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We report muon spin rotation studies of the magnetic field distribution n ( B μ ) of the low-temperature ( T =5 K) vortex state of the high- T c superconductor Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) in an underdoped state ( T c =77 K). In agreement with previous reports we observe a pronounced change in n ( B μ ) with increasing field. The corresponding reorganization of the vortex structure with increasing vortex density is related to a disorder-induced destruction of the vortex lattice. Furthermore, we find evidence for a partial restoration of the vortex lines at higher fields, which may be related to the increase of the vortex–vortex interaction and the subsequent change from single-vortex pinning to collective pinning.

We have used scanning Hall probe microscopy to study the interaction between flux lines and a random array of precipitates in thin YBCO films. Pinning by precipitates has been demonstrated by measuring the distribution and magnetic field profiles of individual flux lines. Flux lines in the film with precipitates have strongly preferred locations as well as a much broader range of shapes and sizes compared to YBCO films without precipitates. We have also observed ``local magnetization'' anomalies, which appear at multiples of the matching field for the random array of pinning sites.

We studied the dynamical motion of flux lines in melt-processed Sm-Ba-Cu-O (SmBCO) bulk-superconductors driven by a magnetic pulse at 77 K. The total amount of trapped magnetic flux (ΦT) as a function of the magnitude of pulse exhibited a peak; the decrease of ΦT for large pulses is attributed to the increase in temperature of the sample due to the resistive force exerted on moving flux lines. Compared to melt-processed Y-Ba-Cu-O, it is found that the penetration of flux lines into the sample requires a larger pulse, reflecting the strong pinning effect of SmBCO.

Isothermal magnetization curves of a superconducting Nb film perforated by a square lattice of Ni dots exhibit quasiperiodic instabilities below ∼4 K, with a field-dependent period equal to the first, second, or third matching fields. The instabilities are found in a range of applied fields well above the saturation matching value, and where a Nb film with the same dimensions and magnetization remained stable. The recovery of matching effects well below T c ∼8.8 K is unexpected, because strong flux gradients generated by the geometric barrier and random pinning suppress the formation of large domains of matched flux lines and dots. The results suggest that terraces of matched flux density may exist at the border of a flux-free zone near the film edge.

The possibility of reducing AC losses in superconducting Bi-2223 tapes with the aid of the reversible motion of flux lines is investigated. It was found that the AC loss was reduced by reducing the size of superconducting filaments, and the behavior was explained by the theoretical model of Campbell. To get a sufficient reduction of AC losses at 77.3K from the prediction using the critical state model, it is necessary to reduce the filament thickness below 2.5μm.

We consider a model of nonintersecting flux lines in a rectangular region on the lattice $$\mathbb{Z}$$ d , where each flux line is a non-isotropic self-avoiding random walk constrained to begin and end on the boundary of the region. The thermodynamic limit is reached through an increasing sequence of such regions. We prove the existence of several distinct phases for this model, corresponding to different regimes for the flux line density—a phase with zero density, a collection of phases with maximal density, and at least one intermediate phase. The locations of the boundaries of these phases are determined exactly for a wide range of parameters. Our results interpolate continuously between previous results on oriented and standard nonoriented self-avoiding random walks.

There are several ways of investigating#ux lines with polarised neutrons. We shall describe our recent work on IN15 at ILL, investigating spatially varying "elds perpendicular to the #uxoid axes, which are present with tilted "elds in anisotropic superconductors. These "eld components may be detected by polarisation analysis of neutrons di!racted by the #ux line lattice, and allow a detailed investigation of #ux structure in such materials as YBCO and NbSe 2 . A further application of polarised neutrons is the use of neutron spin-echo techniques to measure the speed of moving #ux lines. We have recently demonstrated this in an Nb}Ta alloy on instruments IN11 and IN15, by measuring the energy change of neutrons di!racted by #ux lines, which are moving under the in#uence of a transport current. We shall also comment on others’ work on the search for interference terms between #ux lattice and nuclear di!raction signals, and the use of neutron depolarisation for investigation of #ux distributions in superconductors. ( 1999 Elsevier Science B.V. All rights reserved.

