Showing papers in "Journal of Low Temperature Physics in 1971"

Nonlinear waves in the pitaevskii--gross equation.

Abstract: Nonlinear waves, solitary and periodic, are studied exactly in the Pitaevskii-Gross equation for the wave function of the condensate of a superfluid. We also study the relationship between these two waves and Bogoliubov's phonon, and the energies associated with these waves. The creation energy of a solitary wave with amplitudeA is proportional toA3/2. Solitary waves show interesting behavior on their collision due to their localized character. The effect of collision on solitary waves can be described by the phase shift. We give a formula of the phase shift on a collision of two solitary waves. We further discuss the decay of an arbitrary initial disturbance into solitary waves.

Pressure-volume-temperature relations in liquid and solid 3 He

Abstract: Liquid and solid3He P-V-T relations were measured over 026–18 K with concentration on regions near the melting curve The method used a cell whose volume was varied with diaphragms, the positions of which determined the volume and pressure The molar volumes of liquidV lm and solidV sm along the melting curve were consistent with the directly measured volume change on melting ΔV m Below 1 K,V lm , Vsm, and ΔV m were greater than previous results Along the melting curve, the compressibility of the solid became greater than the compressibility of the liquid atT<12 K, the difference rising to 12% at 032 K The thermal expansion of the solid became negative below 030–035 K The melting curve minimum was measured at 28932±0003 atm and 0319±0003 K Starting with the minimum, the melting curve was calculated to 002 K, where it should be useful in thermometry A set of self-consistent data is presented

Magnetic behavior of dilute Cu(Mn) alloys at very low temperatures

Abstract: The static magnetization of dilute Cu(Mn) alloys with Mn concentrations between 4.2 and 106 ppm has been measured between 10 mK and 0.4 K in fields between 1 and 200 Oe. Magnetic ordering is observed and attributed to impurity-impurity interactions. However, a concentration-independent Weiss constant and a decreasing moment per impurity in the low-field, low-temperature limit are evidence for the increasing importance of single-impurity effects with characteristic temperatureT k ∼ 2 mK.

Patterns of magnetic flux penetration in superconducting films

Abstract: Intermediate-state magnetic flux patterns have been observed in thin superconducting films of tin, lead, and indium in perpendicular applied fields of 0.1–100 Oe. The spatial variation in flux density was measured very close to the film with a high-resolution Hall probe which could be scanned in a plane parallel to the surface of the film. The patterns appear to contain both laminar and round normal regions, with the latter predominant. A model for the intermediate state has been developed in which the normal regions are macroscopic flux spots. Experimental results for the number density of these flux spots in 1.1–6.3-μ-thick indium samples are in good agreement with the temperature, field, and thickness dependences of our model; indium samples thinner than 1 µ appear to enter the mixed state. In tin and lead, however, the flux patterns are strongly influenced by flux pinning. Appearance of the flux pattern at the critical field or temperature has been observed and correlated with distinctive features in the resistive transition. The extent of flux penetration into the sample was determined from measurement of the average field and compared for various field-temperature paths to the intermediate state. With the applied field reduced to zero, the magnetic field outside a current-carrying superconducting strip has been measured and indicates that the current distribution within the strip is consistent with the form predicted by Bowers.

Principles and methods of dilution refrigeration. II

Abstract: This paper is an extension of, and complementary to, an earlier paper by Wheatley, Vilches, and Abel. Some important fundamental questions which lead to degradation in the performance of a dilution refrigerator are considered: namely, convection on the dilute side and superfluid on the concentrated side. Experimental results are presented for a film suppressing still used in conjunction with a continuous-heat exchanger (several designs are considered) and a variable number (0–6) of step-heat exchangers of a copper-foil type with a high surface-area-to-viscous-impedance ratio. The first quantitative measurements of viscous heating on the dilute side are presented as well as measurements of thermal resistance on the dilute and concentrated side. Finally, the properties of the refrigerator under external heat load are considered.

