Flux Line Lattice Research Articles

Statics and dynamics of the vortex lattice in high-T c superconductors

Some properties of the flux-line lattice in conventional and high-Tc superconductors are reviewed, with particular stress on phenomenological theories, magnetization curves, vortex lattice in films, nonlocal elasticity, phase diagram of vortex arrangements, vortex dynamics, and geometry effects.

Metastable states of a flux-line lattice studied by transport and small-angle neutron scattering

Flux-line lattice (FLL) states have been studied using transport measurements and small-angle neutron scattering in low-${T}_{c}$ materials. In $\mathrm{Pb}\text{\ensuremath{-}}\mathrm{In}$, the bulk dislocations in the FLL do not influence the transport properties. In $\mathrm{Fe}$-doped ${\mathrm{NbSe}}_{2}$, transport properties can differ after a field cooling (FC) or a zero field cooling (ZFC) procedure, as previously reported. The ZFC FLL is found ordered with narrow Bragg peaks and is linked to a linear $V(I)$ curve and to a superficial critical current. The FC FLL pattern exhibits two Bragg peaks and the corresponding $V(I)$ curve shows an $\mathrm{S}$-shape. This can be explained by the coexistence of two ordered FLLs slightly tilted from the applied field direction by different superficial currents. These currents are wiped out when the transport current is increased.

On the imaging of the flux-line lattice of a type-II superconductor by soft X-ray absorption microscopy

A new method is proposed for the imaging of the flux-line lattice of a type-II superconductor by soft X-ray absorption microscopy. It is shown that the method is very demanding but probably realisable in the foreseeable future. The new method has the potential to image in real space static and dynamical properties of the flux-line lattice at arbitrary external fields and with single-flux-line resolution.

INVERSE MELTING OF VORTEX LATTICE IN LAYERED SUPERCONDUCTORS

Using molecular dynamic simulations for the melting transition of a flux line lattice(FLL) with point disordered pinnings, thermal fluctuations and magnetic interactions between pancake vortices, we study the disorder-driven melting transition from a disentangled and ordered Bragg glass (BG) to an entangled amorphous vortex glass (VG) or a vortex liquid (VL) in the pinning strength-temperature phase diagram. A portion of the BG region is found to be sandwiched in between the VG phase at lower temperatures and VL phase at higher temperatures, exhibiting inverse melting behavior observed recently on BSCCO crystals.

Topological Defects in Moving Charge Density Waves and Flux Line Lattices

Transport phenomena of charge density waves and flux line lattices under quenched randomness are investigated based on the three-dimensional driven random-field XY model at zero temperature. We pay special attention to the role of topological defects, vortex loops, and find that loops are bounded in small region and its number density decreases exponentially with the driving force in relatively high velocity regime. That is, the system behaves as in thermal equilibrium state at temperature proportional to the inverse of the driving force.

Critical currents in vicinalYBa2Cu3O7−δfilms

Most measurements of critical current densities in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films to date have been performed on films where the $c$ axis is grown normal to the film surface. With such films, the analysis of the dependence of the critical current, ${j}_{c}$, on the magnetic field angle is complex. The effects of extrinsic contributions to the angular field dependence of ${j}_{c}$, such as the measurement geometry and disposition of pinning centers, are convoluted with those intrinsically due to the anisotropy of the material. As a consequence of this, it is difficult to distinguish between proposed flux line lattice structure models on the basis of angular critical current density measurements on $c$-axis films. Films grown on miscut (vicinal) substrates have a reduced measurement symmetry and thus provide a greater insight into the critical current anisotropy. In this paper previous descriptions of the magnetic field angle dependence of ${j}_{c}$ in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ are reviewed. Measurements on $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films grown on a range of vicinal substrates are presented and the results interpreted in terms of the structure and dimensionality of the flux line lattice in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. There is strong evidence for a transition in the structure of the flux line lattice depending on magnetic field magnitude, orientation, and temperature. As a consequence, a simple scaling law cannot, by itself, describe the observed critical current anisotropy in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. The experimentally obtained ${j}_{c}(\ensuremath{\theta})$ behavior of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is successfully described in terms of a kinked vortex structure for fields applied near parallel to the $a\text{\ensuremath{-}}b$ planes.

