Flux Line Lattice Research Articles

Step change in equilibrium magnetization across the peak effect in 2H-NbSe 2

Isothermal magnetization measurements across the peak effect (PE) region in a clean superconducting crystal of 2H-NbSe 2 reveal a step increase in the equilibrium magnetization suggestive of a first order phase transition. We relate this observation to the entropy change associated with the occurrence of order–disorder transformation across the PE in a weakly pinned flux line lattice (FLL).

Thermally Activated Depinning of a Driven Flux Line Lattice

We have performed simultaneous measurements of the resonance frequency, damping and resistivity of vibrating Y123 thin films to study the behavior of the depinning of a driven flux line lattice (FLL). The measurements show: (i) the depinning temperature remains unaffected up to a current density of 106 A/m2; (ii) at higher currents the depinning temperature and the width of the dissipation peak as a function of temperature decrease whereas its height increases; (iii) at high enough currents the dissipation at the depinning saturates. The observed “motional narrowing” appears to be in agreement with recently published ideas on a driven FLL with disorder recovering a quasi-ordered or “Bragg-glass” state by sliding it at high enough velocities. The dissipation peak measured at high currents can be quantitatively understood with a diffusion model without free parameters.

Critical current density in highly biaxially-oriented YBCO films: Can we control J/sub c/(77 K) and optimize up to more than 10/sup 6/ amp/cm/sup 2/?

High-J/sub c/ YBCO conductors of the second generation are based on processing of YBCO highly-textured film, It is important to develop deposition techniques to control and optimize flux pinning in such films. The dominant contribution to net pinning force in YBCO films is from the growth-induced dislocations. The average density of such dislocations in low-angle tilt domain boundaries can exceed 10/sup 11//cm/sup 2/. For 2D fluxline lattice (FLL) correlated disorder induced by linear defects, a simplified approach is proposed to get some optimization criteria for the critical current density as a function of domain size, misorientation angle, etc. During YBCO films deposition onto highly-textured buffer layers growth dislocation structures can be varied, Comparison of the high-resolution transmission electron microscopy (HREM) data and J/sub c/(H) angular dependencies for CeO/sub 2/-buffered YBCO films exhibit how the dislocation distribution can affect the angular J/sub c/(H) behavior.

Numerical simulations of elastic properties of flux-line lattices in high-T/sub c/ superconductors

We propose a quantitative model of the effective interaction between the magnetic flux-lines in a layered superconductor. It is derived from the Lawrence-Doniach model with all of its parameters derivable from experiments. Numerical simulations are performed using the Langevin dynamics technique for parameters suitable for Bi-2212. We studied the elastic properties of flux line lattices with various values of interlayer coupling strength and pinning strengths. We show that the softening of the flux-line lattices with increasing temperature is mainly due to the increase of configurational entropy of the lattice. The calculated results show good agreement with experimental observations and provide a unique way to study the properties of flux-line lattices with random pinning.

Theoretical study on vortex glass-liquid transition in pinned superconductors

The vortex glass-liquid transition in pinned superconductors is studied theoretically from the viewpoint of thermal depinning of flux lines. It is clarified that this depinning phenomenon is a transition of the second order. This result is consistent with the fact that the scaling of the current-voltage curves is well explained by the theoretical model of flux creep and flow. It is also found that the degree of disorder of the flux line lattice decreases abruptly with elevating temperature above the transition temperature. This agrees qualitatively with the observation of flux lines using a Lorentz microscope.

Interstitials, vacancies, and dislocations in flux-line lattices: A theory of vortex crystals, supersolids, and liquids

We study a three-dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial, and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials---which are always present in the liquid state---allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally identical to that of the ``flux-line hexatic'' that is a candidate ``normal'' hexatically ordered vortex liquid state.

Flux-line entanglement as the mechanism of melting transition in high-temperature superconductors in a magnetic field

The mechanism of the flux-line-lattice (FLL) melting in anisotropic high-${T}_{c}$ superconductors in $\mathbf{B}\ensuremath{\Vert}\mathbf{c}^$ is clarified by Monte Carlo simulations of the three-dimensional frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature ${T}_{m},$ while no sharp change can be found in the number and size distribution of vortex loops around ${T}_{m}.$ Therefore, the origin of this melting transition is the entanglement of flux lines. Scaling behaviors of physical quantities are consistent with the above mechanism of the FLL melting. The Lindemann number is also evaluated without any phenomenological arguments.

