Muon Diffusion Research Articles

MSR Studies in the Progress Towards Diamond Electronics

The recent development of device quality synthetic diamond dramatically increases the potential of diamond as a wide band gap semiconductor. A remaining obstacle is the lack of shallow n-type dopants. Molecular dopant systems have been shown theoretically to lead to the shallowing of levels in the band gap. Some of these systems involve defect-hydrogen complexes. This, and other phenomena, motivate the study of the chemistry and dynamics of hydrogen in diamond. Much information on this topic has been obtained from Muon Spin Rotation (MSR) experiments. These experiments view the muonium (Mu ≡ μ + e −) atom as a light chemical analogue of hydrogen. Data on isolated muonium in diamond is reviewed, and evidence on formation of N-Mu-N (a shallow dopant candidate), the trapping of Mu at B-dopants, and fast quantum diffusion of muonium are discussed.

Tunneling dynamics in cryocrystals: localization and delocalization

The phenomenon of quantum diffusion of muonium in cryocrystals with rotational degrees of freedom is discussed. The quantum tunneling dynamics and electron transport are considered with the effects of disorder taken into account.

Diffusion of muons in metallic multilayers

The development of the low energy muon beam at PSI opens the possibility of studying muon diffusion in artificially layered structures within the nm scale. Here, we report on first muon diffusion experiments on different Cr/x nm Au / Cr trilayers ( x=19,21,30,39) in the temperature range from 5 to 320 K . If the appropriate implantation energy is chosen, the initial muon implantation profile is centered within the non-magnetic Au layer. Muons stopping in magnetic Cr or penetrating the Au/Cr interface by thermally activated diffusion immediately lose their spin polarization. The depolarization of the LE-μSR signal allows extraction of the time-dependent fraction of muons reaching one of the interfaces.

Transverse field μSR investigation of the flux lattice in Mg 1− xAl xB 2

We investigated the system Mg 1− x Al x B 2, in which the heterovalent substitution of Al for Mg changes both the band filling (different valence) and the bandwidth (lattice contraction due to different ionic radii). The result is the disappearance of superconductivity at about x=0.5. Contrary to earlier findings, our carefully annealed powder samples show no evidence of phase separation. We determined the μSR lineshape in a flux line lattice. We obtain a nearly linear dependence of the second moment of the flux lattice field distribution upon doping, indicating a strong reduction of the super carrier density with increasing x. Muon diffusion is detected by zero field measurements. It persists down to the lowest temperatures also at x=0.4. The doping dependent activation energies are reported.

Coherent quantum diffusion of muonium in a highly disordered medium

We have investigated the quantum diffusion of interstitial muonium atoms in solid mixtures of methane with krypton at temperatures from 10 to 90 K. At sufficiently high concentrations of Kr (above about 25%) the frustration of anisotropic molecular interactions produces an orientational glass phase. Even in this highly disordered medium, muonium exhibits coherent quantum tunneling dynamics with a bandwidth only slightly reduced with respect to that in pure solid methane. The muonium diffusion is shown to be long range rather than local.

Muon spin relaxation study of the magnetic penetration depth inMgB2

The magnetic vortex lattice (VL) of polycrystalline ${\mathrm{MgB}}_{2}$ has been investigated by transverse-field muon spin relaxation (TF-\ensuremath{\mu}SR). The evolution of the TF-\ensuremath{\mu}SR depolarization rate \ensuremath{\sigma}, which is proportional to the second moment of the field distribution of the VL, has been studied as a function of temperature and applied magnetic field. The low-temperature value \ensuremath{\sigma} exhibits a pronounced peak near ${H}_{\mathrm{ext}}=75\mathrm{mT}.$ This behavior is characteristic of strong-pinning-induced distortions of the VL which put into question the interpretation of the low-field TF-\ensuremath{\mu}SR data in terms of the magnetic penetration depth $\ensuremath{\lambda}(T).$ An approximately constant value of \ensuremath{\sigma}, such as expected for an ideal VL in the London limit, is observed at higher fields of ${H}_{\mathrm{ext}}>0.4\mathrm{T}.$ The TF-\ensuremath{\mu}SR data at ${H}_{\mathrm{ext}}=0.6\mathrm{T}$ are analyzed in terms of a two-gap model. We obtain values for the gap size of ${\ensuremath{\Delta}}_{1}=6.0(3)\mathrm{meV}$ $[2{\ensuremath{\Delta}}_{1}{/k}_{B}{T}_{c}=3.6(2)],$ ${\ensuremath{\Delta}}_{2}=2.6(2)\mathrm{meV}$ $[2{\ensuremath{\Delta}}_{2}{/k}_{B}{T}_{c}=1.6(1)],$ a comparable spectral weight of the two bands, and a zero-temperature value for the magnetic penetration depth of ${\ensuremath{\lambda}}_{\mathrm{ab}}\ensuremath{\approx}100\mathrm{nm}.$ In addition, we performed $\ensuremath{\mu}\mathrm{SR}$ measurements in zero external field. We obtain evidence that the muon site (at low temperature) is located on a ring surrounding the center of the boron hexagon. Muon diffusion sets in already at rather low temperature of $T>10\mathrm{K}.$ The nuclear magnetic moments can account for the observed relaxation rate and no evidence for electronic magnetic moments has been obtained.

