Collective Motion of Vortices Induced by A.C. Magnetic Field in the High Anisotropy BSCCO

The microwave dissipation induced by an ac magnetic field collinear to the dc magnetic field in the highly anisotropic BSCCO shows two signals. One, that occurs just below T _c in all superconductors, corresponds to changes in the microwave dissipation of the TAFF resistivity caused by a magnetic modulation. The other signal arises from a double frequency process, where the ac field prepares the vortex system to enable its interaction with the microwave. This signal whose response to the ac field is non-linear (NL) is studied in this work, mostly for the configuration where the dc and the ac magnetic field are parallel the a–b plane. We demonstrate that below B _dc=0.0025 T the ac field interacts with individual non-interacting vortices. Above B _dc=0.005 T, the ac induces simultaneously, collective motions of pinned vortices and Josephson unpinned vortices. The latter has a bell-shaped form and therefore can be identified as an oscillation mode induced by the magnetic microwave field. This oscillation mode is excited by the microwave magnetic field and therefore it differs from the Josephson plasma excitation mode or the vortex excitation mode where both are excited by the microwave electric field. Defects, high temperatures and high ac fields impedes the excitation of this mode. The results are discussed with respect to the vortex shaking effect and other experimental and theoretical results.     

Evidence for unpinned magnetic flux vortices above theI ctransition in the 2223-phase high-T csuperconductor

A similarity in the dc voltage-current (V-I) curves for both direct and alternating transport currents is used to propose that unpinned flux vortices are generated above theI _ctransition for dc transport currents, when Abrikosov flux vortices begin to penetrate the superconductor. Two methods can be used to give a dc voltage drop for an ac transport current: (1) if there is a slight dc offset voltage in the ac current which favors vortex loop collapse as in a traditional dcI _ctest, or (2) if an asymmetric transverse magnetic field is present which favors vortex loop collapse for current in one direction over the reverse direction.     

Dynamic Phase Diagram of Driven Vortices in Bi2Sr2CaCu2O y

The coupled study of noise spectra and ac-dc interference effects was performed to clarify the evolution of the driven vortex state of Bi₂Sr₂CaCu₂O _y single crystals. Broadband noise and interference effects were observed in different regions of the H-T-J (H is magnetic field, T is temperature, and J is driving current density) space, which was closely connected with the change of the dynamic phase of the vortices. The obtained H-T-J phase diagram of driven vortices was found to be rather different from those in conventional superconductors, and those expected by numerical simulations.     

The Influence of Pinning Centers in the Magnetization of the Mesoscopic Superconductors

In this work, we study the mesoscopic superconducting samples with pinning centers using the time-dependent Ginzburg-Landau theory (TDGL). The pinning centers are introduced via the phenomenological function f(r) Sorensen et al. (Physica C 533, 40–43 2017). We calculated the magnetization curves M(H) for some distances d from the boundary of the sample to the position of the pinning center. From this investigation arises the relation between the first magnetic field H _p and the distance d. It shows that the pinning centers located close to the boundary of the sample decrease H _p , and also the existence of two regimes of the penetration of the vortices. The magnetization curves revel the existence of ruddle of jumps for low magnetic fields for small distances d, indicating a complex vortex penetration.     

Evidence for unpinned magnetic flux vortices above theIctransition in the 2223-phase high-Tcsuperconductor

A similarity in the dc voltage-current (V-I) curves for both direct and alternating transport currents is used to propose that unpinned flux vortices are generated above theI _ctransition for dc transport currents, when Abrikosov flux vortices begin to penetrate the superconductor. Two methods can be used to give a dc voltage drop for an ac transport current: (1) if there is a slight dc offset voltage in the ac current which favors vortex loop collapse as in a traditional dcI _ctest, or (2) if an asymmetric transverse magnetic field is present which favors vortex loop collapse for current in one direction over the reverse direction.     

