Showing papers in "Journal of Low Temperature Physics in 1974"

A “Fermi-Liquid” Description of the Kondo Problem at Low Temperatures

Abstract: We take as granted Anderson's statement that in the low-temperature limit the usual Kondos-d model evolves toward a fixed point in which the effective exchange coupling of the impurity with the conduction electrons is infinitely strong. The low-temperature properties (T«T K) are then described phenomenologically in the same spirit as the usual Landau theory of Fermi liquids. The specific heat, spin susceptibility, and resistivity are expressed in terms of a small number of numerical parameters. In the strong coupling case the latter may be obtained via perturbation theory; in the opposite weak coupling limit they must be fitted to Wilson's recent numerical results.

Phase-slip centers and nonequilibrium processes in superconducting tin microbridges

Abstract: We show experimentally that steps in theI–V curves of long, superconducting microbridges nearTc are due to spatially localized voltage units (interpreted as quantum phase-slip centers) which appear at local critical currents determined primarily by variations ofTc along the bridge. We also observe the ac Josephson effect associated with such centers. At low voltages each center carries a time-averaged supercurrent of ∼1/2 Ic and exhibits a temperature-independent differential resistance due to normal current flow governed by the quasiparticle diffusion length. Our phenomenological model of this behavior includes a simplfied description of both the superfluid dynamics and the spatial healing of the resulting disequilibrium between superconducting pairs and quasiparticles. Our data indicate that the relaxation time associated with the nonequilibrium is typical of inelastic scattering times for electrons near the Fermi surface of normal tin.

Temperature dependence of H/sub c2/ and K/sub 1/ in strong coupling superconductors

Abstract: According to the law of corresponding states, the properly scaled critical fields of a BCS superconductor are universal functions of the reduced temperatureT/Tc. In realistic superconductors strong-coupling effects can cause deviations from this universal behavior. We present numerical results for the strong-coupling anomalies in the temperature dependence of the upper critical fieldHc2 and the Ginzburg-Landau parameter κ1. The calculations are based on the Eliashberg theory for strong-coupling superconductors and are performed for several realistic superconductors as well as for a series of model superconductors with increasing coupling strength. It is demonstrated that the magnitude of the deviations can be estimated from the magnitude of the ratioTc/〈ω〉, where〈ω〉 is an average phonon frequency. This rule does not apply to amorphous superconductors. The reason for this is shown to be due to the large weight ofα2F(ω) at low frequencies which has been observed in these materials.

Dynamic polarization of protons, deuterons, and carbon-13 nuclei: Thermal contact between nuclear spins and an electron spin-spin interaction reservoir

Abstract: Hydrogen, deuterium, and carbon-13 nuclear spin systems have been studied in partially deuterated 1,2-ethanediol (CD2OH)2, doped with paramagnetic Crv complexes, between 0.1 and 0.5 K, using the technique of dynamic polarization. Various steady-state and transient measurements demonstrate the existence of a thermal contact between the different spin species of this sample and the electron spin-spin interaction reservoir. The lowest spin temperature attained was about 1.2 mK in a magnetic field of 25 kG, which corresponds to a proton polarization of 97%, to a deuteron polarization of 40%, and to a carbon-13 polarization of 48%.

On the interaction of surface electrons in liquid helium with oscillations of the vapor-liquid interface

Abstract: This paper presents a detailed analysis of the interaction between surface electrons and thermal oscillations (ripplons) of the liquid helium surface. The results obtained enable us to check the validity of the many different approximate descriptions of the electron-ripplon interaction that have been given. The influence of the interaction upon the kinetics of surface electrons also has been studied, with a view to establishing the possibility of obtaining information on the capillary wave spectrum.