Dynamical impurity spin susceptibility in metals

Abstract: The longitudinal and transverse impurity spin susceptibilities are expressed exactly in terms of holomorphic self-energies. Within thes-d model these self-energies are calculated in lowest order perturbation theory thus yielding reasonable approximations for the susceptibilities valid for all temperatures and magnetic fields above the Kondo regime and in the whole frequency domain including the hydrodynamical one. The transverse susceptibility and the longitudinal nuclear spin susceptibility are found to be satisfactorily described by Bloch's equations. In the low-temperature regime the longitudinal relaxation timeT1 exhibits a nontrivial spin and temperature dependence. At low temperatures and high fields the longitudinal localized electron spin susceptibility is found to show a non-Lorentzian double-peak line shape which cannot be described by Bloch's equations.

Some properties of gapless semiconductors of the second kind

Abstract: The authors investigate the physical properties of gapless semiconductors of the second kind, i.e., substances in which the conduction band is in direct contact with the valence band and the energy exhibits a square-law dependence on the momentum in the vicinity of the contact point in all branches of the spectrum in the one-electron approximation. The methods normally applied to strong-coupling field theories (“scaling”) are used to analyze the singular energy-momentum domain in which the Coulomb carrier interaction becomes strong and intractable by perturbation theory. The surface impedance, conductivity, susceptibility in weak and strong fields, and the Hall coefficient are calculated. Some possible experimental approaches are explored.

Electron tunneling into disordered thin films

Abstract: Disordered and recrystallized thin films of Sn, Pb, Bi, and $$Bi_{1 - x} Sb_x $$ both normal and superconducting are investigated by electron tunneling. The films are prepared by evaporation onto a cooled substrate. We studied especially the effect of lattice disorder on the superconducting parameters and on the phonon spectrum which is calculated from the superconducting-electron density of states. The most significant property of the disordered films is an increase of the low-energy-phonon density of states. Anomalies of the tunneling resistance are more or less observed in all junctions. The influence of those anomalies on the evaluation of the superconducting parameters is considered.

Superconductivity, density-of-states models, and specific heat of A15-type compounds V--Ga and V--Si

Abstract: Accurate low-temperature specific heat measurements, together with structural investigations, have been performed in V-Ga alloys with 18–32% Ga and V-Si alloys with 20–27% Si. Calculations of the temperature dependence of the normal electronic specific heat are presented for different band models. The comparison with experiment suggests that very low degeneracy temperatures are indeed characteristic of both V3Ga and V3Si.

On the theory of superconductors containing magnetic impurities: Crystalline field effects

Abstract: We extend to finite concentrations a previous calculation of crystalline field effects in superconductors containing rare-earth impurities. The computations, which have to be done numerically, apply to non-Kramers ions as well as Kramers ions. A comparison between theory and available experimental data is made.

Fluctuations in the resistive transition in aluminum films

Abstract: The excess conductivity due to the thermodynamic fluctuations in aluminum films is experimentally investigated. The excess conductivity is described by the sum of the Aslamazov-Larkin and the Maki-Thompson terms. An empirical formula is found on the relation between the pair-breaking parameter δ(0) in the absence of the magnetic field and the normal-state film resistanceR N sq as δ(0)=6×10−4R N sq . This formula might be explained in terms of the localized moments and the proximity effect in films. The result of the magnetic field dependence of the pair-breaking parameter revealed that δ(0) cannot be described by an effective magnetic field. The temperature dependence of the excess conductivity at higher temperatures systematically deviates from the theoretical values due to the breakdown of the mean-field theory.

