2PO1-40 Spatial structure of quenched, driven and equilibrium vortex arrays near T_c

Harald Haughlin 1, Nathan G. Woodard 2, and Gregory P. Lafyatis 2. 1 Dept. of Physics, University of Oslo, P.O. Box 1048 Blindern,N-0316 Oslo, Norway. 2 Dept. of Physics, The Ohio State University, 174 W 18th Ave, Columbus OH 43210.

Presenting Author: H. Hauglin

We have studied vortex matter structure in an untwinned YBCO single crystal at temperatures up to 0.993T_c using a recently developed atomic beam technique. For the weak fields used, we find a hexatic vortex array with sample wide orientational correlation and translational order with mean square displacement <u(r)²> ~ r. There is no evidence for a disordered vortex liquid phase at temperatures below 0.993T_c. The hexatic vortex array is in thermal equilibrium only within a few K below T_c. At lower temperatures, the vortex array is a pinned vestige of the high temperature equilibrium hexatic structure. This is seen directly in the temperature- and current dependence of the structure factor. We find that transport currents introduce plastic deformations that destroy the long range order of the pinned hexatic phase. Hexatic order is restored by annealing to a few K below T_c. These observations suggest that the low field vortex solid exists in at least two states: A mobile high temperature state and a pinned, immobile state at low temperatures.

Supported by U.S. D.O.E through the Midwest Superconductivity Consortium and the Norwegian Research Council.

2PO1-41 Four-fold basal plane anisotropy of the nonlocal magnetization of YNi₂B₂C

L. Civale 1, A.V. Silhanek 1, J.R. Thompson 2,3, K.J. Song 3, C.V. Tomy 4, and D. McK. Paul 4. 1 Comisión Nacional de Energía Atómica - Centro Atómico Bariloche, 8400 Bariloche, Argentina. 2 Oak Ridge National Laboratory, Oak Ridge, TN 37831-6061. 3 Department of Physics, University of Tennessee, Knoxville, TN 37996-1200. 4 Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom.

Presenting Author: L. Civale

We present studies of the vortex state magnetization of a single crystal of the nonmagnetic borocarbide superconductor YNi₂B₂C, with magnetic field H applied in the square basal plane of the tetragonal crystallographic unit cell. These measurements revealed a four-fold anisotropy in both reversible and irreversible magnetization when H is rotated within the basal plane. This p /2 periodicity occurs deep in the superconductive mixed state. The amplitude of the angular oscillation of the reversible response decreases with H, passes through zero and then reverses sign at a field well below H_c2. On the contrary, the oscillations of the irreversible signal (related to critical currents) decrease monotonically as H increases. In this crystal symmetry, an ordinary superconductive mass anisotropy (as in usual London theory) allows only a constant, isotropic response. However, the observed anisotropy is well explained by a generalized London model incorporating non-local electrodynamics [V.G. Kogan et al., Phys. Rev. B 54, 12386 (1996)], with parameters based largely on complementary experiments.

2PO1-42 Anomalous Angular Dependence of Vortex Melting Transition in Single Crystal Bi₂Sr₂CaCu₂O_8+d

Kazuo Kadowaki 1,2, Jovan Mirkovic 3, and Emiko Sugahara 1. 1 Institute of Materials Science, University of Tsukuba, Tsukuba 305-8573. 2 CREST, Japan Science and Technology Corporation (JST), Japan. 3 Faculty of Sciences, University of Montenegro, 812000 Podgorica, Montenegro, Yugoslavia.

Presenting Author: K. Kadowaki

The vortex states in oblique magnetic fields in single crystal Bi₂Sr₂CaCu₂O_8+d were investigated by means of resistivity measurements using Corbino geometry which excludes surface barriers and provides bulk resistivity data. The first order vortex lattice melting transition, identified by the sharp resistance drop, demonstrated the complex behavior in magnetic fields tilted away from the c-axis and several anomalies in resistivity have been discovered. As the in-plane field H_ab was increased, both melting transition temperature T_m and perpendicular component of melting field H_m//c decreased linearly indicating crossed pancake voritces lattice and Josephson vortex lattice as proposed recently by Koshelev. Above a certain value of H_ab*, T_m and H_m//c sharply changed behavior and became independent of the in-plane field H_ab suggesting quasi-decoupled vortex solid phase. However, as in-plane magnetic field is further increased, we identified several new vortex phases and novel H_m//c versus H_m//ab pghase diagram in the whole angular range including the exact orientation of H//ab, where the melting transition possibly changes its character from the 1st order to 2nd order phase transition.