Effects of Pr doping on the superconductivity and CuO2 interlayer coupling of the Bi2212 system were studied carefully for Bi2Sr2Ca12xPrxCu2Oy (x50 – 0.78) single crystals. Tc was suppressed gradually upon Pr substitution, which cannot be explained in Abrikosov-Gor’kov pair-breaking theory. Instead, the variations of Tc with Pr content, for both as-grown and air-annealed crystals, can be well described by a universal parabolic relation Tc /Tmax51–82.6(n20.16) . The carrier concentration n was proved to decrease linearly with x, which confirms that hole filling is the main reason for Tc suppression. The superconducting volume faction also decreases with Pr content and is proportional to 12bx. This behavior was attributed to the loss of local superconductivity and weakening of CuO2 interlayer coupling due to Pr substitution. The second peak in the magnetization curves of Bi2Sr2Ca12xPrxCu2Oy crystals Bsp was found to decrease with Pr content and is described by Bsp5F0 /(sg) 2 with the anisotropy factor g5g0 /(12Ax) in terms of the dimensional crossover from three-dimensional ~3D! flux lines to 2D pancake vortices. The increase of g with x further demonstrates the destruction of CuO2 interlayer coupling by Pr substitution. @S0163-1829~99!02710-1#

We study force-free configurations of Abrikosov flux lines in the line-liquid and line-crystal limit, near the melting transition at ${H}_{m}.$ We show that the condition for zero force configurations can be solved by appealing to the structure of chiral liquid crystalline phases.

Thermal nucleation of kink-antikink pairs in an elastic string subjected to a washboard potential is analyzed in the limit of low temperature and high damping. The pair nucleation rate is calculated analytically for any value of the tilt up to close the instability threshold. Finite-size effects are quantified by computing the relevant end-point nucleation rate under a wide class of boundary conditions. Applications to the physics of lattice dislocations and flux lines in type-II superconducting materials are outlined.

Critical current densities ${(j}_{c})$ and pinning forces ${(f}_{p})$ in superconducting Pb/Ge multilayers and single WGe films are strongly enhanced by introducing regular arrays of submicron holes (``antidot lattices'') acting as artificial pinning centers. Comparative measurements of ${j}_{c}$ and ${f}_{p}$ for several well-defined antidot diameters $D$ have shown that pinning centers with a size considerably larger than the temperature-dependent coherence length $\ensuremath{\xi}(T)$ are much more efficient than those with a size close to $\ensuremath{\xi}(T).$ Moreover, the antidot size realizing the optimum pinning is field-dependent: we need smaller antidots to optimize pinning in lower fields and larger antidots for optimum pinning in higher fields. Crossover between different pinning regimes is controlled by the saturation number ${n}_{s}$ that defines the largest possible number of flux lines trapped by an antidot. In dependence upon the ${n}_{s}$ value, we have observed various composite flux lattices with vortices at antidots and interstices ${(n}_{s}\ensuremath{\approx}1),$ multiquanta vortex lattices ${(n}_{s}g1),$ and finally we have reached the limit of superconducting networks at ${n}_{s}\ensuremath{\gg}1.$

A new method to study the mixed state of high- T c superconductors by the relaxation of resistivity R ff ( t ) experiments is theoretically and experimentally discussed. The theoretical method about how to calculate the decayed magnetization current J i ( R ff ( t )) and the effective pinning energy of flux lines U ( R ff ( t ), J i ( t )) from R ff ( t ) is discussed. Two equations about J i ( R ff ( t ) and U ( R ff ( t ), J i ( t )), are obtained by the two-kind-of-flux-creeop model. R ff ( t ) experiments are performed at various temperatures and magnetic fields. U - J data are calculated. Reasonable physical parameters are derived by fitting the U - J data with two U - J relation models. Experiments and the U - J relation models support the new method and the two-kind-of-flux-creep model.