Negative self-inductance in superconducting thin wires and weak links

Abstract: One of the most promising implications of the phenomenological Ginzburg—Landau (GL) theory of superconductivity is the possible existence of current-carrying metastable states with a negative effective self-inductance. Microscopically this phenomenon can be explained as a result of the depairing mechanism which, when the center-of-mass velocityvs of the Cooper pairs is sufficiently large, can be so strong that a further increase ofvs will lead to a decrease of the total current. Using a one-dimensional formulation of the GL theory we investigate the thermodynamic stability of these states for different external constraints and obtain the result that a negative self-inductance can only be stable if the length of the system in the direction of the current is smaller than a critical value comparable to the GL coherence length λ/κ. It is an experimental fact that states of negative self-inductance are realized in Josephson junctions and other types of superconducting weak links because the dc supercurrent can be a decreasing function of the phase variable φ. The thermodynamic stability theory can therefore explain why weak links have to be short, and it also provides us with a unifying point of view by treating the phase φ and the current as a pair of thermodynamically conjugate variables for arbitrary one-dimensional systems. An important point is the operational phase definition as a thermodynamic parameter that can be controlled by the experimentalist. This requirement is essential for the general validity of the ac Josephson equation and it implies that φ must depend on the magnetic self-inductance of the system. By applying the GL theory to weak links we can delimit the validity of the usual dc Josephson equationI ∝ sin φ and see that deviations from this functional form are most likely to be found in thin-film bridges of the Anderson-Dayem (AD) type. When the currentI is the controlled variable the conjugate phase variable φ will fluctuate and the magnitude of these fluctuations depends strongly on the functional formI(φ). The phase fluctuations for constantI lead to a reduction of the critical current which will be absent when φ is the controlled variable. The observed microwave enhancement of the critical current in AD bridges, the so-called Dayem effect, can be explained as a result of a switch from current control to phase control, and the fluctuation formulae explain why the effect is negligible in structures exhibiting the classical Josephson sine law for the current-phase relation.

Thermal resistance between powdered cerium magnesium nitrate and liquid helium at very low temperatures

Abstract: Experiments have been performed from magnetic temperatures of 2–20 mK on the effect of minute4He impurities and a magnetic field on the thermal resistance between powdered cerium magnesium nitrate (CMN) and liquid3He. The thermal resistance decreases with decreasingT and increasing small field but is increased dramatically at a givenT by the addition of roughly a monolayer of4He. The resistance is interpreted as resulting from a surface magnetic coupling between CMN and liquid3He.

The superconductivity and magnetic susceptibility of some zirconium-transition-metal compounds; evidence for an anticorrelation

Abstract: The properties of the superconducting transition temperatureT cof the CuAl 2 -type compounds of Zr 2 Co, Zr 2 Ni, Zr 2 Rh, Zr 2 Fe, and Zr 2 Ir are discussed with respect to effects due to alloying and heat treatment. Dilute pseudobinary alloys of transition-metal elements with Zr 2 Rh (T c=11.3 K) produced lower transition temperatures suggesting that the valence-electron concentration of 5.67 electrons/atom gives a maximum inT c for this crystal type. Results for Zr 2 Co (T c=5.0 K) and Zr 2 Ir (T c=7.3 K) show that their transition temperatures are raised somewhat when the electron concentration is increased by alloying. A peak is seen near 5.72 electrons/atom. A peak in the room-temperature magnetic susceptibility in the Zr 2 Co-Zr 2 Ni system occurs near the same electron concentration as the peak inT c. Similar susceptibility behavior takes place in the Zr 2 Rh-Zr 2 Ni system, however, with no peak inT c. Results of susceptibility measurements on Zr 2 Ir and its isomorphic alloys indicate correlation betweenT c and susceptibility. An anticorrelation occurs for Zr 2 Co alloys suggesting the presence of Coulomb interactions. A sharp symmetric drop inT c near the stoichiometric composition as well as a marked decrease of the transition temperature with a low-temperature (600 C) anneal indicate that the coulomb interactions are sensitive to crystalline order. The lattice parameters of Zr 2 Ir are reported as a=6.508 A andc=5.721 A. The superconductivity of Zr 3 Co (T c=3.9 K) and Zr 3 Ir (T c=2.13 K) is reported.