Local structure and thermodynamic properties of clean type II superconductors near H c1 at arbitrary temperature

Abstract: An iterative procedure has been developed to solve Eilenberger's version of the Gor'kov equations numerically The method has been used to compute the structure of flux lines and the lower critical field for clean superconductors as a function of temperature Some information on the vortex lattice has also been obtained by means of a circular cell approximation We find a pronounced reduction in the size of the coreregion (measured, eg, in units of the temperature-dependent coherence length) with decreasing temperature; this results in considerably steeper slopes of the order parameter and the current density at the vortex center There are indications that, among other peculiar effects, these slopes diverge forT → 0 The field at the center of the isolated vortex apparently increases with decreasing temperature down toT=0 The results are compared with experiments and with similar calculations for the dirty limit

On the longitudinal static and dynamic susceptibility of spin-1/2 Kondo systems

Abstract: The impurity spin polarization, static susceptibility, and longitudinal impurity spin relaxation rate are calculated for thes-d model as function of temperature and magnetic field for ferromagnetic and antiferromagnetic exchange coupling. The thermodynamic functions and the dynamical susceptibility are obtained from the impurity relaxation spectrum, which is approximated by taking into account the infrared-like singularities. For antiferromagnetic coupling the zero-field susceptibility obeys a Curie-Weiss law1/χ∼4.6(T+θ) for high and intermediate temperatures and it approaches the finite value1/χ∼3.8θ for zero temperature. The zero-field relaxation rate is much larger than the Korringa value; it decreases with temperature and approaches the nonzero value1/T1∼1.2θ for zero temperature. The relaxation rate decreases with increasing field. The results for the spin polarization agree well with the experimental data for the Cu:Fe alloy.

Superconducting transition temperature of aluminum, indium, and lead fine particles

Abstract: Aluminum, indium, and lead fine particles with free surfaces were made by evaporation in helium gas to study the size dependence of the superconducting transition temperatureT c in very small particles. The transition temperature was determined from the change of diamagnetic susceptibility with temperature. The present experiment shows thatT c rises with decrease of the average diameter $$\bar d$$ for aluminum and indium, while it remains nearly constant for lead. The enhancement factorsT c /T (T isT c for the bulk material) in the case of $$\bar d = 100 {\AA}$$ are determined as 1.45, 1.15, and 1.0 for aluminum, indium, and lead, respectively. The effect of the soft phonon mode arising from the increasing fraction of surface satisfactorily explains the experiment with respect to both the size dependence and the difference among elements by a rather simple model.

Propagation of zero sound in the Balian-Werthamer state

Abstract: The propagation of zero sound in the superfluid state of the type suggested by Balian and Werthamer is studied theoretically. In the collisionless limit the attenuation of zero sound takes place only for ω≥2Δ(T) and at ω=2(3/5)1/2Δ(T), where ω is the frequency of the sound wave and Δ(T) is the temperature-dependent order parameter.

A-15 phases: Occurrence, Geller radii, and electronic structure

Abstract: Reported A-15 phases are tabulated using a comparison between measured and predicted lattice parameter as a criterion. An enlarged set of Geller radii is calculated, and trends in these are used to discuss electronic features of these compounds. The small variation of superconductingT c among some compounds related to Nb3Sn is explained in terms of constant electronic feature deduced from the Geller radii.

Interfering electron quantum states in ultrapure magnesium

Abstract: A detailed analysis is presented of the large-amplitude temperature-insensitive oscillations in the transverse magnetoresistivity of ultrapure Mg single crystals resulting from the direct interference of electron quantum states. A calculation of the relative harmonic content of these interference signals based on the transmission characteristics of a magnetic breakdown-generated interferometer is used to quantitatively study certain aspects of the electron states in Mg as well as details of magnetic breakdown. In particular, values of magnetic breakdown parametersH 0are determined without invoking the complexities of transport theory. An absolute lower limit for the electron quantum state lifetime of τ ≳ 0.5 nsec is obtained (forT=1.5° K), although a best fit to the data gives a value an order of magnitude larger, τ∼5 nsec, which corresponds to quantum phase coherence extending over a distance of 3 mm in these crystals. In addition, this work provides direct experimental verification of the π/2 phase difference between transmitted and reflected electron states at a magnetic breakdown junction. Comparison of the results of this experiment with previous work via an existing semiempirical band structure calculation demonstrates the complete consistency of these measurements with previous Fermi surface data.

The upper critical field of layered superconductors

Abstract: The results of a theoretical study of the upper critical fields of layered superconducting compounds are presented. It is found that for sufficiently decoupled layers the parallel critical fieldsH c2,‖ can be quite large compared to those expected with ordinary type II superconductors and essentially determined by the destruction of the superconductivity in the individual superconducting layers. It is found thatH c2,‖ can be calculated from standard pair breaking theory in terms of a pair breaking parameter appropriate for layered compounds. The pair breaking parameter includes both orbital effects and the effects of Pauli paramagnetism and spin-orbit scattering.