The correlation length of flux lines responsible for the scaling of current-voltage curves in the transition region between the glass and liquid states in high temperature superconductors is argued based on experimental results on various specimens of Bi-based superconductors. From the correspondence between the temperature dependence of the pinning correlation length and the static critical index, v , it is concluded that the responsible correlation length is the pinning correlation length. This insists that the pinning interaction governs the flux lines in the glass state. This hypothesis is supported by the fact that the transition line depends on the flux pinning strength and the dynamic critical index, z , is appreciably influenced by the width of the distribution of flux pinning strength. It is concluded that the so-called vortex glas-liquid transition is a kind of transition of flux lines between the glass state governed by the pinning and the depinned melt state due to the thermal activation.

The study of thermal motion of flux lines as evidenced in NMR measurements is reviewed in the light of our recent results on the nuclear spin-lattice and spin-spin relaxation rates in anisotropic HT c SC YBa 2 Cu 4 O 8 and HgBa 2 CuO 4+δ

We have observed a step in the equilibrium magnetization for the organic superconductor ${\mathrm{\ensuremath{\kappa}}\ensuremath{-}(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})}_{2}{\mathrm{Cu}[\mathrm{N}(\mathrm{CN})}_{2}$]Br characteristic of a transition of the flux-line solid to a liquid of flux lines. The entropy variation at the transition is found larger than that expected from the theory of the flux-line lattice melting in an anisotropic superconductor. We interpret the decrease of the magnetization step magnitude upon a more rapid cooling of the material to be the consequence of the creation of some strong pins.

Based on previously developed melt processing methods, Y2BaCuO5 (211) precipitates with various size were obtained in YBa2Cu3Ox (123). In particular, a wide distribution of 211 size from 100 A to 10 μm has been found to exist in the matrix of 123, and strongly effected the critical current density, Jc. An enhancement of Jc was always found to be associated with the presence of extremely fine 211 precipitates. The flux pinning by these precipitates can be understood by considering the interaction of flux lines with cavities. It was found that although the flux lines are strongly pinned by cavities, the effectiveness decreases with the increasing number of flux lines trapped by them.

The problem of Aharonov - Bohm (AB) scattering on two parallel flux lines of the same magnitude is solved by the method of path integration.

The stability of the flux line lattice has been investigated within anisotropic London theory. This is the first full-scale investigation of instabilities in the `chain' state. It has been found that the lattice is stable at large fields, but that instabilities occur as the field is reduced. The field at which these instabilities first arise, $b^*(\epsilon,\theta)$, depends on the anisotropy $\epsilon$ and the angle $\theta$ at which the lattice is tilted away from the $c$-axis. These instabilities initially occur at wavevector $k^*(\epsilon,\theta)$, and the component of $k^*$ along the average direction of the flux lines, $k_z$, is always finite. As the instability occurs at finite $k_z$ the dependence of the cutoff on $k_z$ is important, and we have used a cutoff suggested by Sudb\ospace and Brandt. The instabilities only occur for values of the anisotropy $\epsilon$ appropriate to a material like BSCCO, and not for anisotropies more appropriate to YBCO. The lower critical field $H_{c_1}(\phi)$ is calculated as a function of the angle $\phi$ at which the applied field is tilted away from the crystal axis. The presence of kinks in $H_{c_1}(\phi)$ is seen to be related to instabilities in the equilibrium flux line structure., Comment: Extensively revised paper, with modified analysis of elastic instabilities. Calculation of the lower critical field is included, and the presence of kinks in $H_{c_1}$ is seen to be related to the elastic instabilities. 29 pages including 16 figures, LaTeX with epsf style

We review some of the assumptions made in the use of muon spin rotation in superconductors: i.e. that the muons are implanted at random positions in the flux lattice, remain static after implantation and do not appreciably affect the properties of the surrounding superconductor; also that the flux lines are straight and static, and that the observed muon rotation frequency spectrum reflects the microscopic distribution of field values. We shall show how evidence for and against the truth of these assumptions in particular cases may be obtained from the μSR results themselves or by comparison with other measurements, and how this in turn may lead to deeper understanding of flux line structure and motion in superconductors.

