Muon spin relaxation and knight shift in the heavy-fermion superconductor UPt3

Positive muon spin relaxation experiments have been conducted on the heavy-fermion superconductor UPt₃ in both the normal and superconducting states for zero, transverse, and longitudinally applied magnetic fields. Below 6 K in zero applied field, the μ⁺ relaxation rate is approximately twice that expected from¹⁹⁵Pt nuclear dipolar relaxation alone. Transverse- and longitudinal-field measurements show that the observe relaxation rate depends on magnetic field and is quasistatic in origin. It is suggested that the onset of very weak (≈10⁻³ μ_B/U atom) magnetic ordering below approximately 6 K is responsible for the observed increase in the relaxation rate. μ⁺ Knight shift measurements in the normal state of UPt₃ show a temperature dependent shift K_μ which tracks the bulk susceptibility X. From the K_μ vs. X plot, a μ⁺ hyperfine field of approximately 100 Oe/μ_B is extracted.     

Non-secular part of nuclear dipolar broadening detected by zero-field spin relaxation of positive muon

The zero-field spin relaxation function of μ⁺ observed in ZrH₂ has revealed that the second moment of the nuclear dipolar broadening is five times larger than the high-field value. This experiment clearly demonstrates the recovery of the non-secular part of dipolar interaction between unlike spins. A general expression of zero-field relaxation function is presented to account for a slow modulation of random fields on μ⁺ found at room temperature.     

Muon/muonium surface interactions

The interactions of muonium (μ ⁺ e ⁻, Mu) with the surfaces of fine silica powders have been extensively studied using zero, longitudinal and transverse field μSR techniques. These studies indicate diffusion and trapping behavior of the Mu atoms on the silica surface, which is strongly influenced by the surface hydroxyl (OH) concentration. Specifically, the presence of the surface OH groups is observed to inhibit the surface mobility of the Mu atoms at low temperatures. Information provided by zero and longitudinal field data suggest a random anisotropic distortion of the Mu hyperfine interaction (RAHD) as the principal relaxation mechanism. A recently developed RAHD spin relaxation theory is used to interpret these data. Additional investigations, using platinum loaded silica, have yielded the first observed surface reaction of Mu. Studies of the interactions of positive muons with surfaces have been also extended to single crystals, where low energy (<10 eV)μ ⁺ andMu ⁻ ions are observed to be reemitted from some materials (e.g., the <100> surface of lithium fluoride). Future applications of these emission phenomena toward the development of a slow^847-3 (or Mu⁻) beam are considered.     

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.     

Positive muons in bismuth: determination of their sites,detection of a large local lattice contraction and giant associated electric field gradients,evidence for short and long range diffusion

Using a high purity Bi single crystal the temperature and orientation dependence of the zero and transverse field muon spin relaxation rate has been studied in detail. The results imply that the ⁺ occupies one of the two possible interstitial sites in the distorted rhombohedral crystal structure of Bi below 10 K and the other site above 80 K. At both sites the nearest neighbor Bi atoms are found to be shifted towards the ⁺ by 10% of their nominal distance, implying a large local lattice contraction. In concomitance extremely strong electric field gradients are manifest at the nn Bi nuclei. An almost temperature independent reduced relaxation rate in the temperature range from 20 K to 60 K is interpreted in terms of short range diffusion along a limited chain of alternating types of sites. Above 100 K both long range and short range diffusion are indicated.     

Hyperfine field and diffusion of μ+ in Fe single crystals

In recent positive-muon spin rotation experiment at TRIUMF on single crystal Fe, a clear temperature dependent change has been observed, for the first time, both in frequency and depolarization rates from 300 K down to 23 K. The μ⁺ depolarization was explained by the μ⁺ diffusion through inhomogeneous dipolar fields and the diffusion constant was found to obey an Arrhenius law (activation energy 17 meV) above 70 K but surprisingly deviated from this at lower temperatures, indicating quantum diffusion. We have also found that the μ⁺ hyperfine field has a temperature dependence slightly stronger than that of the magnetization.     

μSR in UAs

UAs has the NaCl structure and undergoes a first order transition into a type I (single k) antiferromagnetic state at 123 K, followed by a second first order transition at 62 K into a type IA (double k) antiferromagnetic structure. μSR spectra of a powder sample were taken in zero and transverse fields up to 0.3 T. They cover the paramagnetic and the two antiferromagnetic states. The most significant features of our data are: i) a first increase of relaxation rate below T=180 K; ii) a sudden jump in both, relaxation rate and frequency shift at T=123 K, together with a small decrease in initial asymmetry (≈15%); iii) no μ⁺ spin rotation in zero field in the type I state; iv) an overlay, of 3 spectra in the type IA state. Two of these spectra show spin rotation in zero field. Their frequencies are clearly temperature dependent. In a transverse field of 5 and 10 mT the external field adds nearly fully to the internal field. Work supported in part by the Bundesministerium fur Forschung und Technologie, Federal Republic Germany.     

