D. Herlach

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 minimumDminµ+≈1⋅10−13 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.

Muon spin rotation in superconductors

By means of the muon spin rotation technique (μ+SR), the temperature dependence of the magnetic field inside the normal-conducting domains of high-purity tantalum crystals in the intermediate state has been measured in the temperature range 2.36K<T<3.5K. The results agree well with macroscopic measurements of the thermodynamical critical field. It is also shown that the distribution of magnetic fields in the mixed state of niobium single crystals may be determined by μ+SR. Possible applications of these findings to the study of long-range diffusion of positive muons at low temperatures are indicated.

Radio-frequency spin resonance of positive muons in α-iron

Abstract Resonant transitions between the Zeeman levels of spin-polarized positive muons (μ+) implanted into iron foils have been observed at 1040 K by applying a 24·0 MHz transverse r.f. field and varying the longitudinal external magnetic field. The trapping of muons at small concentrations of crystal defects (about 10−7, i.e. of the order of magnitude of the thermal equilibrium concentration of vacancies) was detected and the local magnetic field at the traps determined.

μ+SR study of vacancies in thermal equilibrium in ferromagnets

Muon spin precession frequencies and transverse relaxation rates have been measured on demagnetized iron, cobalt, and FeCo alloys (3 at%–50 at% Co) between room temperature and the Curie temperatureTc. The increase of the relaxation rate in iron between 930 K and 1010 K could be quantitatively attributed to the trapping of positive muons by vacancies in thermal equilibrium, resulting in an enthalpy of monovacancy formation ofH1VF=(1.7±0.1) eV. the smallest vacancy concentrations detected are = 10−8.

What can we learn about critical magnetic phenomena from muon spin rotation experiments

Measurements of the spin precession frequencies ωμ and transvers relaxation rates Γ2 of positive muons (μ+) magnetic phase of several iron-cobalt alloys and coabalt, and in amorphous Feo.91Zr0.09 alloys are discussed with particular reference to the influence of critical phenomena on ωμ and Γ2. Although the temperature dependence ωμ(T) is well described by scaling law ωμ ∝ (Tc−T)β′ where α′ varies strongly with the co concentration in the FeCo alloys, it is shown that the exponent α′ is not identical to the static scalling parameter β describing the critical behaviour of the spontaneous magnetization M. In paramagnetic iron we find Γ2∝(T-Tc)0.72, which is attributed to the effect of dynamical spin fluctuations on the μ+. Due to the apparent difference between the temperature dependence of ωμ and that of M below Tc the frequency shifts observed in the paramagnetic regime are probably not directly proportional to the magnetic susceptibility. In amorphous Fe0.91Zr0.09 allosy frequency shifts and transverse relaxation rates are found up to nearly 2 Tc. Due to the shape of the Fe0.91Zr0.09 sample, demagnetization inhomogeneities certainly play an important rôle.

Muon diffusion and trapping by defects in electron-irradiated Nb and Ta

The transverse spin relaxation of positive muons (μ+) has been measured on Nb and Ta after irradiation with 3 MeV electrons. In high-purity Nb theμ+ diffusivity derived from the trapping at irradiation-induced defects above 100 K is explained in terms of adiabatic hopping. At lower temperatures there is evidence for the dominating processes to be fewphonon incoherent tunnelling and coherent hopping. Annealing results in the formation of new defects capable of trapping theμ+. In Ta at least two types of irradiation-induced defects capable of trappingμ+ survive up to annealing temperatures of 400 K.

Positive mouns in iron: Dipolar fields at tetrahedral sites and jump frequencies at low temperatures

On polycrystalline and monocrystalline iron muon-spin precession frequencies and transverse relaxation rates have been measured down to 0.5 K. In the polycrystalline sample two distinct precession frequencies were observed at and below 1.4 K. They are attributed to the different dipolar fields at magnetically inequivalent tetrahedral interstices seen by muons moving locally around impurities. By contrast, in monocrystalline iron we observed only one precession frequency in monocrystalline iron with a damping rate which increased with decreasing temperature down to 0.5 K. We attribute the difference between the monocrystalline and the polycrystalline sample to different impurity contents. The single-crystal data are discussed in terms of μ+ diffusion by hopping between interstitial sites of tetragonal symmetry. The answer to several open questions is expected from an extension of the measurements to lower temperatures.