In order to increase the critical current density and trapped magnetic field in high Tc superconducting materials, various kinds of inhomogeneities were introduced and used as pinning centers of flux lines. A universal scaling behavior of the pinning force is observed in different high Tc cuprates. We show that this scaling law is a natural result of a unified materials equation for type-II superconductors. This equation agrees reasonably well with recently observed phenomena.

Fluctuation in the distance between flux lines in a superconductor is calculated in a fractal dimension and from that using Lindemann criterion of melting, a field versus temperature phase boundary is deduced for the dendritic phase of a superconductor. This phase boundary is predicted to be B−4∝(1−T FM /T c ) where T FM is the flux-lattice melting temperature. When both the fractal as well as the spectral dimensionalities are considered the phase boundary is predicted to be determined by B8/5∝(1−T FM /T c ).

ac susceptibility measurements were made to study the effects of an ac field on dynamics of textured ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$. The effective activation barrier U, time scale ${\mathit{t}}_{0}$, and velocity scale ${\mathit{v}}_{0}$, of flux diffusion are obtained based on the experiment and nonlinear flux diffusion theory. The result that U(${\mathit{H}}_{\mathrm{ac}}$\ensuremath{\parallel}ab)\ensuremath{\propto}${\mathit{H}}_{\mathrm{ac}}^{\mathrm{\ensuremath{-}}0.26}$ and U(${\mathit{H}}_{\mathrm{ac}}$\ensuremath{\parallel}C)\ensuremath{\propto}-ln ${\mathit{H}}_{\mathrm{ac}}$ shows that the barriers are anisotropic. The time and velocity scale manifest their anisotropy in such a way that [${\mathit{t}}_{0}$ (or ${\mathit{v}}_{0}^{\mathrm{\ensuremath{-}}1}$)(${\mathit{H}}_{\mathrm{ac}}$\ensuremath{\parallel}C)]/[${\mathit{t}}_{0}$ (or ${\mathit{v}}_{0}^{\mathrm{\ensuremath{-}}1}$) (${\mathit{H}}_{\mathrm{ac}}$\ensuremath{\parallel}ab)]\ensuremath{\approxeq}${10}^{3}$, ${\mathit{t}}_{0}$\ensuremath{\propto}(${\mathit{H}}_{\mathrm{ac}}$\ensuremath{\parallel}ab${)}^{1.27}$, and ${\mathit{t}}_{0}$\ensuremath{\propto}(${\mathit{H}}_{\mathrm{ac}}$\ensuremath{\parallel}C${)}^{\mathrm{\ensuremath{-}}0.6}$. These results can be understood if flux lines are considered to be collective diffusion in the vortex glass phase near the viscous flux-flow state. \textcopyright{} 1996 The American Physical Society.

Ordered arrays of columnar defects have been fabricated by direct electron-beam writing on ${c}_{\ensuremath{\perp}}$-oriented $\mathrm{Ya}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}(\mathrm{YBCO})$ thin films. Serving as strong pinning sites, columnar defects cause a 70% enhancement of critical current density ${J}_{c}$ at $T=77$ K in magnetic fields parallel to the $c$ axis. The matching effect of the pinning force density has been observed, due to commensurability between flux lines and arrays of columnar defects. The pinning strength of columnar defects has been compared with that of point defects, and found to be greater than the latter in YBCO films. These results suggest that this way of pinning center fabrication could be a promising tool in studies of the pinning mechanism in high-temperature superconductors.

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures., 10 pages, 3 PS figures, to appear in PRL

The longitudinal elastic correlation length, l 44 , of flux lines along the c -axis is measured using the Campbell method with the magnetic field parallel to the c -axis for a superconducting Bi-2212 single crystal. It is found that l 44 is of the order of 10μm and four orders of magnitude longer than the distance between the CuO 2 planes. In addition, l 44 increases with increasing magnetic field and/or temperature. These results agree well with the theoretical estimate of the pinning correlation length using the observed critical current density. The apparent pinning potential associated with the magnetic relaxation rate is calculated using these results and compared with the experimental result. Agreement is satisfactory. It is also found that the transverse flux-bundle size is as short as the flux-line spacing. It is concluded from these results that the flux lines are rather one-dimensional and strongly coupled along the c -axis.