Muon diffusion in intermetallic compounds of the MoSi2-typestructure

The localization and diffusion of positive muons are studied in three binarymetallic systems, Zr2Cu, Hf2Cu and Ti2Cu, presenting the MoSi2-type structure.Zero-field µSR measurements are interpreted as the muons being static in theTb/Ob interstitial site at low temperatures and, as the temperature isincreased, starting diffusing through the network of Tb sites around the Obsite, until they reach a state occupying simultaneously the four Tb sites.Long-range diffusion is observed above 300 K. Activation energies for thelower-temperature diffusion processes are obtained. The results areinterpreted in terms of the lattice structure characteristics.

Muon spin relaxation study ofLa1−xCaxMnO3

We report predominantly zero field muon spin relaxation measurements in a series of Ca-doped LaMnO_3 compounds which includes the colossal magnetoresistive manganites. Our principal result is a systematic study of the spin-lattice relaxation rates 1/T_1 and magnetic order parameters in the series La_{1-x}Ca_xMnO_3, x = 0.0, 0.06, 0.18, 0.33, 0.67 and 1.0. In LaMnO_3 and CaMnO_3 we find very narrow critical regions near the Neel temperatures T_N and temperature independent 1/T_1 values above T_N. From the 1/T_1 in LaMnO_3 we derive an exchange integral J = 0.83 meV which is consistent with the mean field expression for T_N. All of the doped manganites except CaMnO_3 display anomalously slow, spatially inhomogeneous spin-lattice relaxation below their ordering temperatures. In the ferromagnetic (FM) insulating La_{0.82}Ca_{0.18}MnO_3 and ferromagnetic conducting La_{0.67}Ca_{0.33}MnO_3 systems we show that there exists a bi-modal distribution of \muSR rates \lambda_f and \lambda_s associated with relatively 'fast' and 'slow' Mn fluctuation rates, respectively. A physical picture is hypothesized for these FM phases in which the fast Mn rates are due to overdamped spin waves characteristic of a disordered FM, and the slower Mn relaxation rates derive from distinct, relatively insulating regions in the sample. Finally, likely muon sites are identified, and evidence for muon diffusion in these materials is discussed.

Muon diffusion and relaxation in YCo 2

Muons were expected to gain additional information about the spin fluctuations proposed for this enhanced paramagnetic system. At the lowest temperatures the μ +SR signal can be explained by a static Kubo–Toyabe relaxation function. On raising the temperature an interplay is suggested to occur between muon diffusion and electronic relaxation of “Co-clusters” surrounding a Co vacancy yielding a maximum in the fluctuation rate versus temperature curve. This behaviour is similar to that found in the case of paramagnetic impurities in nonmagnetic metals, the “Co-cluster” moment being the analogue to the impurity spin.

Transition of local muonium dynamics in NaCl

The spectral density C( ω) of the spin fluctuation associated with muonium diffusion in NaCl has been studied to elucidate the origin of temperature-dependent nuclear hyperfine parameter δ ex. The reduction of δ ex with decreasing temperature has been confirmed. Moreover, while C( ω) remains to take a Lorentzian distribution above 15 K, it turns into a completely different spectrum at 3 K well represented by C( ω)∝ ω −1/2, indicating a strong space–time correlation of muonium dynamics.

