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

The diffusivityD _μ 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 monitorsD _μ 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 givesD _μ(4.6 K)=(8±2)·10⁻¹¹m²S⁻¹. The positive temperature coefficient ofD _μ indicates that at liquid-helium temperatures the diffusivity of μ⁺ inNb is mainly due to phonon-assisted tunnelling processes.     

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 estimateD _μ=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.     

Electron mobility in compensated VPE GaAs films

Electron Hall mobilities were measured on a series of intentionally compensated vapor phase epitaxy (VPE) GaAs layers. Using Sn and Zn as dopants, compensation ratiosK=(N_D+N_A)/(N_D-N_A) as high as 50 were obtained. Already for samples with the lowestK values the 300 K mobilities are higher than the 77 K values. In the range 20<T<100 [K] the data may be represented by μ∼T ^α with α increasing from 0.6 to 1.1 with compensation. The experimental μ values are smaller than those predicted from current models in all cases. It appears that scattering at ionized impurities is the dominant process also at temperatures well above 77 K, and that this scattering process is quantitatively underestimated in current models.     

Evidence for complex magnetic order in U2Zn17: A μ+ SR studySR study

μ⁺ SR-measurements in transversally applied magnetic fields of 2000 G and 4000 G on heavy-electron single crystal U₂Zn₁₇ are presented. They reveal that at least two types of interstitial sites are occupied by the positive muons. One of these sites (1/3, 2/3, 5/6) could be identified via induced local dipolar fields which aboveT _N=9.7 K can exactly be derived from the magnetic susceptibility. The corresponding component of the μ⁺-signal exhibits a steplike decrease by about 40% atT _N which is caused by the onset of a very broad distribution of static internal magnetic fields (ΔB≈1000 G) with zero average. Such a field distribution is in distinct contrast to dipolar-field calculations performed for the simple antiferromagnetic structure deduced from neutron diffraction. The remaining 60% of the muons contributing to this component belowT _N are subject to a narrow static field distribution (ΔB≈1 G). The induced dipolar fields at the site (1/3, 2/3, 5/6) are temperature-independent belowT _N. A weak dipolar coupling to the U-moments renders similar observations for muons occupying the second type of interstitial impossible.     

μ+SR studies on superconducting YBa2(Cu1−xFex)3Oy system

Spin-glass like magnetic ordering of iron moments was observed in both orthorhombic and tetragonal YBa₂(Cu_1−xFe_x)₃O_y (x=0.08) by μ⁺SR measurements. In a “Tetra” sample, all the muons sense the superconducting transition at 60 K and magnetic ordering at around 15 K, while in an “Ortho” sample they reveal that two magnetically different parts exist in the sample: about 40% of the sample is superconducting withT _c ≈90K and the remaining part is magnetic withT _M≈33K. These phenomena can be explained in terms of clustering of the Fe atoms in the “Ortho” sample.     

Muon-spin-relaxation investigation of EuMn<Subscript>2</Subscript>O<Subscript>5</Subscript>

The magnetic properties of the EuMn₂O₅ multiferroic (samples consisting of single crystals and ceramic samples) have been investigated by the muon-spin-relaxation (μSR) method in the temperature range of 10–300 K. Below the magnetic ordering temperature T _N = 40 K, the loss of the polarization of muons and the effect of the external magnetic field have been observed. Both phenomena can be explained by an additional channel of the depolarization of muons owing to the appearance of muons in a medium with a low electron density due to the charge separation process (the redistribution of the electron density in the phase transition process). The “memory” phenomenon has been revealed in a sample in the external magnetic field; the memory relaxation time depends on the size of the structure units of the samples (single crystals or ceramic grains).     

μSR studies on CeAl2

μSR studies on REAl₂ type compounds have so far given rather inconclusive results since no μSR frequency has been observed in the ordered magnetic states. Therefore, the results from the paramagnetic region [1,2] have been interpreted without detailed knowledge of the muon site or the mobility of the muons. In the present study of a single crystal sample of CeAl₂ we investigated in some detail the paramagnetic temperature range including the transition region to magnetic ordering around 3.6 K. The ordered magnetic state is antiferromagnetic with a modulated structure [3], and the absence of a spontaneous μSR precession signal belowT _N is therefore not unexpected.     