Measurements of the $^{89}\mathrm{Y}$ NMR linewidth \ensuremath{\Delta}\ensuremath{\nu} and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ have been performed in an oriented powder sample of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ (${\mathit{T}}_{\mathit{c}}$ = 81 K) for both ${\mathbf{H}}_{0}$\ensuremath{\parallel}c and ${\mathbf{H}}_{0}$\ensuremath{\perp}c at ${\mathit{H}}_{0}$ = 9.4 and 5.9 T. Evidence for the effects of thermal motion of flux lines (FL's) below ${\mathit{T}}_{\mathit{c}}$ is presented and the microscopic correlation times of the FL motion are derived by using a simple model. From the temperature and field dependence of ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ an effective correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{e}}$ describing the pseudodiffusion of two-dimensional (2D) pancake vortices is extracted. The effective activation energy of the FL motion is found to be inversely proportional to the magnetic field, supporting the similar conclusion recently obtained in ${\mathrm{HgBa}}_{2}$${\mathrm{CuO}}_{4+\mathrm{\ensuremath{\delta}}}$. From the temperature dependence of \ensuremath{\Delta}\ensuremath{\nu} another correlation time \ensuremath{\tau}, different from ${\mathrm{\ensuremath{\tau}}}_{\mathit{e}}$, is obtained. It is argued that the correlation times derived from \ensuremath{\Delta}\ensuremath{\nu} and ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$, respectively, refer to different motional regimes below and above the irreversibility temperature ${\mathit{T}}_{\mathrm{irr}}$. \textcopyright{} 1996 The American Physical Society.

We study the interplay between a novel vortex-loop unbinding in finite magnetic field at T=T_V and flux-line lattice (FLL) melting at T=T_M in type-II superconductors. The FLL melts due to nucleation of vortex loops parallel to c-axis, connected to flux lines. For moderate anisotropy, phase coherence along c-axis is lost at T_V > T_M due to an ab-plane vortex-loop unbinding with loops located close to thermal FLL fluctuations. For large anisotropy, phase coherence along c-axis is lost at T_V < T_M due to nucleation of ab-plane vortex-loops uncorrelated to flux lines., 4 pages, 3 postscript figures

Flow of 2D flux lines confined to narrow channels has been studied. In the solid, (in)commensurability between lattice and channel width cause mobility oscillations from which the actual channel width follows. In the liquid, the oscillations disappear and flow is dictated by the shear viscosity h. By repeated experiments for different channel widths, h is determined for the first time. It diverges according to h ~ j2 1sT , Bd. An indication for the hexatic-to-liquid transition is also observed. [S0031-9007(96)00579-0]

We report the upper critical field H c2 of single crystalline Sr 2 RuO 4 , which is the only known layered-perovskite superconductor without copper. The ratio H c2∥ ab / H c2∥ c = 26 indicates that the ruthenate is a highly anisotropic superconductor. In addition, we found a peculiar second dissipation peak only when the flux lines, as well as their induced motions, are within the ab -planes.

The electrical resistance R in a superconducting Ba1−xKxBiO3 single crystal is studied as a function of the temperature T and the current I. The measurements performed without applied magnetic field indicate that the flux lines are generated by the self-field and that several transitions contribute independently to the R(T) and R(I) characteristics. A phenomenological expression of the R(T, I) dependence is proposed.