Experimental determination of the molar volume and derivation of the expansion coefficient, entropy change on compression, compressibility, and first-sound velocity for liquid 3 He from 35 to 1200 mK and from the saturation pressure to 24 atm

Abstract: The molar volume of liquid3He,V(P, T), was determined from measurements of the dielectric constant over the temperature range 35–1200 mK and from the vapor pressure to 24 atm. Analytical expressions were fitted to the molar volumes in order to calculate the isobaric expansion coefficient αP, the isothermal compressibility κK T, and the first-sound velocityc 1; the expansion coefficient was integrated numerically to arrive at the entropy change on compression. Values ofV(P, T) and the derived quantities are presented in tabular form at even temperatures and pressures. From this work it was found thatV(0, 0)=36.873±0.015 cm3/mole and thatc 1(0, 0)=178.4 m/sec, about 2.5% lower than the presently accepted value of 183.4 m/sec.

Cluster specific heats in copper-rich Cu-Ni alloys: The effect of iron

Abstract: The specific heats of three Cu-Ni and two Cu-Ni-Fe samples have been measured in the range 0.4–6 K at compositions in the range 20–43% Ni and ∼0–0.2% Fe. The results are described in terms of a Schottky function from which the number of levels and the cluster concentration are determined for each composition. Addition of iron to the 20%-Ni sample results in ∼1/2 cluster per Fe atom added. The specific heat increases in a magnetic field (known for one sample), which is compatible with the Schottky-like function description of the anomalous term in the specific heat, but is incompatible with the Einstein function description. Another possible interpretation of the observed specific heat anomalies is given in terms of an intercluster cooperative phenomenon.

Calculations of van der Waals forces across films of liquid helium using Lifshitz theory

Abstract: Lifshitz theory of van der Waals forces is used to calculate film heights and third-sound velocities for films of liquid helium on substrates of BaF2 and CaF2. The calculated film heights are in excellent agreement with the experimental values of Anderson and Sabinsky for film thicknesses ≳50 A. At smaller distances, despite unavoidable theoretical uncertainties due to incomplete dielectric data, comparison of theory with experiment indicates that any “dense” layer adjacent to the substrate has an effective thickness of less than a single atomic layer.

Intermediate state of thin superconductors.

Abstract: The purpose of this study was to examine the state of a thin type-I superconductor in a magnetic field to determine its dependence on the specimen thickness and on the value of the Ginzburg-Landau parameter κ. Three materials (aluminum, indium, and In0.99Pb0.01) with values of the Ginzburg-Landau parameter ranging from 0.19 to 0.34 were studied. Specimen thicknesses ranged from 200 to 200,000 A. All of the materials studied were type-I or nonlocal superconductors in the bulk. Yet, it has been predicted that they would behave in ways characteristic of type-II or local superconductors if the specimen were sufficiently thin. For intermediate thicknesses the specimens were expected to be in one of many possible states. We have inferred from critical field studies that the structure of the intermediate state in thin type-I superconductors is equivalent to the type-II vortex state for very thin films (d ≪ ξ0), and to the type-I macroscopic domain state for very thick films d ≳ 2ξ(t). For thicknesses between these limits the intermediate-state structure takes on many forms as the area of each normal domain and the amount of flux threading it increases with increasing thickness.

Kondo effect in single crystals of dilute Y-Ce alloys

Abstract: The magnetic susceptibility and electrical resistivity of Ce impurities in single crystals of Y-Ce alloys were measured at temperatures down to 1.5 K in the directions parallel and perpendicular to thec axis of the crystal. The experimental results were interpreted in terms of the Kondo effect and the crystal-field effect. The data show that the crystal field of Y splits the2 F 5/2 ground state of the Ce 3+ ion into three doublets, the lowest doublet specified byj z =±1/2. The susceptibility, resistivity, and specific heat results at low temperatures show evidence for the existence of a bound state due to the anisotropic Kondo interaction. Analysis of the low-temperature resistivity data yields a Kondo temperature of 40 K, which is independent of the current direction and the Ce concentration. The susceptibility and the resistivity at 0 K are nearly isotropic.