Muonium in ice

Muonium has been studied in single crystals of H₂O and D₂O. Two-frequency precession in low transverse fields and a single zero-field oscillation indicate a small anisotropy of axial symmetry in the muonium hyperfine interaction. The anisotropy is shown to be the cause of the hitherto unexplained temperature independent contribution to muonium spin relaxation in polycrystalline samples. Relaxation rates for 99 K–263 K are reported for muonium in a single crystal of H₂O. Relaxation is attributed to electron-nuclear dipolar coupling of muonium to lattice protons, modulated by translational diffusion of muonium alongc-axis channels of the ice lattice. A simple model for H and Mu diffusion in ice is investigated.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

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.     

Recent results on hyperpolarized<Superscript>3</Superscript>He−<Superscript>4</Superscript>He liquid mixtures

Laser optical pumping in low magnetic field provides very high nuclear polarizations in gaseous helium mixtures, and is used to prepare polarized liquid. Wall relaxation in glass cells is effiently reduced using cesium coatings, and bulk longitudinal relaxation times are measured. In highly magnetized samples, dipolar fields control the spin dynamics in anisotropic volumes and weak external magnetic field inhomogeneities. Long lived magnetostatic modes are observed by pulsed NMR. Detailed analysis of their frequency and damping gives information on magnetization density and spin diffusion coefficient in polarized mixtures. Experiments are performed above 0.2 K on mixtures with³He concentrations of order a few percents or larger. When phase separation occurs, the³He-rich phase retains a high polarization.     

Free precession and transverse relaxation of hyperpolarized <Superscript>129</Superscript>Xe gas detected by SQUIDs in ultra-low magnetic fields

We studied the free precession of the nuclear magnetization of hyperpolarized ¹²⁹Xe gas in external magnetic fields as low as B₀ = 4.5 nT, using SQUIDs as magnetic flux detectors. The transverse relaxation was mainly caused by the restricted diffusion of ¹²⁹Xe in the presence of ambient magnetic field gradients. Its pressure dependence was measured in the range from 30 mbar to 850 mbar and compared quantitatively to theory. Motional narrowing was observed at low pressure, yielding transverse relaxation times of up to 8000 s.     

Zur Theorie der Kernspinrelaxation bei einem Austausch zwischen zwei Bereichen

Using REDFIELD 's theory of relaxation and SILLESCU 's master equation treatment of molecular reorientation, the longitudinal and transverse nuclear spin relaxation functions have been calculated in a two phase system with different magnetic interaction energies. The interaction HAMILTON ian represents the dipolar coupling amongst the nuclei in region (a, 1) and between a nucleus and a paramagnetic ion in region (b, 2). Assuming a strong electron spin relaxation which is statistically independent from the nuclear relaxation, a situation realized in paramagnetic solutions and adsorbate systems, the problem simplifies considerably. If some correlation, expressed by a correlation coefficient c, is lost in each transfer between the regions, a longitudinal relaxation time T^(c)_1m can be defined, as long as the life time τ_b in the region with the lower mobility is not comparable with the correlation time τ₁ in the other phase. Without any restriction, however, one time constant T^(c)_2m should characterize the decay of transverse magnetization as a good approximation. The apparent correlation times, determined from experimental data without any knowledge of the coefficient c, differ only slightly from the effective correlation times (in general less than 10%), in contrast to the case of equal interaction energies in both regions. If the interaction HAMILTON ian does not vary under the exchange (e. g. dipolar interaction between the nuclei in both regions) the results of the wellknown statistical treatment of BECKERT and PFEIFER are obtained. Neglecting any correlation at each transfer (i.e. c = 0) the relaxation rates are weighted averages, which correspond to the fast exchange case in the theory of ZIMMERMAN and BRITTIN with the effective correlation times τ_ca = τ_a?τ₁/τ_a+τ₁ and τ_cb = τ_b?τ₁/τ_b+τ₁.     

DIRECT MEASUREMENT OF TRANSVERSE RELAXATION TIME OF INTERMOLECULAR MULTIPLE QUANTUM COHERENCES IN NMR

A one-dimensional NMR method is presented for measuring the transverse relaxation time, T_2,n, of intermolecular multiple quantum coherences (IMQCs) of coherence order n in highly polarized spin systems. The pulse sequence proposed in this paper effectively suppresses the effects of radiation damping, molecular diffusion, inhomogeneity of magnetic field, and variations of dipolar correlation distance, all of which may affect quantitation of T_2,n. This pulse sequence can be used to measure not only IMQC transverse relaxation time T_2,n(n>1) quickly and directly, but also the conventional transverse relaxation time. Experimental results demonstrate that the quantitative relationship between T_2,n(n≥1) and T₂ is T_2,n≈T₂/n. These results will be helpful for understanding the fundamental properties and mechanisms of IMQCs.     

μ+ Diffusion in copper below 4 K reconfirmed by LF-μ+SR

Muon spin relaxation in longitudinal magnetic field (LF-μ⁺SR) reveals separately the static width of the local dipolar field distribution at the μ⁺ and the μ⁺ hopping rate in the copper lattice at 4.2 and 0.7 K, confirming that muon hopping between octahedral interstitial sites increases at lower temperatures.     