Study of μ-catalyzed fusion in H-D mixtures

Muon-catalyzed fusion was first observed in the pdμ system, and remains a good test of our understanding of the underlying molecular and nuclear processes. In contrast to the ddμ and dtμ systems, no resonant behavior is expected, which considerably simplifies the dynamics. We will discuss data taken with solid H-D mixtures of 0.05%, 2%, 15% and 75% D₂. In these measurements we observed simultaneously muons from pdμ→μ+ ³He and γs from pdμ→μ ³He + γ. A simulation code incorporating the relevant physics processes has been developed for the analysis of this data. Preliminary results are presented for the fusion and molecular formation rates. This new data stringently tests the currently-accepted fusion scheme. A new value of the astrophysical S-factor is derived. This revised version was published online in August 2006 with corrections to the Cover Date.     

Chiral invariant phase space event generator

The Geant4 CHIPS model simulates both decay and nuclear capture of negative muons. In hadron level models the muon is captured by a proton, p(μ,ν_μ)n , and the neutron transfers to the nucleus only 5MeV, which is not enough to split a nucleon from the nucleus, while the measured spectra of emitted nucleons reach 80MeV. In CHIPS, which considers asymptotically free quark-partons, the muon can be captured by a quark, u(μ,ν_μ)d , and transfers 52MeV to the nucleus. This capture mechanism fits the main part of the nucleon spectra, while the high-energy part of the spectra is not fitted. A precise fit of the high-energy part of the nucleon spectra can be made if the muon decay μ → dˉν_μ is taken into account.     

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.     

Monte Carlo simulations of the <Emphasis Type="Italic">μ</Emphasis>CF processes kinetics in deuterium gas

The kinetics of muon-catalyzed-fusion processes (μCF) in pure D₂ gas have been studied by means of Monte Carlo simulations for various target temperatures and densities. In particular, the role of resonant and non-resonant ddμ formation in μCF has been investigated. It has been shown that non-resonant formation can be directly observed at very short times in the neutron time spectra from μCF for low-density D₂ targets. The time spectra of neutrons from the low-temperature ortho-D₂ and para-D₂ gas targets have been calculated. These spectra display a strong ortho-para effect, which agrees with experimental results for the dilute-gas D₂ targets.     

MuSR/μ+SR studies in KDP and DKDP

The temperature dependence of muon interactions has been studied in ferroelectric KDP ( H₂KPO₄) and DKDP ( D₂KPO₄) using conventional μSR and muon spin resonance spectroscopy. In longitudinal field measurements, a fast relaxing component and a slow relaxing component were observed. The slow relaxing component is attributed to diamagnetic muons. The muon spin resonance measurements indicate that the fast relaxing component results from some muonium like species: either normal or anomalous. In zero field and weak longitudinal field μSR (0–100 G), a remarkable peak in the fast relaxing component is observed around 220 K in both KDP and DKDP. An additional feature is also seen around 300 K. The amplitude of the resonance measurement has a broad minimum around 200 K which corresponds to the maximum in the relaxation rate in longitudinal field (100 G). The temperature dependence of the muonium relaxation rate in KDP is almost identical to that of DKDP. The diamagnetic fraction also shows almost no difference in relaxation rate or asymmetry for DKDP and KDP. This revised version was published online in August 2006 with corrections to the Cover Date.     

Total and transport elastic cross-sections for excited muonic and pionic hydrogen atoms

The results of an experiment on muon catalyzed dd-fussion in HD gas are presented. The experiment was performed at the muon beam of PSI using a high-pressure ionization chamber filled with pure HD-gas of low D₂ concentration on the level 1%, at temperatures 50, 150 and 300 K. The non-resonant character of ddμ-molecule formation on HD molecules was confirmed by measuring the ratio of yields of the two ddμ-fusion channels, R=Y(³He,n)/Y(³H,p), which proved to be close to unity. The ddμ formation rate was found to vary from λ_ddμ-HD=0.05· 10⁶ s^-1 at T=50 K to λ_ddμ-HD=0.12· 10⁶ s^-1 at T=300 K, in agreement with the theoretical prediction. A prominent peak at t<60 ns was observed in the time spectrum of fusion neutrons indicating a resonant contribution of ddμ formation from epithermal dμ atoms. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of the Parameters of Muon-Catalyzed Fusion in Double D/T Mixture at High Temperature and Density

Experiments on the study of the muon catalyzed fusion (μCF) process in a double D/T mixture of hydrogen isotopes in the temperature range 300–800 K at densities 0.3–0.5 LHD are performed at the JINR phasotron. The values of the effective μCF parameters (cycling rate λ _c , neutron yield Y _n , muon losses w) are obtained. Tentative dtμ-molecule formation rates on D₂ and DT molecules (λ _dtμ−d and λ _dtμ−t ) are obtained for different mixture temperatures and densities. The results obtained show that λ _dtμ−t increases with temperature, but its value is smaller than theoretical predictions. This revised version was published online in August 2006 with corrections to the Cover Date.     