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

We have measured the transverse spin relaxation of positive muonsμ+ 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 theμ+ in monovacancies. Between 215 K and 60 K theμ+ diffusivity is well described by the Flynn-Stoneham law (multi-phonon incoherent tunnelling between ground states) with an activation enthalpyHa = (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.

Muon location and mobility in high-purity metals

Positive muons are expected to be easily trapped by imperfections including impurities in metals (Seeger 1975). Therefore it is essential to study muon diffusion and localization on well-characterized high-purity materials. The sensitivity to impurities has been confirmed by recent ~SR studies on Nb (Birnbaum et al. 1978, Borghini et al. 1978). In this note we report results of DSR experiments on high-purity monocrystals of beryllium, tantalum, and niobium. Starting from high-purity material, the Be target was vacuum melted and zone-refined i0 times resulting in a residual resistivity ratio F ~ R2g3K/R4.2K = 400, corresponding to a purity of 99.993 wt% (Aldinger 197~).0f the remaining 70 wt.ppm impurities, the principal constituent was iron. The preparation of the Ta (F = 5000, interstitial C+O+N<5 at 9 and Nb (F = 3000, N<2 at.ppm, 0 < 1 at.ppm, Ta ~ 5 at.ppm) targets is described elsewhere (Gladisch et al. 1978). The experimental setup used in our measurements is similar to that of Dorenburg et al. (1978)._The ~SR data were analyzed by computing the mean polarization P for each precession period of the muon spin and assigning it to the time t at the centre of the period. In order to obtain the depolarization rate A e ~ t~l(~(t e) Z P(O)/e),) suitable theoretical functions were adapted to the experimental ~(t in the cases of Be and Ta. In the case of Nb, however, the rapid decrease of polarization allowed t e to be found by mere interpolation. The temperature dependence of A e in Be was measured in 24.6 mT external magnetic field transverse to the muon polarization and at angles of O, 50,and 90 degrees with respect to the c-axis of the hcp lattice structure. No significant orientation dependence of A e was found at any of the investigated temperatures. Therefore, in Fig.1 only averaged values are shown, except for temperatures around lOOK, where the maximum A e values are found. Here the results for individual orientations are given separately. They are also presented in Table I, together with results of calculations using van Vlecks theory under the assumption that muons are located either on tetrahedral or octahedral interstitial sites in an unrelaxed Be lattice 9 For completeness, we also include polycrystalline averages of the theoretical values for these types of interstitial sites. These results are in accordance with the assumption that quadrupole coupling (Hartmann 1977) suppresses the orientation dependence of A e at lOOK in a similar way as in Cu, where comparably weak orientation and field dependences were found up to ~50 mT (Camani et al. 1977). The magnetic field strength B_ above which dipolar coupling (nuclear spln I, gyromagnetlc ratlo YI) starts to determine the orientation dependence of A e is given by

Muons in type-II superconductors: μ+ diffusion in ultra-pure niobiumdiffusion in ultra-pure niobium

The diffusivityDμ of positive muons (μ+) in the mixed state of superconducting high-purity, high-perfection niobium single crystals is investigated by measurements of the relaxation of the transverse muon spin polarization (μ+SR). The method makes use of the strong magnetic field gradients existing in the mixed state of Type-II superconductors and monitorsDμ through the variation of the magnetic field felt by the μ+ during their diffusion through the crystals. For μ+ near the centres of the flux lines inNb it givesDμ(4.6 K)=(8±2)·10−11m2S−1. The positive temperature coefficient ofDμ indicates that at liquid-helium temperatures the diffusivity of μ+ inNb is mainly due to phonon-assisted tunnelling processes.