The pinning-force density and the irreversibility field are measured for Bi-2223 tape wires at various temperatures under the magnetic fields normal and parallel to the c -axis. It is found that the scaling laws of pinning-force density in the low- and high-temperature regions and the temperature dependence of the irreversibility field are formally the same between the two field directions in spite of some anisotropy factor, suggesting that the pinning mechanism is essentially the same for the two field directions. These results are compared with the numerical calculation based on the flux-creep model. The experimental results are well explained by the theory including the anisotropic property. The pinning potential estimated from the flux-creep theory at 80 K and 1.0 T is of the order of several 10 meV and the factor of the anisotropy is about 1.3. The value of the pinning potential under the magnetic field along the c -axis suggests that the flux lines are strongly connected along this direction. The longitudinal elastic correlation length of the flux lines is of the order of several μm and this supports the hypothesis. The pinning characteristics of a Bi-2223 tape wire to which the strong pinning centers are successfully introduced are discussed using the flux-creep theory for evaluating the potential of this material for application. The irreversibility field for the direction parallel to the c -axis is estimated to be sufficiently high even at 77.3 K and it is concluded that Bi-2223 has a sufficient potential for application.

We have observed the anomalous magnetization of Bi 2 Sr 2 CaCu 2− x Ni x O 8 ( x = 0 and 0.02) single crystals. Anisotropy decreases with iodine intercalation although it expands the space between CuO 2 layers. Iodine intercalation seems to suppress the magnetization anomaly for Ni = 1% crystals, but not for Ni = 1% substituted crystals. We have discussed these results in terms of the increase of anisotropy by Ni substitution and the dimensional crossover of flux lines. Effects of both oxygen concentration and substitution of a magnetic element for the Cu site on the anisotropy of Bi 2 Sr 2 CaCu 2 O 8 crystals show the same tendency as the case of the YBa 2 Cu 3 O 7 superconductor.

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization ( M ) anomalies, appearing at matching fields H m = m φ 0 / S in superconducting films with the antidot lattices having a unit cell area S , are successfully explained. These anomalies are, analogues of the well-known M ( H ) cusp at H c 1 , but for the onset of multi-quanta ( m +1)φ 0 -vortices penetration at each subsequent matching field H m . It is shown that the M ( H ) curve between the matching fields H m H H m +1 follows a simple M ∝ln( H − H m ) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of the M ( H , T ) curves convincingly demonstrates that a new type of the critical state B =const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.

Microscopic structures of (Hg, Re)Ba2Can−1CunOy (nominally n = 4) have been investigated by means of high-resolution electron microscopy. Remarkable structural changes were detected during the observations. The lattice images viewed along the a-axis showed an ordinary intergrowth of members with mostly n > 4 in the matrix of the n = 4 host lattice. On heating crystals by a weak electron beam, dense rows of nm size domains accompanied by large strain fields appeared selectively at the intergrowth layers. However, further heating by an intense electron beam wiped off these domains, and strain-free lattices were recovered. These successive changes in the microstructure are interpreted in terms of the two-dimensional disproportionation of Re content on the Hg sites. It is suggested that the observed small domains with a typical size of 3 nm parallel to a 10 nm normal to intergrowth layers may provide promising pinning centers for flux lines in the mixed state.

The role and nature of interactions between three or more pancake vortices (i.e., multipancake interactions) in layered superconductors is investigated. To this purpose, in the framework of the Lawrence-Doniach model a compact expression for the energy of an Abrikosov vortex line is derived. It is shown that multipancake interactions can be understood as electromagnetic coupling between Josephson current densities in different layers.

I determine the scaling behavior of the free energy barriers encountered by a flux line in moving through a three-dimensional random potential. A combination of numerical simulations and analytic arguments suggest that these barriers scale with the length of the line in the same way as the fluctuation in the free energy.