Positive muon diffusion and localization sites in GdNi 5

GdNi 5 is a simple metallic ferrimagnet with well understood magnetic properties. It has been used in the past as a testing ground for validating muon spin relaxation theories. Here we report on the muon diffusion and site localization in its paramagnetic phase, i.e., above 30.85 K. The muon localizes at the interstitial 3f sites over the whole temperature range. Below ∼70 K the interstitial 6m sites become populated as well. These sites form a ring surrounding the (0,0, 1 2 ) site and the muon can occupy all these sites within its lifetime. Above 40 K the muon residing time in these sites is relatively short and it jumps to the 3f site by a quantum diffusion process.

Muon sites and diffusion in doped lithium oxide

We present muon-spin relaxation results for pure and doped lithium oxide, and deduce the muon site and the diffusion rates. Samples were doped with fluoride and hydroxide ions both of which carry a nuclear moment. These ions with charge −e substitute in place of an oxide ion with charge −2e, so must be accompanied by a corresponding vacancy on the Li + sublattice. The static muon relaxation rate is the same in all samples, showing that the muons are not trapped at or near the anion impurity sites. Muons occupy Li + vacancy sites at around 150 K and this suggests that the vacancies and anion impurities are well separated. The variation of hop rate with temperature is also almost identical for all the samples. This suggests that the impurities do not play any role in the hopping mechanism at this length scale. The doped samples show a significantly larger diamagnetic muon fraction than the pure material, probably a result of differences in electron mobility.

Muon spin polarization behavior in media with polarized nuclei

A description of a muon spin-polarization behavior in condensed media with polarized nuclei is given. These objects could be obtained at low temperatures (T⩽0.03 K) and in external magnetic fields B∼20 kG . It is shown that the μSR-technique gives in this case new opportunities for a precise study of a muon diffusion in metal lattices and an accurate measurement of the Knight shift at the muon. Moreover, μSR gives new opportunities to measure low temperatures and to get a good accuracy for measurements of the magnetic moments of some nuclei.

µSR studies of elemental boron, modelling interstitial protons with implanted positive muons

Studies of positive muons implanted into solid elemental boron illustrate the various µSR techniques of muon spin rotation, relaxation and resonance. The chemical behaviour of positive muons and protons being similar, the local magnetic dipole and electrical quadrupole interactions with the boron nuclei determined by these measurements should characterize the crystallographic site and electronic structure of interstitial protons. Muon diffusion through the boron lattice becomes significant only above 500 K, with an activation energy of 0.33(2) eV, as determined from motional narrowing of the rotation spectrum and evolution of the zero-field relaxation function. The strong spin–spin couplings in boron prove suitable for demonstrating various techniques of radiofrequency and level-crossing resonance, and also a novel form of spin echo detected in null external field. Copyright © 2000 John Wiley & Sons, Ltd.

Light hydrogen isotopeμ+in Sc andα−ScHxsolid solutions

The response of Sc and $\ensuremath{\alpha}\ensuremath{-}{\mathrm{ScH}}_{x}$ systems $(0<~x<~0.25)$ to the implantation of positive muons, i.e., light H isotopes, has been studied by ${\ensuremath{\mu}}^{+}\mathrm{SR}$ spectroscopy in high and low transverse magnetic field, and in zero field (ZF). The investigation covered a temperature range from 300 K down to 2 K, for various orientations of the single-crystal samples with respect to the field or initial ${\ensuremath{\mu}}^{+}$ polarization. Below 30 K the positive muons occupy, in pure Sc, a localized ``fast-tunneling'' state, extending over two adjacent, interstitial-tetrahedral (T) sites above and below the $\mathrm{ab}$-atomic plane of the hcp lattice. In $\ensuremath{\alpha}\ensuremath{-}{\mathrm{ScH}}_{x},$ a fraction of the muons stays in this tunneling state, while for the other part, the muons pair with a H atom, to form the analog of the T-pair state H-Sc-H aligned along the c axis, specific to the ${\ensuremath{\alpha}}^{*}$ phase. The electric-field gradients, of muonic as well as intrinsic-crystalline origin, acting on the nuclei near the ${\ensuremath{\mu}}^{+}$ influence the results at low and zero magnetic fields. Their characteristics and the H-concentration dependences are evaluated. For the ZF-data analysis a newly developed uniaxial version of the Kubo-Toyabe formula was applied. Above 30 K the long-range diffusion of positive muons becomes noticeable; a two-state model explains very well the data. It assumes the ${\ensuremath{\mu}}^{+}$ to be, alternatively, in a state of free diffusion between localized-tunneling states or in a ${\ensuremath{\mu}}^{+}$-Sc-H trap. The model describes the repeated ${\ensuremath{\mu}}^{+}$-capture and release processes with three characteristic correlation times, which follow Arrhenius laws. The parameters, e.g., activation energies and preexponential factors, are compared to the parameters of the H and D dynamics in $\ensuremath{\alpha}\ensuremath{-}\mathrm{ScH}{(D)}_{x}.$ From $\ensuremath{\mu}\mathrm{SR}$ measurements in a deuterated sample $(\ensuremath{\alpha}\ensuremath{-}{\mathrm{ScD}}_{0.10})$ one infers very similar behaviors of the ${\ensuremath{\mu}}^{+}$ in D and H solid solutions in the Sc host.