Expanding the Frequency Range of the Solid-State T1 ρ Experiment for Heteronuclear Dipolar Relaxation

Solid-state spin–lattice relaxation in the rotating frame permits the investigation of dynamic processes with correlation times in the range of microseconds. The relaxation process in organic solids is driven by the fluctuation of the local magnetic field due to the dipole–dipole interaction of the probe nuclei (¹³C,¹⁵N) with ¹H in close proximity. However, its effect is often hidden by a competing relaxation process due to the contact between the rotating frame ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. In most cases the latter process becomes superior for the commonly applied low and moderate spin-lock fields and practically does not provide information about the molecular dynamics. To suppress this undesired process and to expand the dynamic range of T_{1 ρ} experiments, we present two approaches. The first one uses a resonance offset of the frequency of the spin-lock irradiation, which leads to a significant enhancement of the effective spin-lock frequency without the application of destructive high transmitter powers. We derive the theory and demonstrate the applicability of the method on various model compounds. The second approach utilizes heteronuclear ¹H decoupling during the ¹³C/¹⁵N spin-lock irradiation which disrupts the contact between the ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. We demonstrate the method and discuss the results qualitatively.     

Valence fluctuations in ternary europium compounds

We outline the possibility to study europium valence fluctuations with the μSR method and report on μSR experiments on the intermetallic compounds EuPdAs and NdPdAs. Above a magnetic transition at 15 K the temperature dependence of the relaxation rate in the trivalent neodymium system behaves like a typical localized moment system. In the valence fluctuating europium compound the zero field relaxation rate levels off at 1.0\ μs^-1 above 40 K. Furthermore, the relaxation enhancement in transverse field experiments is much smaller than expected for a pure dipolar coupling. Therefore an isotropic hyperfine coupling of typical strength is assumed and a valence fluctuation rate of 0.8 μs^-1 at 200 K is derived. Below the magnetic transition at 5 K a disordered spin freezing is concluded in EuPdAs. This revised version was published online in July 2006 with corrections to the Cover Date.     

μ + SR studies of antiferromagnetic chromiumSR studies of antiferromagnetic chromium

μ ⁺ SR measurements have been performed on Cr single crystals at temperatures 60 mK≤T≤295 K in applied magnetic fields 0≤B _appl≤1.5 T. The temperature dependence of the observed precession frequencies and transverse relaxation rates can be explained by the assumption that theμ ⁺ are hopping between adjacent tetrahedral interstices. At temperaturesT≤11 K evidence for an interaction between theμ ⁺ and the spin-density waves in Cr has been found. The directions and magnitudes of the lattice magnetic moments are unaffected by the applied magnetic fields.     

The influence of the stoichiometry on the Eu nuclear spin-spin relaxation in EuO single crystals

The ¹⁵³Eu spin-spin relaxation for two spherical EuO single crystals of different composition has been measured for two saturating field values of 2 and 6 T. The relaxation can be described by two time constants, a short one increasing with the magnetic field, arising from the Suhl-Nakamura coupling and a long one, due to the dipolar coupling, which is field independent. It is shown that the number of nuclei which are relaxed due to the dipolar coupling increases at increasing magnetic fields, in agreement with the Suhl-Nakamura theory. For the sample which is nearly stoichiometric the relative number of nuclei which is relaxed due to the SN coupling is much larger than for the sample which contains an excess of Eu atoms.     

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. Work supported by the Bundesministerium für Forschung und Technologie, Bonn, Fed. Rep. of Germany     

Radiative process in strong magnetic fields

Abstract

The behavior of electromagnetic processes in strong magnetic fields is currently of great interest in high-energy astrophysics. Observations of neutron stars indicate that magnetic fields larger than 10¹² Gauss exist in nature. In fields this strong, where electrons behave much as if they were in bound atomic states, familiar processes undergo profound changes and exotic processes become important. Strong magnetic fields affect the physics in several fundamental ways: energies prependicular to the field are quantized, transverse momentum is not conserved and electron/positron spin is important. The relaxation of transverse mometum conservation allows first order processes and their inverses: one-photon pair production and annihilation, synchrotron/cyclotron radiation and absorption, which are kinematically forbidden under field-free conditions. The first two are essentially quantum-mechanical and hence significant only in fields whose strength approaches the critical field, B _cr = 4.414 × 10¹³ Gauss. One-photon pair production is likely to be the dominant source of e ⁺ -e ^? pairs in fields exceeding 10¹² Gauss. While synchrotron radiation and absorption are observable as classical electromagnetic processes in weak fields, they are considerably different in high fields, where the classical synchrotron radiation formulae can violate conservation of energy, and predict too large an emissivity and electron energy loss rate. The second-order processes: two-photon pair production and annihilation and Compton Scattering, are also modified in strong fields. The discreteness of e ⁺ - e^? pair states causes resonant behavior in the cross sections and decreases the second-order rates from their free-space values. These processes play an important role in modelling high energy emission from pulsars and gamma-ray bursts.