A study has been made of the decay of the trapped magnetisation in superconductors when exposed to a crossed field. Numerical results have been compared with the theory of Brandt and Mikitik (2002 Phys. Rev. Lett. 89 027002) which solves the problem for a thin strip superconductor. FlexPDE with the A formulation and COMSOL with the H formulation were both used. Simulations of a strip with a cross section aspect ratio of 20 showed good agreement with theory both for the case of a transverse field larger than the transverse penetration field and for one smaller. In the latter case the magnetisation saturates as predicted, however the simulations show a slow decay after many cycles. In the case of stacked YBCO tapes the movement of flux lines is very small and the effects of the reversible motion were investigated. This can decrease the decay initially for very thin decoupled tapes, but cause a steady decay after very large numbers of cycles. Simulations on stacked strips showed that the decay constant increased approximately linearly with the number of strips. When combined with the theory for one tape this can explain the very slow decay observed in previous experiments. Experimental results were qualitatively in agreement with theory and simulations but showed some discrepancies. However there are a number of differences between the experimental situation and theory so good agreement is not expected.

We consider a model of oriented, non-intersecting flux lines on the lattice Zd, where each flux line is assigned a Boltzmann factor omega per unit length and a fugacity y. We prove the existence of free energy, both for y>0 and for y=-1, and show that it is independent of y for y>0. Using upper and lower bounds in terms of exactly solvable models, we rigorously establish that, for all y>0, the model has a phase transition at omega =1/d. For omega

Voltage-current characteristics were measured for Ag-clad (Bi, Pb)2Sr2Ca2Cu3O10 multifilamentary samples at 77 K, with magnetic field H parallel to the c-axis. The data were fitted by V=V0 exp[-(l*/l)mu ], where l is the critical current with no thermal excitations. The parameter mu was obtained from logd(In V)/d/3] versus log l plots, where the data give straight lines for each of the fields. The lines for the fields 30 mT

A model of a type-II superconducting cylindrical shell is established to verify the properties of distorted flux lines using the London theory. The field distributions inside and outside the superconducting region are determined. Moreover, the current density and the forces on the vortex segments are calculated using these field distributions. Finally, the Gibbs free energy of the system is obtained in compact form which can be easily applied to real-life application. As the shell tends to a rigid cylinder agreement with previous results is achieved.

The positions of columnar pins and magnetic flux lines determined from a decoration experiment on BSCCO were used to calculate the single--particle density of states at low temperatures in the Bose glass phase. A wide Coulomb gap is found, with gap exponent $s \approx 1.2$, as a result of the long--range interaction between the vortices. As a consequence, the variable--range hopping transport of flux lines is considerably reduced with respect to the non--interacting case, the effective Mott exponent being enhanced from $p_0 = 1/3$ to $p_{\rm eff} \approx 0.5$ for this specific experiment., Comment: 10 pages, Revtex, 4 figures appended as uu-encoded postscript files, also available as hardcopies from tauber@cmt.harvard.edu

Flux phases have been studied in superconducting Pb/Ge multilayers with a square lattice of submicrometre holes. Sharp peaks in the magnetic-field dependence of the critical current have been observed at integer Hm and rational Hk/l matching fields. At integer fields an artificial flux line crystal is formed, consisting of a stable square lattice of single or multiple flux quanta trapped by the holes. The existence of such a crystal leads to the quantization of the pinning force. New rational flux lines patterns at H = Hk/l, qualitatively different from those previously seen in superconducting networks, have been identified.

We studied YBa2Cu3O7−x ceramic samples during external magnetic field increase from 200 to 4000 Oe at 77 K using acoustic emission and magnetization methods. We observed a small magnetic anomaly near 2500 Oe. This observed magnetic anomaly was accompanied by acoustic emission impulses of activity equal to ~20 s−1. These impulses are thought to be Bean's mixed-state field Hs. Based on Bean's theory, the full penetration field H* has been calculated to be ~1200 Oe. The possible mechanism of acoustic emission signals due to interaction between flux lines during the formation of a mixed state inside a sample is discussed.

