Specific heat and magnetization of superconducting niobium in the mixed state

The thermodynamics of the mixed state of niobium is reconsidered. Critical fieldsH _c (t),H _c1(t),and H _c2(t), Maki parameters ₁ and ₂, magnetization, and specific heat are measured with a computer-controlled magnetometer and calorimeter. The results show quantitative discrepancies with the isotropic Gorkov-Brandt theory over almost the whole mixed state. Computations based on Fermi surface anisotropy using a scaling ofH _c2 provide a much better agreement with the experimental magnetization curves already in the limit of weak nonlocality, thus suggesting a numerical evaluation of the anisotropic terms in the Gorkov-Brandt theory.     

Rectification effect in thin-film superconductors in small,oscillatory magnetic fields

We have observed the generation of dc voltages across super conducting films of lead and tin due to the presence of a static magnetic fieldH ₀ upon which a small, oscillatory magnetic field component is superimposed. The voltages are created without an external current passing though the samples. They change sign with a reversal of the static fieldH ₀. The voltages are related to superconductivity and seem to be caused by a nonsymmetric penetration into the specimen of the magnetic field variation. During one cycle of the magnetic field oscillation a small fraction of the total flux entering and leaving the sample appears to be pumped across the specimen in a preferential direction. The thickness of the films ranged between 0.16 and 2.5 µm. The frequency and the amplitudeH ₁ of the oscillatory field was varied from 5 to 120 kHz and from 0 to 2 G rms, respectively. The rectified voltage varies between the different samples and depends uponH ₀, ,H ₁, and the orientation of the film relative to the magnetic field. It generally shows a sharp peak near the critical magnetic field. Small rectified voltages caused by the oscillatory field were observed far above the nominal, critical magnetic fields of the films. Apparently, these voltages were associated with the film edges and the enhancement of the critical field at the edges.Based on work performed under the auspices of the U.S. Atomic Energy Commission.     

The effect of neutron irradiation damage on the magnetic behavior of superconducting niobium in stationary fields

The effect of irradiation with fast neutrons (at reactor ambient temperatures up to doses of 1.5×10²⁰ n/cm²) on the magnetic behavior in stationary fields of superconducting niobium samples has been studied. Surface effects have been removed by oxidation of the samples. Irradiation leads to an increase ofH _c2, which disappears after annealing the samples at 400°C. Also, the irreversibility of the magnetization increases and a peak effect is induced in the magnetization curves. These effects, due to an increased bulk pinning, are rather small, except in the samples irradiated with the highest dose. Electron microscope pictures showed that this is due to the fact that only for the highest dose do the clusters of interstitials which are introduced in the sample by the irradiation form extended defects, with sizes larger than the coherence length ξ. A discussion is given of te surface barrier before and after irradiation, of theH _c2 shift due to the irradiation, and of the increased irreversibility of the magnetization. It turns out that nearH _c2 the irradiation damage has to be treated as line defects, rather than as point defects, whereas at lower fields neither the critical state formula of Labusch for point pinning nor that of Good and Kramer for line pinning describes the experimental results exactly, although the differences do not seem to be very dramatic. We conclude that in the lower field region a combination of point and line pinning occurs. The peak effect has been discussed in a foregoing paper.     

The effect of neutron irradiation damage on the magnetic behavior of superconducting niobium in alternating fields

Alternating field permeability experiments are reported on superconducting niobium samples irradiated with fast neutrons at reactor ambient temperatures. The results are compared with theoretical predictions derived from several critical state models. Fundamental differences are observed, even when the static magnetization curves are described quite well by the same model. This leads to the conclusion that for small periodic movements of the flux lattice the vortices are not in the critical state.Communication No. 410a from the Kamerlingh Onnes Laboratorium.Now with the Reactor Centrum Nederland, Petten, Netherlands; temporary address: Max Planck Institute für Plasmaphysik (Abt. Technik), 8046 Garching bei München, BRD.     

The mixed state of superconducting networks

The equilibrium phase of a superconducting network has been investigated below the superconducting critical temperature in the framework of the Ginzburg-Landau theory. It is found that the properties of the mixed state are entirely governed by the flux quantization effect in the loops of the array. Quantitative predictions are made for the spatial configuration of the order parameter, the supercurrents pattern, and the equilibrium magnetization in an extended square network.     