First-order vortex lattice melting in twinnedNdBa2Cu3O7−ysingle crystals

We report on the observation of a first-order melting transition of the flux-line lattice in a twinned ${\mathrm{NdBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}y}$ single crystal by transport (for both $H\ensuremath{\parallel}c$ and $H\ensuremath{\parallel}\mathrm{ab}$ directions) and magnetization measurements. The position of kink and hysteresis in resistance and magnetization jump coincides in the $B\ensuremath{-}T$ plane. The observed melting transition is a strong function of ${\mathrm{O}}_{2}$ partial pressure during growth. The first-order transition becomes continuous and the peak in critical current density first emerges with oxygen partial pressure \ensuremath{\geqslant}0.07%. Our results demonstrate the existence of a first-order melting transition in a twinned RE-123 system containing rare-earth magnetic ions.

Non-resonant microwave absorption studies in Bi 1.6Pb 0.4Sr 2Ca 2Cu 3O 10+ x

Non-resonant microwave absorption (NRMA) studies have been carried out on Bi 1.6Pb 0.4Sr 2Ca 2Cu 3O 10+ x pellets sintered for different durations varying from 24 to 168 h by using EPR technique. A detailed study of the temperature dependence of the NRMA signal amplitude, peak-to-peak width, hysteresis area has been carried out. Apart from showing a flux line lattice (FLL) melting temperature T m( B) (60–70 K), it is interesting to note that hysteresis loops showed the anomalous magnetic behaviour in the entire temperature regions even far below the fluctuation regime. The results are discussed in terms of several current models for the NRMA effects as well as for its anomalous magnetic hysteresis behaviour.

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in \epsilon=4-D. At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value p_c=6/\pi\sqrt{\epsilon}. For p<p_c the medium is always flat. Critical exponents are calculated in a double expansion in \mu=p^2/p_c^2-1 and \epsilon=4-D and fulfill the scaling relations of random field models.

Thermal depinning of flux lines in superconductors

The thermal depinning of flux lines on the irreversibility line is investigated from a viewpoint of thermodynamics using the coherent potential approximation theory, a kind of statistical theory for flux pinning. The effect of thermal activation is approximately introduced by making the pinning potential shallow following the theoretical scheme by Yamafuji et al. It is shown that the thermal depinning is the transition of the second order. Since the vortex glass–liquid transition, which is considered to be identical with the thermal depinning, is originally predicted to be the second-order transition, the present theoretical result is reasonable. The present result also suggests that the irreversibility line observed at higher temperatures and at lower fields than the critical point for weakly pinned superconductors is also the transition line of the second order. In addition, it is shown that the degree of disorder of the flux line lattice decreases fast, suggesting a quick recovery of the order of the lattice with elevating temperature above the critical temperature.

Flux-Line Lattice Structures in UntwinnedYBa2Cu3O7−δ

A small angle neutron scattering study of the flux-line lattice in a large untwinned single crystal of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is presented. In fields parallel to the $c$ axis, diffraction spots are observed corresponding to four orientations of a hexagonal lattice, distorted by the $a\ensuremath{-}b$ anisotropy. A value for the anisotropy, the penetration depth ratio, of ${\ensuremath{\lambda}}_{a}/{\ensuremath{\lambda}}_{b}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.18\left(2\right)$ was obtained. The high quality of the data is such that second-order diffraction is observed, indicating a well ordered FLL. With the field at 33\ifmmode^\circ\else\textdegree\fi{} to $c$, a field dependent reorientation of the lattice is observed around 3 T.

Vacancy and interstitial defects in the vortex lattice of superconducting thin films

A method developed previously for the lattice of infinitely long parallel Abrikosov vortices in type-II superconductors is extended to vortices in thin superconducting films. The self-energy and interaction energy of vacancies and interstitials in the triangular lattice of vortices in the film are calculated within London theory. Various stable and metastable equilibrium configurations of the flux-line lattice around such point defects are found, similar to the result for long vortex lines. In particular, the vacancy with highest (sixfold) symmetry usually does not exhibit the lowest energy, and the defect energies are very small compared with the binding energy of one vortex due to the relaxation of the surrounding vortex lattice. The interaction between point defects is weak, but is attractive as opposed to the long parallel Abrikosov vortex case where the defect interaction can be repulsive in some cases.