2PO1-43 Monte Carlo Simulation of Layered High Temperature Superconductors

Andrew R. Price 1, Simon J. Cox 1, Hans Fangohr 1, and Peter J. de Groot 2. 1 Dept. Electronics and Computer Science. 2 Dept. Physics and Astronomy, University of Southampton, SO17 1BJ, United Kingdom.

Presenting Author: A.R. Price

We present results from Monte Carlo simulations of the vortex state in layered high temperature superconductors. We use a set of potentials derived from the Lawrence-Doniach free-energy functional which incorporates (i) intra-layer coupling (ii) inter-layer Josephson and electromagnetic interactions [1]. We report on a novel technique for performing an in-plane infinite lattice summation for the intra-layer interactions [2]. This provides a minimum 50,000 times faster speed-up in the simulations over previous naive methods which add periodic images in shells of increasing radius [3]. We present results of the numerical B-T phase diagram in both the pure and pinned system and obtain good agreement with available experimental/theoretical results.

[1] Kramer, C., 1996. Multi-pancake interactions and elastic properties of flux lines in layered superconductors. Physica C 256, pp. 236-244.

[2] Fangohr, H., Price, A., Cox, S., DeGroot, P.A.J. and Daniell, G.J., 1999. Efficient methods for handling long-range forces in particle-particle simulations. Submitted to J. Comp. Phys.

[3] Ryu, et. al., 1996. First-order melting and dynamics of flux lines in a model for YBa₂Cu₃O_7-d . Phys. Rev. B 54, pp. 1320-1333.

2PO1-44 Inter-layer phase difference and flux-line entanglement at first-order melting transition of high-T_c vortex systems

Yoshihiko Nonomura and Xiao Hu, National Research Institute for Metals, Tsukuba, Ibaraki 305-0047, Japan

Presenting Author: Y. Nonomura

The phase difference between the nearest-neighbor superconducting layers is directly related to the frequency of the Josephson plasma resonance, and therefore can easily be measured experimentally. Recently large jumps of this quantity are reported in BSCCO on the melting line and the second-peak line. In order to clarify the mechanism of such phase transitions in high-T_c vortex systems, we investigate the three-dimensional frustrated XY model by large-scale Monte Carlo simulations. We analyze systems of various anisotropy constants and flux densities. We find that the jump of the phase difference at the melting temperature is proportional to the flux density and the square of the anisotropy constant. This scaling relation does not hold well for larger anisotropy constants, where the value of jumps saturate to experimental ones for BSCCO. The jump on the second-peak line is also studied by introducing point pins to the present model. The jump on the melting line is suppressed when the density of point pins is increased. We also find that the percentage of entangled flux lines abruptly changes on the first-order transition lines. This mechanism is specific to melting transitions in three dimensions, and is consistent with sharp jumps of the inter-layer phase difference.

2PO1-45 Simulated phase diagram of high-T_c vortex systems with point pins

Yoshihiko Nonomura and Xiao Hu, National Research Institute for Metals, Tsukuba, Ibaraki 305-0047, Japan

Presenting Author: Y. Nonomura

Point pins play essential roles in determining the phase diagram of high-T_c vortex systems. As a model of such systems, we utilize the three-dimensional frustrated XY model. Point pins are introduced as randomly-distributed weak plaquettes in each superconducting layer. We measure the helicity modulus along the c-axis (HMc), the specific heat, the structure factor and the percentage of entangled flux lines [1] by large-scale Monte Carlo simulations. We find that the phase diagram of this system is described as follows: (1) The Bragg glass (BG) phase is characterized by the Bragg peaks for a triangular lattice and a finite HM_c (i.e. superconducting). (2) The vortex glass (VG) phase is represented by a finite HM_c without Bragg peaks. (3) Both the HM_c and Bragg peaks vanish in the vortex liquid (VL) phase. (4) Both the VL-BG and VG-BG transitions are of first order characterized by the delta-function peak of the specific heat and the sharp jump of the percentage of entangled flux lines. (5) The VL-VG transition is of second order characterized by the smooth vanishing of the HM_c. These findings are consistent with recent experiments on YBCO and BSCCO.

[1] Y. Nonomura, X. Hu, and M. Tachiki, Phys. Rev. B 59, R11657 (1999).