Estimation of non-linear effective flux diffusion barrier U(J, Hd, T) and critical current density of polycrystalline (Bi-Pb)-2223 using ac susceptibility measurements

The complex ac susceptibility of polycrystalline Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_10+δ pellet as a function of temperature, ac field amplitude, frequency and dc field is reported. Data have been analyzed using a non-linear flux diffusion model, where thermally assisted vortices diffuses over an effective pinning barrier. Using the temperature corresponding to the peak in χ″, the dependence of the effective barrier potential U(T, H_d, J) on temperature, dc field and current density has been determined and the results are found to be consistent with those reported earlier. The critical current density (J_C) as a function of dc field is also estimated using the extracted barrier and compared with those obtained from I-V characteristics at 77 K. This agreement between the calculated and measured values indicates that estimation of J_C of HTSCs using magnetic methods (viz. ac susceptibility) should be based on frequency-dependent non-linear models.     

Spontaneous Generation of Single Vortices and Anti-Vortices in Superconductors with Restricted Geometries

We study the nucleation of vortices in a thin (thickness ≪ penetration depth) mesoscopic superconducting disc in an applied magnetic field perpendicular to the disc (i.e., parallel to the axis of the disc). We write down an expression for the free energy of the system with an arbitrary number of vortices and anti-vortices at finite (non-zero) temperatures. For a given applied field, we minimize the free energy to find the optimal position of the vortices and anti-vortices (the configuration which minimizes the energy). We show that, whereas at zero temperature anti-vortices do not nucleate, anti-vortices do penetrate the disc at finite temperatures. We also calculate the magnetization of the disc as a function of the applied field and hence determine the different configurations possible in which a fixed number of fluxoids can penetrate the disc.     

High-field Josephson magnetic resonance in high-temperature superconductors

The possibility of high-field Josephson magnetic resonance (HFJMR) in high-temperature super-conductors (HTSCs) is theoretically demonstrated. The HFJMR mechanism is related to the Josephson oscillations in intergranular junctions of a polycrystalline HTSC, which are caused by the penetration of Abrikosov vortices into the grains. In fields within H _c1 ≤ H < H _x (where H _c1 is the first critical field and H _x is the field corresponding to vortex separation from pinning centers in the grains), measurements of the microwave absorption spectra of a sample can be used for investigations of the HTSC macrostructure and the properties of vortex matter. In the latter aspect, the HFJMR method is analogous to the SQUID technique.     

Evidence for two superconducting components in oxygen-annealed single-phase YBaCuO

The complex susceptibility of a sintered YBaCuO superconductor is strongly dependent on a.c. field amplitude, h. Very small values of h must be used for the real part of susceptibility, χ′, to reach a value corresponding to bulk diamagnetism just below the critical temperature, T_c. The imaginary part, χ″, represents hysteresis loss in the sample. Thus, χ″ versus temperature becomes positive when h exceeds the lower critical field, H_cl of the superconductor.Annealing the material in oxygen gives rise to two distinct components, a relatively high-T_c, high-H_cl superconductor (denoted as ‘G’ or ‘good’) and a relatively low-T_c, low-H_cl superconductor (denoted as ‘B’ or ‘bad’). Curves of susceptibility versus increasing temperature reflect the dual nature of the annealed sample: χ′ has an inflection point at T_c of the B component and approaches zero at T_c of the G component, while χ″ has a peak at each T_c. Both critical temperatures decrease linearly with increasing h, though at very different rates. H_cl of the G component is considerably greater than H_cl of the B component. The lower critical fields are linearly decreasing functions of temperature.Two models might explain the susceptibility data. In the grain model, the G component consists of superconducting grains and the B component is either intergranular material, unfavourably orientated anisotropic grains, or oxygen-depleted grain boundaries. In the surface model, the G component is in the interior of the sample and the B component is at the sample's surface. This condition could arise if there was oxygen depletion at the surface subsequent to total enrichment during annealing.     

