Interaction of flux tubes in a type I superconductor

The repulsive interaction between multiquantum flux tubes in type I superconducting lead films has been studied magnetooptically. Two or three flux tubes were trapped in a long and narrow region of slightly reduced film thickness, and the flux tube positions were recorded as a function of an applied Lorentz force pressing the tubes against each other. At distances larger than about the flux tube diameter our results agree well with the magnetic monopole model, which only takes into account the magnetic stray field outside the superconducting film. At smaller distances deviations from the monopole model occur due to the influence of the cross-sectional shape of the flux tubes and of the wall of the tubes upon the energy of the flux tube configuration. These influences have been taken into account by means of a subdivision model in which the flux-containing region of each tube is divided into a large number of flux portions each of which is approximated again by a magnetic monopole. For sufficiently high compression due to the Lorentz force, we have observed fusion of two individual flux tubes. Upon reduction of the Lorentz force, the fused flux tubes separate again. The process of fusion and separation shows distinct hysteresis. This behavior is also well explained by our subdivision model.     

Model calculations of the time-dependent flux-flow voltage in a thin-film type I superconductor

The temporal structure of the flux-flow voltage is calculated in the current-induced dissipative state of a thin-film type I superconductor. The instantaneous voltage generated by multiquantum flux tubes moving through a superconducting specimen depends upon both the instantaneous velocity and a geometry-dependent function of the position of the flux tube relative to the measuring circuit. The flux-tube velocity is strongly affected by the transport-current distribution, by the short-range edge-pinning effect, and by the repulsive interaction of simultaneously moving flux tubes. For a measuring circuit with leads kept far from the specimen surface, both nonuniform contributions due to the flux-flow velocity and the geometry-dependent function simultaneously cause the instantaneous voltage to peak when flux tubes nucleate and annihilate at the sample edges. Our model calculations reproduce reasonably well the experimental results obtained from signal averaging measurements.     

Distribution of pinning forces on trapped flux in a type I superconductor

The distribution density of the strength of pinning sites is investigated in superconducting lead films by counting the number of trapped flux tubes as a function of a monotonically increasing applied transport current. The flux tubes contain 100–200 flux quanta and are detected by high-resolution magnetooptics. Experiments were performed with Pb films containing only natural pinning sites and in samples containing artificial pinning centers in the form of small circular pits etched into the film surface. A detailed theoretical discussion is given of the various forces acting upon a pinned array of flux tubes. If edge pinning is dominant, the critical Lorentz force inducing steady-state flux flow is much larger than the force required for removing trapped flux tubes from the sample. This can be understood from the spatial dependence of the Gibbs free energy of the flux tubes near the sample edges.Supported by a grant from the Deutsche Forschungsgemeinschaft.Operated for the U.S. Department of Energy by Iowa State University under contract No. W-7405-Eng-82. This research was supported by the Director for Energy Research, Office of Basic Energy Sciences, WPAS-KC-02-02-03, and by the NATO Research Grants Program.     

Dynamic resistance in a type I superconductor

A linear response theory approach is proposed to calculate the dynamic resistance of a type I superconductor in the intermediate state. The approach is introduced by solving the case of a long, straight wire using a generalized London model; results are presented for that case.     

Curved flux line near the edge of a type II superconductor

Applying the London theory, we show that the energy due to the interaction between the ends of the flux lines near their outlet points on the surface of a type II superconductor may be neglected. The interaction of a straight or curved flux line with the edge of a superconductor is considered. At the edge of the sample the surface barrier opposing the entry of the vortices has a value lower than that at the planar surface. The energy barrier is maximum for a planar surface, whereas it is zero at the edge of a superconductor with two perpendicular surfaces.     

Observation of magnetic flux frozen in high conductivity metal during flux jumping in a type II superconductor

In the concentric arrangement of a superconducting tube and a high-conductivity aluminium cylinder, the magnetic flux variation arising from flux jumps occurred only within the superconducting tube itself, whereas the magnetic flux in the normal metal was almost completely frozen during the flux jumps. Provided that the magnetic flux was completely frozen in the normal metal, the energy released by a flux jump was calculated to be equal to a quarter that released by a complete flux jump. It was found that the magnetic diffusion time-constant was much larger than that given by $\text{L}{}^2\text{π}{}^2\text{D}{}_{\mathrm{m}}$.     