2PO1-46 Vortex Glass Transition versus Vortex Percolation

Michael Ziese, Department of Superconductivity and Magnetism, Institut für Experimentelle Physik II, Universität Leipzig, Linnéstrasse 5, 04103 Leipzig, Germany

Presenting Author: M. Ziese

In experimental studies of vortex dynamics in disordered high temperature superconductors a scaling of the transport properties is observed. This has often been interpreted within the vortex-glass model. However, the experimentally determined critical exponents are far from universal and show a systematic dependence on the pinning strength. Here, these findings are interpreted within the percolation model of vortex dynamics. Since the percolation transition is a second order transition, scaling relations similar to those of the vortex-glass model can be derived. The non-universality of the critical exponents is related to the real material structure via a bond-distribution function. The shape of this distribution curve is determined as a function of the Larkin pinning-length from existing experimental data.

2PO1-47 E-j Relation in the Vortex-Melting Region of High Temperature Superconductors

Hao Jin, Lin Chen, Yu Heng Zhang, Structure Research Laboratory, USTC, Hefei 230026, P.R. China

Presenting Author: H. Jin

It seems that in the vortex-melting region, the vortex-glass model, collective-pinning model and logarithmic j-dependent barrier model, etc., are not suitable to describe the E-j relation and the magnetic relaxation in the flux dynamics of the high temperature superconductors, however, the pinning still exists in this temperature region. This paper calculates the E-j relation under the Bean's model while considering the backward hopping (which is the hopping from low barriers to high ones). The theoretical results show that both positive and negative curvature can appear in the lnE-lnj curves. We also give the judgement for either positive or negative curvature appearing. Experimentally, the lnE`lnj curves show only single curvature in most cases, the origin of that has also been discussed in the paper.

2PO1-48 Nonuniform state in 2D superconductors: structure of the vortex lattice

Manuel Houzet and Alexandre Buzdin, Laboratoire de Physique Théorique, Université Bordeaux I, F-33405 Talence Cedex, France

Presenting Author: M. Houzet

In 2D layered superconductors under a high magnetic field, when the upper critical field H_c2 is determined by both the orbital and Pauli effects, a new kind of solutions for the superconducting order parameter could be realized at low temperature. They correspond to higher Landau levels (LLs) and they are the generalization of the nonuniform Fulde-Ferrel-Larkin-Ochinnikov (FFLO) state in the presence of the orbital effect.

The structure of the vortex lattice in the new phases should be obtained by a linear superposition of such solutions, at some fixed LL. In order to determine it, we have derived a generalized Ginzburg-Landau functional near the tricritical point of the FFLO transition, when weak orbital and strong Pauli effects are present. We have found that the stability of the structures does not depend anymore on the Abrikosov parameter beta_A and we have determined the new criterion.

At this stage, we have compared the vortex lattices resulting from the generalisation of the Abrikosov lattice at higher LL, in the square and hexagonal symmetry. We have found that near the tricritical point, when the solution corresponds to lowest LL (n=0), the more stable lattice remains the triangular one, whereas it becomes square at n=1 LL.

2PO1-49 Experimental evidence of the decoupling line in Bi2212 single crystals by electronic transport measurements

David Thopart, Charles Simon, Vincent Hardy, and Antoine Maignan, Laboratoire CRISMAT, ISMRA, CNRS, UMR 6508, Caen, France

Presenting Author: D. Thopart

Both in-plane r _ab and out-of-plane r _c resistivities have been measured on Bismuth 2212 single crystals with a magnetic field applied along the c-axis direction. The temperature dependence of the resistivity ratio, r _ab/r _c, is the one predicted by Koshelev et al. for the behavior of pancake « vortex gas » [1]. In this model, the c-axis dissipation is assumed to arise from incoherent planar diffusive motion of the decoupled pancake vortices and the resulting phase slips between the neighboring Cu-O layers.

In order to measure lower dissipation levels, we have performed ac susceptibility measurements. We have then observed a thermally activated behavior as it is predicted by the loop creation model and we have found that the high temperature limit of the thermally activated behavior corresponds to the low temperature limit of the Koshelev’s model. This latter is also caracterized by the onset of the in-plane resistivity drop. Consequently, our data suggest that this line is a dimensional cross-over which describes the decoupling of the liquid state into a decoupled pancake « vortex gas » state.

[1] Koshelev et al., Phys. Rev. Lett 76, 1340, (1996).