First μ+SR studies on thin films with a new beam of low energy positive muons at energies below 20 keV

At the Paul Scherrer Institute slow positive muons (μ⁺) with nearly 100% polarization and an energy of about 10 eV are generated by moderation of an intense secondary beam of surface muons in an appropriate condensed gas layer. These epithermal muons are used as a source of a tertiary beam of tunable energy between 10 eV and 20 keV. The range of these muons in solids is up to 100 nm which allows the extension of the μ⁺SR techniques (muon spin rotation, relaxation, resonance) to the study of thin films. A basic requirement for the proper interpretation of μ⁺SR results on thin films and multi-layers is the knowledge of the depth distribution of muons in matter. To date, no data are available concerning this topic. Therefore, we investigated the penetration depth of μ⁺ with energies between 8 keV and 16 keV in Cu/SiO₂ samples. The experimental data are in agreement with simulated predictions. Additionally, we present two examples of first applications of low energy μ⁺ in μ⁺SR investigations. We measured the magnetic field distribution inside a 500-nm thin High-T_C superconductor (YBa₂Cu₃O_7-δ), as well as the depth dependence of the field distribution near the surface. In another experiment a 500-nm thin sample of Fe-nanoclusters (diameter 2.4(4) nm), embedded in an Ag matrix with a volume concentration of 0.1%, was investigated with transverse field μ⁺SR. This revised version was published online in August 2006 with corrections to the Cover Date.     

Relaxation and shift of the precession frequency of the spin of a negative muon in n-type silicon

The residual polarization of negative muons in n-type silicon with impurity density (1.6±0.2) · 10¹³ cm⁻³ is investigated as a function of temperature in the range 10–300 K. The measurements are performed in an external magnetic field of 0.08 T oriented transversely to the spin of the muons. Relaxation of the muon spin and a shift of the precession frequency are observed at temperatures below 30 K. The relaxation rate at 30 K equals 0.25±0.08 μs⁻¹. The shift of the precession frequency at 20 K equals 7 · 10⁻³. Both the relaxation rate and the shift of the precession frequency increase as the temperature decreases. At temperatures below 30 K the relaxation rate is described well by the relation Λ=bT ^−q , where q=2.8±0.2. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 539–543 (10 April 1996)     

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (Mu_T) and the diamagnetic states (μ^d), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (Mu_BC) and μ^d. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond. This revised version was published online in August 2006 with corrections to the Cover Date.     

μ + Knight shift and spin relaxation in indium single crystalKnight shift and spin relaxation in indium single crystal

μ ⁺ SR measurements have been performed in a single crystal indium sample between 12 K and 300 K with a stroboscopic μSR spectrometer. The muonic Knight shiftK _μ and the muonic depolarization rate σ were obtained for various angles θ between the tetragonal crystallinec-axis and the direction of the external field. The isotropic part ofK _μ is only weakly temperature dependent and is consistent with the estimated Pauli spin susceptibility value. At a temperature of 12 K the angular dependence ofM ₂ (the second moment of the field distribution at the muon, obtained from the measured σ(θ) values) allows a clear determination of the muon location — the symmetric tetrahedral site. The observed anisotropicK _μ cannot be explained by the dipoles at the In atoms responsible for the bulk magnetic susceptibility but probably originates from an anisotropic Pauli spin susceptibility.     

Positive muons in single crystal sodium fluoride: A simple spin system

We report on the relaxation of positive muons (μ ⁺) stopped in a single crystal of sodium fluoride at 15±0.2K. At this temperature theμ ⁺ is believed to be static, and the observed time dependence of theμ ⁺ spin polarization is seen to deviate from the familiar Kubo-Toyabe form at late times. Specifically these data exhibit oscillations in the long time tail, which are attributed to hyperfine transitions between theμ ⁺ and neighboring spins. Quantitative comparison of these data to exact quantum mechanical calculations indicates that most of the time dependence can be explained by considering only interactions with the first shell (i.e., two fluorine and two sodium nuclei), and suggests strongly that the muon occupies a site along the <110> axis, midway between two fluorine nuclei.     

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.