Losses in superconducting cables in pulsed magnetic fields

Measurements have been carried out of superconducting cables of different types in pulsed magnetic fields. Three types of samples have been made from multifilamentary Nb_0.5  Ti_0.5 superconductors: one, a cluster of isolated wires; two, a double-layer twisted flat cable; and three, one-layer twisted tube samples. Dependences have been studied of ac losses on the amplitude, direction and change velocity of the magnetic field as well as on the diameter of filaments and twist pitch. It is shown that the ac losses in unsoldered samples are close to those in the cluster of isolated wires.     

Resistive superconducting transition of κ-type BEDT-TTF organic superconductors in a magnetic field

The superconducting transition of the organic compoundsκ-(BEDT-TTF)₂ X is studied by resistive measurement in a magnetic field up to 10 T applied normal to the conducting plane. For the salts withX=Cu[N(CN)₂]Br andX=CuCN[N(CN)₂] the transition shows fanshaped broadening caused by superconductivity fluctuation. For theX=Cu(NCS)₂ salt the resistivity shows a peak in the transition region in a magnetic field below 4 T.This phenomenon is suppressed in defect-reduced samples for intralayer conduction. We discuss this peak in relation to the thermal fluctuation on the Josephson junction structures in this salt.     

Microwave response of superconducting thin films in magnetic fields

We calculate the complex conductivity of a superconducting thin film in a tilted magnetic field. Use is made of the time-dependent Ginzburg-Landau equations to deal with the dynamical behavior of the order parameter associated with the vortex motion in response to the microwave. The reactive part of the conductivity at zero frequency vanishes identically due to the vortex motion and the conductivity resembles that in the flux-flow regime of the type-II superconductor, unless the dc magnetic field is parallel to the film surface with high precision.     

Transverse critical fields of small superconducting elliptical cylinders

Using the Ginzburg-Landau theory the transverse critical field of small (a«₀,b»₀) cylinders of elliptical cross section has been calculated for an arbitrary angle between the field and the axes of the ellipse. The criterion for second-order phase transitions has been found. While the equations readily reduce to the case of the circular cylinder, they do not reduce to the case of the flat film. The reasons for this are discussed.Work supported by a grant from the National Science Foundation.     

Electrodynamic field equations for composite superconducting structures in the mixed state

Governing vector partial differential equations for the linear electrodynamic response of an isotropic type-II superconductor in the mixed state are derived. A continuum theory of vortex motion is used, and two-fluid effects are also accounted for. The governing equation is sufficiently general to reduce to either normal metal or dielectric material results in special limits. The complex-valued conductivity tensor of the mixed state is made explicit, and is also discussed for an anisotropic superconductor. The theory is illustrated with a planar superconducting waveguide problem, wherein the complex propagation constant, phase velocity, and surface impedance are obtained.     

Edge pinning in superconducting thin films in perpendicular magnetic fields

Two-dimensional systems of bosons and fermions are studied at zero temperature by means of variational calculations. When viewed as a function of the quantum parameter = ²/m in the variational context, bosons are found to undergo a second-order liquid-to-gas transition, whereas, contrary to expectations, fermions are found to undergo a first-order transition with a region in which liquid and gaseous phases can coexist. Although these results are qualitatively the same as those in three dimensions, it is emphasized that, for two-dimensional fermions, the underlying physics is quite different. These results are examined critically in view of the special properties of two-dimensional systems. It is found that critical values of are rigorously lower bounds, and it is further argued that the essential features of these results remain valid. Finally, the implications of these results for experiments on submonolayer physisorbed helium and spin-aligned hydrogen systems are discussed.This research was supported, in part, by the National Science Foundation under grants DMR76-14447 and DMR73-02609.This research was performed as part of the NSF Independent Research Program. However, any of the opinions expressed herein are those of the author (LHN) and do not necessarily reflect the views of the NSF.     

The performance of thin film superconducting bolometers in magnetic fields

Thin films of pure superconducting metals and alloys can be used as rapid response bolometers over a wide temperature range if a small magnetic field is applied. The characteristics of various films are discussed together with a brief consideration of methods of use.     

Resistive state and charge imbalance waves in superconducting indium bridges with large cross section

We have investigated the Josephson behavior in indium microbridges with 2 µm thickness, 5–8 µm width, and 9–21 µm length. The resistive behavior of the bridges can be described by a dynamic model consisting of an ideal Josephson oscillator emitting charge imbalance waves into the adjacent superconductor. From the analogy between the charge imbalance wave equation and the telegraph equation a useful equivalent circuit is obtained, as pointed out recently by Kadin et al. The Josephson behavior in the different regimes of amplitude and frequency of the rf current superimposed upon the dc current is discussed.     