Interaction between a ferromagnet and a high-temperature superconductor at the interface in thin-film heterostructures

The development of high-temperature superconductor (HTSC)/ferromagnet thin-film heterostructures is a promising direction in their application to spin-wave electronics. The state of the HTSC-ferromagnet interface determines the nature of the propagation of the surface magnetostatic waves in the heterostructure. The formation of the HTSC films in the heterostructures involves thermal treatment at high temperatures, which results in the diffusion interaction of the HTSC films and the ferromagnet. The heterostructure consists of a YBa₂Cu₃O_7−x HTSC film deposited by pyrolysis on an Y₃Fe₅O₁₂ ferromagnetic film grown epitaxially on a (111)-oriented gadolinum-gallium garnet Gd₃Ga₅O₁₂ substrate. The interdiffusion is studied from the intensity distribution curves of the x rays of iron (Fe), barium (Ba), copper (Cu), and silver (Ag), the last introduced into the HTSC in the amounts of 5–50 wt.%. The thin-film heterostructures are studied in the microwave range. A correlation is found between the state of the interface and the microwave characteristics. Pis’ma Zh. Tekh. Fiz. 23, 69–73 (June 26, 1997)     

Magnetic flux relaxation in a pulse-magnetized Y-Ba-Cu-O superconductor

Trapped flux relaxation at the center of a single-domain Y-Ba-Cu-O superconductor upon pulsed field magnetization has been studied at T = 78 K. In the case of a weakly magnetized sample, the induction increases according to a logarithmic law and the creep rate (defined as S = −dlnB/dlnt) is negative. As the amplitude H _a of the magnetizing field grows, the creep rate decreases, changes sign, passes through a maximum, and tends to zero. The nonmonotonic behavior of S(H _a ) is explained by a nonuniform radial distribution of the temperature during the magnetization pulse.     

Josephson behavior in large-cross-section bridges of type I superconductor

Current-induced breakdown of superconductivity has been investigated in superconducting indium bridges with large cross section (thickness 2 µm; width 15–200 µm) and 4–20 µm length. Under rf radiation, Josephson steps in the voltage-current characteristics have been observed in all In bridges less than about 80 µm wide. A model for explaining our results must combine the current-induced nucleation of trains of flux tubes, containing many flux quanta, with a single-quantum relaxation process. We propose a model according to which the nucleation of the flux tubes near the sample edge proceeds via single flux quanta. We have studied the variation of the amplitude of the Josephson steps with rf power, and reasonable agreement with the Bessel function behavior expected from the simple voltage-source model of a superconducting weak link has been found in some cases.Supported by a grant from the Deutsche Forschungsgemeinschaft.     

Study of dissipative intermediate state of a reentrant thin-film superconductor

We analyse the current-voltage (I–V) characteristics of a thin-film sample of the ferromagnetic superconductor ErRh₄B₄ within a simple heating approximation. The results demonstrate that the salient features of the experimental nonlinearI–V characteristics observed in the dissipative intermediate resistance state can be readily understood within the framework of this approximation. The magnitude of the thermal boundary conductance of the interface between the film and its thermal environment is found to be typically of the same order as that generally observed during Kapitza-like heat transfer between solids, suggesting that the strength of the thermal coupling of the film to the substrate dominates the electrical behavior of a reentrant thin-film superconductor.     

Flux nucleation in the current-induced resistive state of a constricted type I superconductor

The current-induced resistive state in a constricted type I superconductor is characterized by a train of flux tubes traversing the sample perpendicular to the direction of the applied current following its nucleation at the sample edge. The temporal structure of the nucleation process can be investigated by attempting to synchronize this process with small periodic current pulses superimposed on the direct bias current. The resistive dc voltage is then to be measured as a function of the pulse parameters such as frequency and width. We have performed such experiments at 4.2 K on constricted Pb films of 6–8 m thickness and 100 m width. Simultaneously with the electrical measurements the dynamic behavior of the flux tubes was directly observed using a stroboscopic magnetooptical method for magnetic flux detection. Our electrical measurements clearly show how the size of the nucleated flux tubes varies with the direct bias current and the nucleation frequency. The positive wall energy in the Pb films results in a lower limit for this size as expected. The influence of the preceding flux tubes still existing within the constriction upon the flux nucleation process is revealed in detail. All observations can be understood from a consideration of the energy balance during the flux nucleation process.Supported by a grant of the Deutsche Forschungsgemeinschaft.     