Superconductivity in new A-15 niobium alloys

Abstract: A number of previously unreported A-15 Nb alloys have been studied, using samples prepared by dual target sputtering.T c was measured resistively and structure determined by x-ray diffraction. Samples were “chemically” analyzed by anodization. New alloys include A-15 Nb3Si and pseudobinary derivatives, as well as some derivatives of “Nb3P.”T c and the A-15 lattice parameter were surveyed for these, and for previously studied alloys related to Nb3Al, Nb3Ga, and Nb3Ge. The “chemical” variation ofT c was slight, except near pure Nb3Si and for alloys based upon “Nb3P,” where the samples show considerable disorder. Maxima inT c occur for the alloys Nb3Al0.7Ge0.3 and Nb3Al0.5Ga0.5. The first is well known; trends measured here indicate that the second may be equally high. It is proposed that the dominant factor forT c in this group of alloys is the state of order achieved in the samples. No evidence was seen to associate enhancedT c with A-15 phase boundaries.

Neutron diffraction studies of the morphology of flux line crystals in type II superconductors

Abstract: Neutron diffraction measurements on flux line single crystals in different type II materials are reported. It is shown that the type, the perfection, and the orientation of the vortex lattice with respect to the metal crystal mainly depend on the symmetry of the crystal axis which is parallel to the magnetic field. Results on samples with twofold, fourfold, and sixfold symmetry axes are represented and compared with theoretical predictions. We further studied the dependence of the widths of rocking curves on temperature and flux density and show that there is a close connection between the mosaic spread of the vortex lattice and its elastic properties.

Local Structure and Thermodynamic Behavior of Dirty Superconductors in the Mixed State at Arbitrary Temperature

Abstract: A recent dirty-limit version of the Gor'kov theory is used to calculate numerically the self-consistent structure and free energy of isolated vortices and of the vortex lattice in the circular cell approximation at arbitrary temperature and Ginzburg-Landau parameter κ. This yields the lower critical fieldHc1, the magnetization curve, the electronic specific heat, and the density of states at the Fermi surface. The results are discussed and compared with experiments.

Measurements of the Relaxation of Quasiparticle Branch Imbalance in Superconductors

Abstract: An imbalanceQ in the quasiparticle populations of thek>k F andk

Ultrasonic dispersion and attenuation near the liquid-gas critical point of 3He

Abstract: We report ultrasonic dispersion and attenuation measurements near the liquid-gas critical point of 3He at frequencies from 0.5 to 5.0 MHz and densities from 0.89ϱ c to 1.15ϱ c . The singular part of the sound attenuation and the dispersion on the critical isochore ϱ c = 0.0414 g/cm3 are analyzed in terms of the Kawasaki-Mistura theory. If the Ornstein-Zernike order parameter correlation function is assumed in the analysis, good agreement with our data is achieved, except close to the critical temperature T cin the high-frequency region, where ω* = ω/ωD ≫ 1. Here Ω D is the characteristic relaxation rate of the critical fluctuations. From a fit of the theory to our data, and assuming the inverse correlation length κ is expressed by κ = κ0ɛΝ, where ɛ = (T−Tc)/Tc with Ν = 0.63, we obtain κ0 = (3.9 ± 0.4) × 109 m−1. It is found that a more realistic form of the correlation function, as proposed by Fisher and Langer and calculated by Bray, yields even poorer agreement with out data than does the classical Ornstein-Zernike form for Ω* > 10. The same difficulties appear in the analysis of the available data for xenon. Thus, the present mode coupling theory is unable to satisfactorily describe the acoustic experiments on fluids near the liquid-vapor critical point over a large range of reduced frequencies Ω*. In the appendix, we reanalyze previously reported ultrasonic data in 4He, taking into account the nonsingular term of the thermal conductivity. Using Ν = 0.63, we obtain a good fit of the experiment to the theory in the hydrodynamic region with κ0 = (5.5 ± 1) × 109 m−1.