Anisotropy in ac losses near the irreversibility field of Bi2Sr2CaCu2O8

The ac susceptibility under a biased dc field near the irreversibility field (H _irr) of a Bi₂Sr₂CaCu₂O₈ single crystal has been measured. The frequency dependence, the ac-power dependence, and the nearly lossless character of the?″ vs.H _dc curve forH∥a-axis have been roughly explained from a reversible (elastic) fluxoid motion, while those forH∥ c-axis have been explained from a thermally assisted flux-flow (TAFF) model. The obtained parameters are discussed in relation to anisotropic flux-pinning mechanisms in the layered structure of this compound.     

Asymmetry of the Pinning Force in Thin Nb Films in Parallel Magnetic Field

The pinning force, F _p, is studied in Nb films of different thickness in parallel magnetic field H. The asymmetry in the magnetic field dependence of F _p has been observed for two opposite directions of the transport current. The effect is less pronounced for thin and thick films where, respectively, single vortex pinning and pinning of the internal vortices, is relevant. At intermediate thickness, where the pinning mechanism is mostly caused by surface effects, an asymmetry in the F _p(H) dependence is clearly visible. The different surface barriers that vortices should overcome to enter the sample from opposite sides of the film explain the effect, as confirmed by numerical calculations. These have been obtained by solving the Ginzburg?CLandau equations with asymmetric boundary conditions which take into account the different superconducting properties of the film?Csubstrate and film?Cvacuum interface. Such difference can also explain the reduction of the critical current usually observed in thin films as a function of their thickness.     

Vibrating reed study of the flux line dissipation of ceramic and single-crystal (Ba,K)BiO3

Vibrating reed (VR) and dc and ac magnetic susceptibility measurements were performed on a nominal single crystal of composition (Ba_0.64K_0.36)BiO₃ in an applied magnetic fieldH. Field-cooling and field-sweep data revealed multiple peaks in the reed dissipation 1/Q located below the superconducting transition temperatureT _c (≈29.6 K forH=0). A shoulder or onset (with increasingT) of dissipation appears forT≤18 K, which may be a signature of a flux lattice melting transition. VR data for dense ceramic samples of composition (Ba_0.625K_0.375)BiO₃ (T _c=28.6K) exhibit a relatively narrow and smooth peak in 1/Q that corresponds well to a broad, intermediate-temperature peak in the crystal data. Resistivity experiments demonstrate that the single ceramic peak occurs well below the temperature at which the electrical resistanceR≈0, suggesting that the higher-temperature crystalline peaks are positioned close to the upper critical field line and may be strongly dependent upon grain size or surface properties. Both ac and dc susceptibility data show no clear evidence for multiple phases or gross compositional inhomogeneities in the crystalline sample. Our results demonstrate that the VR technique is an extremely sensitive method to probe sample inhomogeneities and their role in flux pinning phenomena.     

Vortex Dynamics in a Superconducting Film with a Kagome and?a?Honeycomb Pinning Landscape

The vortex dynamics in a superconducting thin Al film with a periodic Honeycomb or Kagome array of antidots has been investigated by electrical transport measurements. The large values of the superconducting coherence length and penetration depth of the Al films guarantee a maximum of one flux quantum trapped per pinning site. This allows us to directly compare the experimental results with previous theoretical investigations based on molecular dynamics simulations. For the Kagome lattice, two submatching features not anticipated theoretically at H/H ₁=1/3 and 2/3, where H ₁ is the field at which the number of vortices coincides with the number of pinning sites, are observed. Possible corresponding stable vortex patterns are suggested. For the Honeycomb pinning landscape, the commensurability effects are in agreement with the theoretical expectations. A preliminary analysis of the vortex mobility in this lattice shows the presence of a weak vortex guidance.     