Critical magnetic fields of a Kondo superconductor: ZnMn

Abstract: The superconducting critical fields of pure Zn and of a series ofZnMn alloys have been measured as a function of temperatureT down to 0.06 K. The critical fields have been used to calculate the entropy difference between the normal and superconducting states. For all the alloys studied, the entropy in the superconducting state is proportional toT asT → 0, indicating a finite density of states at the Fermi energy. We interpret this result as evidence for the existence of localized bound states within the energy gap centered at the Mn impurities. Results obtained for the depression ofTc, for the critical field atT=0, for the jump in specific heat atTc, and for the law of corresponding states are also presented and compared with the predictions of the Abrikosov-Gor'kov theory. A simple expression relating the critical fields of these alloys to the Mn concentration has been found to be in very good agreement with experiment.

Superconducting beryllium films.

Abstract: Resistance-vs.-temperature measurements were made on a series of beryllium films condensed on liquid-helium cooled surfaces. Two vapor sources designed to reduce contamination were used and films were prepared on both crystalline quartz and glass substrates. The samples were superconducting with a transition temperature ofT c =9.6±0.1 K as indicated by a sharp falloff of resistance on cooling. This qualitatively confirms earlier reports of the superconductivity of quenched beryllium films. The transition curves were, however, appreciably sharper and the transition temperature about a degree higher than previously reported. Good agreement found from sample to sample indicates that the residual impurity concentration was small enough to be unimportant and that the observed transition temperature is characteristic of pure beryllium. The phase of beryllium responsible for the highT c value disappeared on annealing in the range 40–60 K. No indication was found of a reportedT c ≈6-K phase. Beryllium films thicker than about 750 A broke up during deposition, indicating the presence of large stresses.

Heat capacity of helium submonolayers on a nonuniform surface

Abstract: Data of McCormick, Goodstein, and Dash, and Stewart and Dash, for heat capacities of3He and4He films on Ar-plated copper in the submonolayer region have been analyzed on the basis of a model of a long-range variation of adsorption potential. This variation allows the adatoms to form small islands on the surface. The total heat capacity of the film is the sum of two contributions, one a Fermi-like contribution due to surface heterogeneity, and the other a two-dimensional Debye-like contribution due to molecular vibrations. The data are roughly consistent with a Debye temperature of 32K for all the4He data and 38 K for the3He data. The role of surface heterogeneity in the heat capacity of films is briefly discussed.

The coefficient of self-diffusion of liquid neon

Abstract: The coefficient of self-diffusion of liquid neon is measured by means of the capillary method within the temperature range of 25–43 K and in the pressure range of 10–100 atm A natural neon-isotope mixture with 91%22Ne and a mixture enriched to 99%22Ne were available for the measurements The measured runs show in the representation log D=f(1/T) and logD=f(p), respectively, straight lines in good approximation

The Kondo effect inZnMn

Abstract: The magnetic susceptibility of Zn alloys containing 7.6–182 ppm Mn were measured in the range 1.4–4.2 K. The zero-field susceptibility can be described by a Curie-Weiss law with a concentration-independent intercept on the temperature axis, which yields a Kondo temperatureT K =0.24 K. A value for the effective number of Bohr magnetons on a Mn atom ofp=4.66 is found. Resistivity was measured on specimens containing 7.8–38 ppm Mn in the range 0.1–4.2 K. The resistivity of all specimens was proportional to logT at high temperatures but, except for the lowest concentration specimen, it showed evidence of ordering below 0.5 K. The data for the 7.8-ppm Mn specimen showed no evidence of ordering down to 0.1 K, and could be fitted to the formula of Hamann. Allowing for potential scattering, the resistivity at 0 K is found to be 45 µΘ · cm/at. % Mn. This value is in agreement withd-wave unitarity limit when corrected for the appreciable deviation of the Fermi surface in zinc from a free-electron sphere.