Model calculations of flux-tube nucleation in thin-film type I superconductors

In the current-induced resistive state, multiquantum flux tubes are nucleated at the edge of thin-film strips of type I superconductors. The nucleation process can be theoretically described by an extended Gibbs free-energy barrier model. Within this model the size of the nucleated flux tubes is obtained by minimizing the total energy of the flux tube. The dependence of the flux-tube size on the nucleation rate and the transport current is calculated including the influence of the preceding flux tubes and the positive domain wall energy of type I superconductors. The interaction with the preceding flux tubes generates a steplike decrease of the flux-tube size with increasing nucleation frequency, whereas the wall energy establishes a minimum value of the flux-tube size. These calculations are in good agreement with recent experiments on the nucleation process of multiquantum flux tubes.Financial support provided by the Deutsche Forschungsgemeinschaft.     

Creation of the two-dimensional mixed state and its motion in a type I superconductor

An experimental study of the statics of the two-dimensional mixed state in hollow lead wires is presented. The results confirm the theoretical predictions of a model given in a previous paper and are similar to the measurements already reported on tin specimens. By introducing an axial current-carrying wire into the hole of the tin samples, it was possible to also investigate the motion of this state when it undergoes a displacement from the external surface to the interior. A theoretical model is proposed that agrees well with the experimental results and establishes the conditions required to reach the stationary situation.     

Flux-flow instability in a type II superconductor

The stability of the flux-flow state in a superconducting slab is studied. The flux-flow kinematics is based on the Boltzmann equation. To investigate the interaction between the flux lines, the relaxation function is derived. The instability of the flux-flow state is associated with the growth of the autocorrelation function at the characteristic frequency of the flux-line collective mode. Thus the upper critical current value is obtained.     

Model pinning centers and spatial distribution of the Lorentz force in a type I superconductor

Flux tubes which are pinned at well-defined pinning sites in a type I superconductor can be used as a microprobe for the local force at the location of the pinning center. The method requires a measurement of the driving force which just cancels the well-known pinning force of a particular pinning site. Such information can easily be obtained using the high-resolution magnetooptical technique for magnetic flux detection. We report on measurements performed at 4.2 K with superconducting lead films of 6 m thickness. Well-defined pinning sites could be realized in the form of small circular indentations (diameter 3 m; depth 0.2 m) etched into the surface of the Pb films. By a suitable geometric arrangement of the pinning sites the dependence of the driving force upon the sample coordinate can be studied. As an example, we have investigated the spatial dependence of the Lorentz force in a current-carrying strip. Our results agree reasonably with the existing models for the various forces acting upon a flux tube.Supported by a grant from the Deutsche Forschungsgemeinschaft.     

Hysteresis in the flux flow characteristics of a type II superconductor associated with the presence of normal metal precipitates

Unusual history-dependent flux flow properties are observed in a Pb_0.871Sn_0.129 alloy as tin precipitates from solution at room temperature. We find that the critical currents and flux flow curves depend upon the field history, the current history, and the orientational history of the sample. Two volume pinning force curves are observed with different force magnitudes and field locations of the force peak, depending upon whether the field is cycled to high fields or zero field before the force is measured. Flux flow noise measurements in these samples yield very low noise, consistent with our recent model, which predicts low noise in samples with closely spaced pinning centers that interrupt the flux motion. The experimental results are explained in terms of the formation of a nonequilibrium flux line lattice in the presence of precipitates, and the response of such a lattice to current, field, and orientational changes.Research Supported by U.S. ERDA Grant No. EY-76-S-02-2890. Items of equipment used in this work were provided by a Research Corporation Grant.     

Tunable generation of correlated vortices in open superconductor tubes

As shown theoretically, geometry determines the dynamics of vortices in the presence of transport currents in open superconductor micro- and nanotubes subject to a magnetic field orthogonal to the axis. In low magnetic fields, vortices nucleate periodically at one edge of the tube, subsequently move along the tube under the action of the Lorentz force and denucleate at the opposite edge of the tube. In high magnetic fields, vortices pass along rows closest to the slit. Intervortex correlations lead to an attraction between vortices moving at opposite sides of a tube. Open superconductor nanotubes provide a tunable generator of superconducting vortices for fluxon-based quantum computing.     

Second law implications of a magnetocaloric effect adiabatic phase transition of type I superconductor particles

Abstract

The nature of the thermodynamic behaviour of type I superconductor particles having a cross-section less than the Ginzburg-Landau temperature dependent coherence length ξ(T) is discussed for a magnetic field-induced adiabatic phase transition from the superconductive state to the normal state. The magnetocaloric effect adiabatic phase transition of a particle-dimensioned specimen is characterized by a decrease in entropy, suggesting a quantum limit to traditional formulations of the second law, evidenced by attainment of a final process temperature below that resulting from the isentropic magnetocaloric effect adiabatic phase transition of a bulk dimensioned specimen.