Nuclear magnetic resonance in small superconducting particles. I

A theoretical treatment of the effects of superconducting fluctuations on nuclear spin-lattice relaxation in small particles given by imánek, Imbro, and MacLaughlin is refined, taking into account the Zeeman energy and the pairbreaking effect introduced by a magnetic field dependence of impurity vertex corrections. The dimensions of the particle are supposed to be less than the coherence length and the penetration depth, but still large enough for electronic levels to have a continuous spectrum. In this paper, spin-orbit interactions are not considered, though they have a large effect on the role of the Zeeman energy. Calculations are valid in the dirty limit and at temperatures not necessarily close to the transition temperature of the bulk superconductor. The spin susceptibility and the nuclear spin-lattice relaxation time are calculated as functions of the particle size and the field. The former turns out to be in good agreement with the theoretical results by Mühlschlegel, Scalapino, and Denton, in which energy levels are considered to be discrete. It is shown that the Zeeman energy and the pair-breaking mechanism give opposite effects on the behavior of the relaxation time at low temperatures. Recent experiments have found a characteristic field dependence of the relaxation time, which is reproduced fairly well by the present calculations.     

Nuclear magnetic resonance in small superconducting particles. II

The effects of superconducting fluctuations are investigated in a small metallic particle with spin-orbit scattering at the surface and impurity sites. The spin susceptibility and the nuclear spin relaxation time are calculated, using the Green's function method developed in a preceding paper. At low temperatures the spin susceptibility takes a value closer to that of Pauli paramagnetism than in the case without spin-orbit scattering. The effect of the Zeeman energy on the relaxation time is reduced. It decreases the enhancement of the relaxation time. These results are in good agreement with NMR experiments for tin particles.     

Flux flow in type II superconducting wires in longitudinal magnetic fields

The resistive behavior of a type II superconducting wire in the presence of a longitudinal applied magnetic field is studied. The experimental data obtained are compared with the predictions of a phenomenological model based on viscous flux flow. For appropriate surface conditions the model is in satisfactory qualitative agreement with observations. The problems involved in obtaining a numerical value for the flux flow resistivity from longitudinal field I–V data are discussed. Estimates of the flux flow resistivity are made and are shown to be in order-of-magnitude agreement with accepted values.     

Effective microwave surface impedance of superconducting films inthe mixed state

The effective microwave surface impedance of multilayer structures made of high-T_c superconducting films in the mixed state, lossy dielectrics, and normal metals are theoretically calculated. The linear response of the superconductor to a microwave field is analyzed within both transmission line theory and the framework of a self-consistent treatment of vortex dynamics reported by Coffey and Clem (1991). The microwave properties are investigated as a function of static field and film thickness for nonresonant structures. The effect of substrate thickness on the resonant phenomenon is carefully studied as well. Numerical results reveal that the substrate resonance in the Meissner state behaves like a parallel lumped-parameter resonator, while in the vortex state it behaves as a series lumped resonant circuit. The basic distinction suggests that care should be taken in microwave applications when using superconducting films in the vortex state     

超导强磁场诱导织构技术在功能材料制备中的应用

超导强磁场能够诱导磁各向异性材料形成织构组织,显著改变材料的组织和性能,已经成为功能材料制备的一个重要手段.本文探讨磁场诱导磁各向异性材料形成织构组织的机制,综述强磁场诱导织构组织的研究现状,并展望这项技术在功能材料制备中的应用前景.     

Resistive behavior of the superconducting surface sheath of alloys

Measurements are reported of the surface resistance of dirty type-II superconductors driven into the surface-sheath regime by a static magnetic field,H ₀ parallel or nearly parallel to the sample surfaces and transverse to the microwave current, in which condition the latter can excite fluctuations of the order parameter. A recent calculation by Maki has suggested that the surface resistance would be influenced by the presence of Kulik's vortex state even when the sample surface is polished and is as nearly as possible parallel toH ₀. It is therefore proposed that the sample surface should be decomposed into elements which make different angles withH ₀, and the distribution of these angles described by a Gaussian. ₂ (t) is deduced from the surface-resistance measurements nearH _c3, so interpreted, and a temperature variation, ₂ (t)/₂(1), is found which agrees reasonably with theory and with magnetization data, [₂(1)=lim_{t 1} (₂)]. It is suggested that the anomalously large variation of ₂ (t) reported by Fischer and Maki may have resulted from failure to take Kulik's vortices into account. In magnitude, present ₂(1) data agree with theory but not with magnetization data.