Magnetic flux penetration into a superconducting double stripline with an edge barrier

An analytical solution to a problem concerning the behavior of a superconducting contour comprising two parallel thin-film strips in a magnetic field of increasing strength. The entrance of vortices into the films, which are free of bulk inhomogeneities, is controlled by an edge barrier (of the Bean-Livingston or geometric type). It is established for the first time that the Meissner state can be realized in two regimes: the classical Meissner state in the interval of magnetic field strengths 0≤H≤H _s (where H _s is field strength corresponding to the entrance of the first vortex) and the state in the interval H _s≤H≤H _c for which vortices formed on the boundaries of the films penetrate into the gap. For H≥H _c, the magnetic flux penetration is accompanied by the appearance of a mixed state in the films. Expressions describing the inductance of the superconducting circuit in the entire range of magnetic fields are also obtained for the first time.     

Magneto-transport Properties and Thermally Activated Flux Flow in Ba(Fe 0 . 9 1 Co 0 . 0 9 ) 2 As 2 Superconductor

Thermally assisted flux flow (TAFF) based on magneto-resistivity and ac susceptibility measurements is studied in a Ba(Fe_0.91Co_0.09)₂As₂(T _c=25.3 K) sample in magnetic fields up to 18 T. In addition to the upper critical field μ ₀ H _c2 and the coherence length ξ(0), the flux flow activation energy U(T,H) has also been determined. The resistive transition width is proportional to μ ₀ H, in contrast to Tinkham’s theoretical prediction. By applying Fisher’s model, the glass melting transition temperature T _g, which occurs in the upper TAFF state and not in the zero resistivity vortex solid regime, is calculated. The onset of TAFF temperature and the crossover temperature T _x from TAFF to flux flow are determined. By contrasting the ac susceptibility data with the resistivity data, considerable flux penetration appears even in the zero resistivity state, in addition to ac losses. The H-T phase diagram is drawn and shows weak pinning regime as the field approaches μ ₀ H _c2, and the strength of the weak pinning decreases to 0 with increasing magnetic field from 0 to 18 T.     

Approximate Solutions of the Nonlinear Schr?dinger Equation for Ground and Excited States of Bose-Einstein Condensates

I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N₀ limit of the vortex critical frequency for a > 0, by approximate solution of the time-independent nonlinear Schrödinger equation.     

Measurements of Turbulence Onset and Dissipation in Superfluid Helium with a Silicon Double Paddle Oscillator

We have studied experimentally the response of a silicon single crystal double paddle oscillator submerged in superfluid helium from the lambda point to 1.55 K. Measuring the resonance frequency and dissipation on three modes of this high Q system allows us to study the dissipation at the onset of turbulence in the flow around the paddle. The critical velocity V _c for turbulence onset decreases with temperature. If we use the density of the normal component of the superfluid to obtain a Reynolds number Re associated with V _c we find a value which is largely temperature independent. This result is different from the behavior previously found by other authors below 1 K, where the quantized vorticity (extrinsic nucleation) is observed at velocities more than an order of magnitude greater. In our temperature range, we conclude that the transition is governed by the normal fraction acting as a classical fluid. The laminar regime shows a dissipation that is proportional to the viscous drag calculated by well known formulas for an object oscillating in a liquid. We also find a decrease in resonance frequency in the turbulent regime which is clearly observed but hard to reproduce from run to run.     

Magnetization reversal and ferrimagnetism in Pr1−x Nd x MnO3

Detailed magnetic properties of Pr_{1? x} Nd _x MnO₃ (x = 0.3, 0.5 and 0.7) have been reported. All the samples crystallize in orthorhombic perovskite structure with Pnma space group. Magnetization measurements under field cooled (FC) protocal reveal magnetization reversal at low temperatures and low magnetic field. This indicates clear evidence of two magnetic sublattices aligned opposite to each other. There is a well-defined maximum around 48 K in the x = 0.7 sample (i.e. Pr_0.3Nd_0.7MnO₃) in the χ′ value which is identified as paramagnetic to ferrimagnetic transition. The peak value shifts to higher temperature with decrease of x and width of the maximum broadened. It is also observable that with decrease of Nd, both the value of χ′ and χ″ decrease. An attempt is made to explain the magnetization reversal within the framework of available models.