The surprisingly rapid relaxation of the sustainable current density in the critical state of single crystalline Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ is investigated for magnetic fields oriented parallel to the c-axis and to the $ab$--plane respectively. Due to the inadequacy of standard analysis procedures developed for flux creep in the high temperature superconducting cuprates, we develop a simple, straightforward data treatment technique that reveals the creep mechanism and the creep exponent $\mu$. At low magnetic fields, below the second magnetization peak, $\mu$ varies only slightly as function of temperature and magnetic flux density $B$. From the data, we determine the temperature- and field dependence of the effective activation barrier for creep. At low temperatures, the measured current density approaches the zero--temperature critical current density (in the absence of creep) to within a factor 2, thus lending credence to earlier conclusions drawn with respect to the pinning mechanism. The comparable values of the experimental screening current density and the zero-temperature critical current density reveals the limited usefulness of the widely used "interpolation formula"., Comment: Physical Review B (2012) Accepted

${}^{75}\phantom{\rule{-0.16em}{0ex}}$As NMR spin-lattice relaxation ($1/{T}_{1}$) and spin-echo decay ($1/{T}_{2}$) rate measurements were performed in a single crystal of Ba(Fe${}_{0.93}$Rh${}_{0.07}$)${}_{2}$As${}_{2}$ superconductor. Below the superconducting transition temperature ${T}_{c}$, when the magnetic field $\mathbf{H}$ is applied along the $c$ axes, a peak in both relaxation rates is observed. Remarkably that peak is suppressed for $\mathbf{H}\ensuremath{\perp}c$. Those maxima in $1/{T}_{1}$ and $1/{T}_{2}$ have been ascribed to the flux lines lattice motions and the corresponding correlation times and pinning energy barriers have been derived on the basis of a heuristic model. Further information on the flux lines motion was derived from the narrowing of ${}^{75}\phantom{\rule{-0.16em}{0ex}}$As NMR linewidth below ${T}_{c}$ and found to be consistent with that obtained from $1/{T}_{2}$ measurements. All the experimental results are described in the framework of thermally activated vortices motions.

The changes of the microstructures of bulk single-phase Eu1−xDyxBa2Cu3O7−δ and Eu1−yGdyBa2Cu3O7−δ superconductors due to (Dy, Gd)-doping were investigated by the Mossbauer effect. The pinning potentials of the samples were calculated by magnetization relaxation analysis. The interaction between the magnetic moment of magnetic rare-earth cations and flux lines in these samples was considered as a predominant pinning mechanism in highTc superconductors in this paper.

Using a vibrating-reed technique, we studied the flux penetration in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystals in the strong pinning regime well below the irreversibility line. The resonant frequency and damping of the vibrating superconductor are dramatically enhanced by the nonuniform and hysteretical penetration of the flux lines at low temperature. Using a critical-state model, we determine the critical current density ${\mathit{J}}_{\mathit{c}}$ to be about 3.5\ifmmode\times\else\texttimes\fi{}${10}^{6}$ A/${\mathrm{cm}}^{2}$ at 4.2 K. We also found that ${\mathit{J}}_{\mathit{c}}$ obeys an exponential temperature dependence and the flux creep at low temperature can be characterized by a low activation energy barrier on the order of 20 K.

Thermal motion of the flux lines (FL) gives rise to fluctuating magnetic fields. These dynamic fields couple to the nuclei in the sample and relax the nuclear spins. Based on a model of harmonic fluctuations, we provide a theoretical description of the nuclear spin-lattice relaxation (NSLR) process due to the fluctuating FLs in clean type-II superconductors. At low fields, the calculated longitudinal relaxation rate $T_1^{-1}$ is enormously enhanced at temperatures just below $T_c$. At intermediate fields, the resulting $T_1^{-1}$ exhibits a peak structure as a function of temperature, which is eventually suppressed as the field is increased. The vibrational modes which have components propagating along the FLs play an essential role in the $T_1^{-1}$ process.

The dynamical behavior of magnetic flux in superconducting Tl-Ba-Ca-Cu-O films has been studied using the Nernst effect. Large temperature gradients of \ensuremath{\sim}${10}^{5}$ K/cm and, correspondingly, large thermal forces on flux lines were obtained by pulsed laser heating of films. Due to the large thermal driving forces it was possible to observe, at temperatures well below ${\mathit{T}}_{\mathit{c}}$, the transition from thermally assisted flux flow to flux creep and viscous flux flow.