The synthesis of Nb 3 Ge by RF sputtering

Abstract: The conditions necessary for the formation of Nb 3 Ge by low-pressure rf sputtering with a superconducting transition temperatureT c >21 K have been investigated. Samples have been deposited onto cooled substrates so that the film is first amorphous and then is crystallized by a subsequent annealing, and onto hot substrates, in which case the film is crystalline upon deposition. The highestT c samples were obtained for a substrate temperature of 735±25° C. The optimum substrate temperature is the same as the optimum annealing temperature for crystallizing films which were first deposited onto cooled substrates. Special conditions are necessary for the formation of single-phase A15 samples of Nb 3 Ge with an optimumT c . We have utilized the collisions that the sputtered atoms undergo with the sputtering gas molecules to thermalize the sputtered atoms. We report here on sputtering in both krypton and in argon.

Vortex nucleation in deformed rotating cylinders

Abstract: Superfluid states in a rotating elliptic cylinder are studied with semiclassical hydrodynamics. Two distinct approaches are used to obtain the critical angular velocity for the appearance of a vortex: (1) Equilibrium thermodynamics predicts that ω c1 increases monotonically with deformation at fixed cross-sectional area. (2) Predictions based on a critical slip speedv c at the walls depend on the detailed form ofv c ; the resulting ω c need not vary monotonically with deformation. The analogous situation in a rectangular cylinder is also discussed.

An important parameter in high-temperature superconductivity

Abstract: It is widely held that the single most important parameter describing the strength of the electron-phonon interaction in superconductivity is the mass enhancement factor λ, and that the maximum possible transition temperature for a given class of materials (e.g., the polyvalent metals) is attained for a very large value, λ≈3, of the parameter. We show that it is not likely that the highest attainable values ofT c will reflect such large values of λ. Instead, we expect that they will be associated with values of λ that do not differ greatly from a value of about 1.5, and with very large values of the parameterA, whereA is the area under the electron-phonon interaction spectrum α2 F(v). This is certainly the case forNb 3 Sn, which has aT c of 18 K.

Properties of the flux line lattice in hysteretic type II superconductors. II. Neutron depolarization experiments

Abstract: Neutron depolarization experiments made on the same samples as investigated previously by neutron diffraction experiments (part I of this report) are presented. The correlations between crystal lattice and flux line lattice are shown to lead to a different field dependence of the average misalignment of the flux lines compared with polycrystalline materials. The average tilting angles are found to depend strongly on the magnetic field and to differ for increasing and decreasing fields in the same way as the mutual misorientations of singlecrystalline flux line blocks in the plane perpendicular to the field. For a known defect structure the tilting angles may be used to calculate the average displacement of the flux lines and the basic pinning forces.

Phonon reflection at a cleaved sodium fluoride-helium film interface

Abstract: High-frequency phonons (hω/kB≳10 K) have been reflected on the solid side of a sodium fluoride-helium-4 interface. The reflectivity was measured as a function of helium film thickness and it was found that most of the change occurs below a pressure of 0.1 of the SVP at ∼1.1 K, when the helium film is a few atomic layers thick. The largest change in reflectivity occurs for transverse phonons, which travel along longer paths than the specularly reflected phonons. It is suggested that the incident phonons excite surface modes which desorb some of the surface bound helium atoms.

Review paper: Fermi surfaces of the ferromagnetic transition metals

Abstract: Recent experimental studies of the electronic properties of the 3d ferromagnets iron, cobalt, and nickel are reviewed in relation to models for the majority-spin and minority-spin band structures and Fermi surfaces. Attention is focussed on the experimentally observed consequences of spin-orbit coupling; this interaction causes the band structures and Fermi surfaces of these metals to depend on the orientation of the magnetization vector, and it can result in the formation of “spin-hybridized” sheets of the Fermi surface. A discussion is also given of the use of the de Haas-van Alphen effect to search for changes in the ferromagnetic band splitting as a function of temperature.

The superconducting transition temperature and its high-pressure behavior of tetragonal Nb3Sn

Abstract: The superconducting transition temperatureTC of the tetragonal phase of a Nb3Sn single crystal was determined calorimetrically to be 17.78±0.02 K. It is suppressed by the application of hydrostatic pressure at a rate of −(1.40±0.05)×10−5 K bar−1. The previous observations of double superconducting transitions in Nb3Sn and other A15 compounds are discussed.

