffusivity exhibits a minimumD _min ^µ+ 110^–13 m² s^–1 near 125 K, which is explained by a transition from coherent to incoherent tunneling. With the help of an estimated trapping cross section a monovacancy concentration of ~3 × 10^–4 after 125 K annealing is deduced, in good agreement with measurements of the residual electrical resistivity. As expected, the vacancy recovery shows up in an irreversible decrease of the damping above ~ 175 K.Work supported by the Bundesminister für Forschung und Technologie and by Schweizerisches Institut für Nuklearforschung (SIN). Requests for reprints and correspondence should be addressed to A. Seeger, MPI für Metallforschung, Heisenbergstraße 1, D 7000 Stuttgart-80, Germany     

The use of positive muons in metal physics

The present status of work in metal physics by the new method of “muon spin rotation” is reviewed. This spectroscopy is based on the spin interactions of positive or negative muons and resembles NMR as far as the interpretation of interactions in metals is concerned. The positive muon behaves in several respects as a light isotope of hydrogen in metals. Local properties like site symmetry, local magnetic field, dynamic effects from surrounding spins as well as effects from the diffusion of the particle itself can be measured with high sensitivity.A brief review of the technical aspects is given. The problems of diffusion of light positive particles in metals are discussed, with regard to specific mechanisms at low temperatures, trapping of muons by impurities, etc. The local electronic structure around this kind of impurity in normal metals as well as ferromagnets has been subject to a large nnumber of studies. Other applications include the interaction of muons with other kinds of defects, the study of metal hydrides and measurements on the dynamics of spin glasses.     

Measuring macroscopic diffusion of positive muons in metals

Conclusions We have discussed some schemes for measuring the diffusion coefficient for positive muons in metals, using diffusion over macroscopic distances. The method offers some promise of yielding diffusion information over wider temperature ranges and a greater variety of metals than the presently used technique. The major difficulty in applying the laminate scheme will be fabricating suitable, well-characterized targets that are thick enough to stop a significant fraction of the ⁺ beam. The use of a surface (i.e., 4 MeV) ⁺ beam appears most promising, but this brings with it formidable technical problems in heating and cooling the targets. We may hope that these problems will be attacked vigorously and effectively in the near future.Research performed under the auspices of the U.S. Department of Energy.     

Effect of positive muon trapping by dislocations

Aluminum was deformed at room temperature so that vacancies are annealed out and only dislocations are remained. The muon spin depolarization rate was found to be decreased as the temperature is raised. This indicates that some trapping-detrapping occur. Fitting the spin relaxation to the calculated spin relaxation function for the trapping-detrapping model, the values of the activation energy for the trapping rate and detrapping rate and of the depolarization rate at the trapping are found to be 25 meV, 66 meV, and 0.24 sec^–1, respectively for the best fit. This indicates that positive muons diffuse to dislocations and diffuse along dislocation lines and are trapped at a jog of the dislocation, and detrap from the jog.     

Positron trapping by defects in plastically deformed copper

When compared to current theories, positron lifetimes in plastically strained copper are indicative of diffusion limited positron trapping, with diffusion constant D₊ ≈ 4 × 10^?2 cm²/s in dislocations of effective capture radius $\text{r}{}_{\mathrm{<mtext>d</mtext>}}\text{≈ 70}\text{A}\text{?}$.