The adiabatic approximation and Fröhlich model in the theory of metals

Abstract: Based on the adiabatic expansion for metals, a method is developed whereby it is possible to compute the nonadiabatic corrections to the energy of any order by standard perturbation theory and diagram techniques. It turns out that in addition to the Frohlich one-phonon Hamiltonian the many-phonon Hamiltonians also play a significant role in the theory of metals. Inasmuch as the ground state of the system corresponds to adiabatic perturbation theory, the largest correction to the energy and phonon frequency is of the order(m/M) 1/2, as opposed to the results deduced from the Frohlich Hamiltonian. The expression for the ordinary self-energy contribution differs substantially from its expression in the Frohlich model, and the equation for the pairing self-energy contribution coincides up to terms of order(m/M) 1/2 with the corresponding equation in the Frohlich model. The expression for the critical temperature is discussed.

Dynamical fluctuation of the order parameter and diamagnetism of superconductors. I. Dirty limit

Abstract: Limiting ourselves to dirty superconductors, we study theoretically the fluctuation-induced diamagnetism above the superconducting transition We find that the dynamical fluctuation is extremely important except in the immediate vicinity of the transition region [ie,T℞T c(H) orH℞H c2(T), whereH c2 is the upper critical field] and that this contribution does account for a large discrepancy between previous calculations and the recent experiment by Gollub, Beasley, and Tinkham

Heat capacities of Ar, Ne, 4 He-Ar, and 4 He-Ne films adsorbed on Cu at low temperatures

Abstract: Heat capacities of Ar and Ne monolayers adsorbed on Cu are measurable at 1–4 K. Temperature dependences are similar to the low-temperature law for harmonic oscillators, but the empirical characteristic temperatures of 11–15 K are much lower than can correspond to independent adatoms oscillating in substrate sites. The magnitudes and temperature dependences do not match those predicted for surface modes of an absorbent coated with inert impurities or for the collective modes of epitaxial films. A model involving the excitations in non-epitaxial films appears to offer an explanation of the observed magnitudes and temperature dependences. The heat capacities of4He adsorbed on preplated Ar or Ne show little variation with the number of Ar layers, or between Ar and Ne coatings.

Magnetic impurity pairs in dilute Cu(Fe) alloys at very low temperatures

Abstract: The temperature-dependent static magnetization of several dilute Cu(Fe) alloys with Fe concentrations between 102 and 478 ppm has been measured in fields between 1 and 200 Oe and at temperatures between 9 mK and 0.4 K. At higher temperatures and in small fields, the magnetization displays the following concentration, field, and temperature dependences:M ∝ c 2 HT −2/3. At lower temperatures, magnetic ordering is observed. These results are interpreted in terms of the behavior of pairs of impurities acting as individual entities. They are quite likely correlated with the anomalous low field, low-temperature observations made in previous measurements of the resistivity and specific heat of the Cu(Fe) system.

54 Mn in Fe for ultralow temperature thermometry

Abstract: Experimental investigations into the accuracy of nuclear orientation thermometry are reported.54Mn in iron, a primary thermometer useful from 2–40 mK, gives consistent thermometry using both scintillation (3×3 in.-NaI) and solid-state (40-cc-Ge) detectors.60Co-in-iron temperatures are consistent with the54Mn temperatures above 10 mK, but are about 10% higher at 4 mK.125Sb in iron registers a temperature that is perhaps 2 or 3% lower over the 4–15 mK region. Some of the techniques required for the utilization of this type of thermometry are discussed.

The Hall coefficient of Pd and some β-phase PdH alloys

Abstract: Measurements of the Hall coefficient have been made, from 4.2 to 220 K, for Pd and some β-phase PdH alloys. The results for Pd have a temperature dependence of a form which is given quite well by the model of Kimura and Shimizu. The results for the alloys show an anomaly at 50 K, and a time dependence below this temperature, which is similar to that shown by the electrical resistivity.