Muon–proton correlated diffusion in TiHx

The diffusion of positive muons embedded in the hydrogen sub-lattice of metal hydrides becomes highly correlated with the motion of the protons at temperatures high enough to cause rapid diffusion of the hydrogen. Hydrogen blocking and hopping diffusion dictate that the motion of the lighter particle should be more rapid than that of the heavier but the contrary has been reported in many experiments on metal hydrides. A convincing explanation of this ‘slow muon problem’, in which the muon diffusion rate is apparently less than the proton diffusion rate, has not been given so far. The present experiment confirms the existence of slow muons in TiH x for x ∼2 but show that as x is reduced the correlation times associated with the motion of the muons and hydrogen atoms become more comparable.

Consistent model for the screening of slow muons in metals

By using a sum rule for scattering phase shifts at the Fermi level, a consistent screened potential of a slow positive muon in an electron gas is constructed. This consistent model potential is applied in the theoretical characterizations of the overlap parameter in muon quantum diffusion, the retarding force of the electron gas, and the Knight shift. Comparisons with available experimental results are made, and a good agreement is found.

Modeling hydrogen inCuInSe2andCuInS2solar cell materials using implanted muons

Muon spin rotation experiments on ${\mathrm{CuInSe}}_{2}$ and ${\mathrm{CuInS}}_{2}$ were performed in the context of a study on the effect and behavior of hydrogen on chalcopyrite solar cell materials. The microscopic information delivered by implanted positive muons can be applied to the hydrogen case by analogy. It was found that the major fraction of the muons is in a diamagnetic environment but, at low temperatures, a fraction of 5--10 % has a paramagnetic surrounding. In ${\mathrm{CuInSe}}_{2}$ the site of the diamagnetic muon is tentatively assigned to the antibonding site close to Se and the onset of muon diffusion on a microsecond time scale is observed between 200 and 250 K. The pre-exponential factor for the hop rate and the activation energy are ${\ensuremath{\nu}}_{0}=3.4\ifmmode\times\else\texttimes\fi{}{10}^{10} {\mathrm{s}}^{\ensuremath{-}1}$ and ${E}_{a}=220$ meV. Above 250 K trapping occurs. The diffusion behavior in ${\mathrm{CuInS}}_{2}$ is similar, but the onset is shifted by 50 K to higher temperatures.

Muon sites and diffusion in barium cerate

We have studied proton diffusion and trapping in barium cerate using muon spin relaxation, where positive muons behave as a `light isotope' of protons. The pure material and samples doped with Sc 3+ show trapping at around 200 K near paramagnetic Ce 3+ ions. Nd 3+ doping (which gives high proton conductivity at high temperatures) shows muon diffusion down to below 100 K. The results obtained also suggest the presence of weak paramagnetism, even in the pure material.

Muon sites and diffusion in lithium oxide

Muon spin relaxation measurements have been performed on the alkali metal oxides and in order to model the behaviour of hydrogen impurities in these materials. Lithium oxide has been suggested as a suitable blanket material for fusion reactions, hence the need to understand the location and dynamics of ions in the crystalline lattice. This oxide becomes a fast ion conductor at high temperatures and our experiments also provide information on the ion dynamics. Muon implantation into these oxides at low temperatures creates mainly neutral muonium (the analogue of the hydrogen atom) with a smaller fraction (%) of positive muons at interstitial sites closely associated with ions. At higher temperatures (T > 100 K) the proportion of formed increases, and there is an increased tendency for trapping at substitutional lattice sites. A sharp decrease in relaxation rate was observed in at temperatures above 250 K and from this temperature dependence we calculate the activation energy for muon hopping relative to the ions, which are also mobile, to be approximately 90 meV.