Density of states, entropy, and specific heat for dirty type II superconductors at arbitrary temperature

Abstract: Using a recent dirty-limit version of the Gor'kov theory, we calculate numerically the analytic continuation of the thermal Green's function onto the real axis. The order parameter and the magnetic field are determined self-consistently within the circular cell approximation of the vortex lattice. From the Green's functions one obtains the density of states and various thermodynamic quantities. The results are compared with experiments and an approximate theory by Takayama and Maki.

Thermoelectric power above the superconducting transition

Abstract: The thermoelectric power in the fluctuation region above the superconducting transition temperatureT c is studied theoretically. Use is made of the time-dependent Ginzburg-Landau (TDGL) equation due to Ebisawa and Fukuyama, which includes the correction term of the order ofT/μ as well, whereT is the temperature and μ is the chemical potential. It is shown that the thermoelectric power tends to zero as (T−T c ) ln [T/(T−T c )] and as (T−T c ) as the temperature approaches the transition temperatureT c for the two-dimensional and the one-dimensional systems, respectively.

Thermal conductivity of niobium in the purely superconducting and normal states

Abstract: The thermal conductivity λ of four niobium samples has been measured between 1 and 10 K, both in the superconducting and normal states. The specimens differed in their crystal defect structures due to annealing at different temperatures (dislocations, grain boundaries) and, in one case, to subsequent fast neutron irradiation (dislocation loops). A procedure has been developed with which the electron and phonon contributions to the thermal conductivity can be separated with an accuracy not hitherto obtainable. All the samples proved to have the same energy gap at 0K:δ(0)=(1.95±0.02)kT c . The phonon conductivity in the superconducting stateλ has been compared with the formula of Bardeen, Rickayzen, and Tewordt extended for scattering mechanisms other than phonon-electron interaction. For the unirradiated samples at $${\text{T}} \lesssim 0.15T_{\text{c}} $$ , λ p s is proportional toT 2, showing that dislocations are mainly responsible for the phonon scattering. The results are qualitatively in agreement with the theory of Klemens, giving a rough indication that the grain boundaries may be considered as arrays of line dislocations. Dislocation loops introduced by the neutron irradiation turn out to behave like clusters of point defects. A second consequence of the irradiation is an enhancement of the original dislocation scattering term.

Direct observations of the magnetic structure in thin films of Pb, Sn, and In

Abstract: Direct, high-resolution observations of magnetic structures in evaporated films of the type I superconductors lead, tin, and indium are presented for a range of applied fields. The films are polycrystalline and range in thickness from 200 to 20,000 A. the transition from the intermediate state to the mixed state is observed. The observation of the single-fluxoid vortex mixed state in the thin films with Ginzburg-Landau parameter κ less than\(1/\sqrt 2\) confirms theoretical prediction by Tinkham, Maki, and Lasher. No ordered array of vortices is observed and this is shown to be caused by the effects of the grain boundaries on the magnetic structures.

Superconductivity of thin Nb 3 Sn films under tensile stress

Abstract: Thin Nb3Sn films on bendable quartz substrates have been prepared by different methods. These films exhibit an initial tensile stress. Bending the samples by two methods under known conditions results in quantitative changes of tensile stress and in relative changes of the superconducting transition temperature. On the average a “tension coefficient” of about $$\Delta T_c /\Delta \sigma \approx - 5 \times 10^{ - 3} K/kp mm^{ - 2} $$ has been found for all samples. A certain influence of the preparation conditions has been observed. The results are in fairly good agreement with similar types of earlier measurements.

Critical thicknesses for the transition from intermediate- to mixed-state behavior in superconducting thin films of Pb, Sn, and In

Abstract: Recent direct observations of the magnetic structure in thin films of Pb, Sn, and In are discussed relative to resistance measurements on the same films and to earlier experimental and theoretical work on thin films. Comparison to the theoretical results of Maki and Lasher is made and it is found that these results predict reasonably accurately the critical thickness separating intermediate-and mixed-state behavior in the thin films studied. This implies that the critical thickness has been overestimated in earlier work on similar films. It is suggested that this accounts, in part, for the high values obtained for the pure, bulk Ginzburg-Landau parameter in those experiments.