Neutron Scattering from the Flux Line Lattice in the Cubic (K, Ba)BiO3 Superconductor

Small Angle Neutron Scattering has been used to observe diffraction from the flux line lattice in the fully isotropic (K, Ba)BiO3high Tcsuperconductor. We show that the flux lines are ordered into a hexagonal lattice at low field (H < He∼ 0.6T ≪ Hg (0) where Hgis the second order vortex glass transition field). The diffracted intensity continuously drops to zero as the field is increased towards He. Those observations are in good agreement with recent theoritical works which suggested that the formation of dislocations becomes favorable above Heleading to a glassy structure. The field Helies close to the onset of the second peak in magnetization measurements indicating that this peak is related to the change in the vortex structure.

Flux-Line Entanglement as the Mechanism of FLL-Melting Transition in Anisotropic HTSC

The mechanism of the flux-line-lattice (FLL) melting in anisotropic high-Tcsuperconductors inB ‖ ĉis clarified by Monte Carlo simulations of the 3D frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature Tm, while no sharp change can be found in the number and size distribution of vortex loops around Tm. Therefore, the origin of this melting transition is the entanglement of flux lines. Scaling behaviors of the melting temperature Tmare consistent with this one-dimensional character of the entanglement mechanism of the FLL melting. That is, Tmdoes not depend on the system size in the ab plane, while it is scaled by the system size along the c axis, Lc, as Tm(Lc) − Tm(∞) ∝ Lc-d, d = 1.

First Order-Like Out-of-Plane Resistive Transition in YBa2Cu3O7−δ for B Exactly Parallel to ab-Planes

Melting transition of a flux line lattice// ab -planes has been studied in twinned YBa 2 Cu 3 O 7−δ single crystals using transport measurements along the c -axis. In contrast to previously studied geometry with field and current in planes (W.K. Kwok et al., Phys. Rev. Lett. 72 , 1088 (1994)), a step-like c -axis resistive transition has been found for exact field alignment along ab -planes. The angular dependence of ρ c with rotation of the crystal around the c -axis was studied. The results show that below the resistive step, the pinning force is anomalously increased when the field is aligned along ac ( bc )-crystal facets.

Hysteresis in the field-induced magnetic structure in TmNi 2B 2C

Using small-angle neutron scattering we have studied the flux line lattice and the magnetic structure in TmNi 2B 2C. With an applied field parallel to the crystalline c-axis several magnetic and flux line lattice symmetry transitions have been reported. The subject of this paper is the field-induced magnetic structure and how it is influenced by the flux line lattice symmetry. We find that the domain splitting of the field-induced magnetic structure is hysteretic, and appears to be determined by the history of the flux line lattice symmetry.

Nonlinear flux-line dynamics in vanadium films with square lattices of submicron holes

Commensurability effects between the superconducting flux-line lattice and a square lattice (period d=1thinsp{mu}m) of submicron holes (diameter D=0.4thinsp{mu}m) in 1500 {Angstrom} vanadium films were studied by atomic-force microscopy, dc magnetization, ac susceptibility, magnetoresistivity, and I-V measurements. Peaks in the susceptibility and critical current at matching fields are found to depend nonlinearly upon the value of external ac field or current, as well as the inferred symmetry of the flux-line lattice. {copyright} {ital 1999} {ital The American Physical Society}

Collective pinning of a flux-line lattice with screw dislocations

The energy of screw dislocations of a flux-line lattice in Type-II superconductors is calculated taking account of dispersion of the tilt modulus. On the basis of this calculation, the collective-pinning theory for the plastic case, proposed by Mullock and Evetts, leads to correlation lengths of a flux-line lattice much shorter than that for the elastic case leads, and much better theoretical fits to experimental results in Nb3Ge and 2H-NbSe2−xSxare obtained. Furthermore, the intermediate state between three-dimensional disorder and two-dimensional disorder in a flux-line lattice is predicted when the screw dislocations trigger the dimensional crossover.

Isothermal Elastic Constants of Flux-Line Lattice in Layered Superconductors

A model of the effective interaction between the magnetic flux-lines in a layered superconductor is derived from the Lawrence–Doniach model. We show analytically that the intralayer interaction energy can be evaluated using the Ewald summation technique. The melting of flux line lattices is studied using Langevin dynamics simulation of the model with various values of interlayer coupling strength and pinning intensities. The thermal fluctuation terms of the isothermal shear modulus are found to increase sharply at the melting transition temperature for systems with or without pinning, while the structural order parameters were close to zero at all temperatures for systems with strong pinning. The melting of the pinned flux-line lattice is discussed in the context of its elastic properties.