K. P. Döring

Zero-field muon spin rotation in monocrystalline chromium

Spin precession of positive muons in chromium in zero applied magnetic field is reported for the first time. The observations cover the temperature range from about 2.5 K to 10 K and thus pertain to the so-called longitudinal spin-density wave (LSDW) state of antiferromagnetic Cr. The conclusions that may be drawn from the existence of one rather sharp spin precession line are discussed, among them the estimateDμ=2.4·10−14 m2 s−1 for the muon diffusivity at 4 K. Considerable evidence exists for a strong interactions of μ+ with the charge-density waves that are likely to accompany the LSDWs in Cr.

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.

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.

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.

Muonium in ultra-pure and Si-doped germanium

The influence of the isoelectronic impurity silicon ([Si]=1012−1018 cm−3) on the spin precession signals of positive muons in ultra-pure germanium crystals is investigated between 5 and 340 K in transverse magnetic fields of 0.5 to 27.5 mT. Normal (“isotropic”) muonium atoms Mu are formed in all samples with about the same probability (≈ 0.7). Down to quite low temperatures (20 K) Mu is found to diffuse very rapidly through the Ge matrix and to become ionized by interaction with the Si atoms. Another ionization process, presumably due to the screening of theμ+ by the increasing number of free charge carriers, sets in at about 180 K.

Muon trapping and diffusion in Al and In after electron irradiation at 9 K

The transverse spin relaxation of positive muons has been measured on an Al single crystal and on polycrystalline In after irradiation with 2 MeV electrons at 9 K or 11 K, sample transfer at 4.2 K, and various subsequent annealing treatments. The Al data are analysed in terms of diffusion-limited trapping by vacancies. This yields a muon diffusivityDμ which within experimental accuracy is proportional toT between 4 K and 50 K, indicating that in this temperature intervalDμ is dominated by one-phonon-assisted incoherent tunnelling. In In only very small effects due to the irradiation could be observed. The muons appear to be localized in octahedral interstices. From the motional averaging taking place above about 20 K the diffusivity ofDμ in In is deduced.

COMPUTATION OF TRANSVERSE MUON-SPIN RELAXATION FUNCTIONS INCLUDING TRAPPING- DETRAPPING REACTIONS, WITH APPLICATION TO ELECTRON-IRRADIATED TANTALUM*

A new technique for the economical evaluation of transverse muon spin relaxation functions in situations involving μ+ trapping at and detrapping from crystal defects is applied to electron-irradiated Ta exhibiting relaxation maxima at about 35 K, 100 K, and 250 K. The longrange μ+ diffusion is shown to be limited by traps over the entire temperature range investigated. The (static) relaxation rates for several possible configurations of trapped muons are discussed, including the effect of the simultaneous presence of a proton in a vacancy.