Clean-limit pair breaking and two-dimensional vortex dynamics in ferromagnet-superconductor heterostructures

Superconductivity in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ films of thickness ${d}_{\mathrm{Y}}<500\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ sandwiched between ferromagnetic and nonmagnetic epitaxial layers has been probed. The irreversibility temperature ${T}_{\mathrm{irr}(\mathrm{H})}$ in the vortex state maps onto a clean-limit pair-breaking temperature ${T}_{\mathrm{c}(\mathrm{H})}$, and a universal relation exists between the pair-breaking field ${H}_{\mathrm{pb}}$ and an effective thickness ${d}_{\mathrm{eff}}(<{d}_{\mathrm{Y}})$ of the superconductor. The vortex response in these two-dimensional (2D) films indicates a crossover temperature $T*$, which separates two regimes of flux motion controlled by formation of dislocations $(T>T*)$, and migration of preexisting dislocations and dislocation pairs $(T<T*)$ in the 2D flux line lattice.

Flux-Line Lattice Distortion inPrOs4Sb12

We report that the flux-line lattice in the cubic superconductor Pr(Os4Sb12 is strongly distorted from an ideal hexagonal lattice at very low temperatures in a small applied field. We attribute this to the presence of gap nodes in the superconducting state on at least some Fermi-surface sheets.

Supercooled vortex liquid and quantitative theory of melting of the flux-line lattice in type-II superconductors

A metastable homogeneous state exists down to zero temperature in systems of repelling objects. Zero ''fluctuation temperature'' liquid state therefore serves as a (pseudo) ''fixed point'' controlling the properties of vortex liquid below and even around melting point. There exists Madelung constant for the liquid in the limit of zero temperature which is higher than that of the solid by an amount approximately equal to the latent heat of melting. This picture is supported by an exactly solvable large $N$ Ginzburg - Landau model in magnetic field. Based on this understanding we apply Borel - Pade resummation technique to develop a theory of the vortex liquid in type II superconductors. Applicability of the effective lowest Landau level model is discussed and corrections due to higher levels is calculated. Combined with previous quantitative description of the vortex solid the melting line is located. Magnetization, entropy and specific heat jumps along it are calculated. The magnetization of liquid is larger than that of solid by $% 1.8%$ irrespective of the melting temperature. We compare the result with experiments on high $T_{c}$ cuprates $YBa_{2}Cu_{3}O_{7}$, $DyBCO$, low $% T_{c}$ material $(K,Ba)BiO_{3}$ and with Monte Carlo simulations.

Measurement of the shear strength of a charge density wave.

We have explored the shear plasticity of charge density waves (CDWs) in NbSe3 samples with cross sections having a single microfabricated thickness step. Shear stresses along the step result from thickness-dependent CDW pinning. For small thickness differences the CDW depins elastically at the volume average depinning field. For large thickness differences the thicker, more weakly pinned side depins first via plastic shear, and shear plasticity contributes substantial dissipation well above the depinning field. A simple model describes the qualitative features of our data and yields a value for the CDW's shear strength of approximately 9.5 x 10(3) Nm(-2). This value is orders of magnitude smaller than the CDW's longitudinal modulus but much larger than corresponding values for flux line lattices, and in part explains the relative coherence of the CDW response.

High-field state of the flux-line lattice in the unconventional superconductorCeCoIn5

Ultrasound velocity measurements of the unconventional superconductor CeCoIn_5 with extremely large Pauli paramagnetic susceptibility reveal an unusual structural transformation of the flux line lattice (FLL) in the vicinity of the upper critical field. The transition field coincides with that at which heat capacity measurements reveal a second order phase transition. The lowering of the sound velocity at the transition is consistent with the collapse of the FLL tilt modulus and a crossover to quasi two-dimensional FLL pinning. These results provide a strong evidence that the high field state is the Fulde-Ferrel-Larkin-Ovchinikov phase, in which the order parameter is spatially modulated and has planar nodes aligned perpendicular to the vortices.

Influence of twin boundaries on the flux-line-lattice structure inYBa2Cu3O7−δ: A small-angle neutron scattering

The influence of twin boundaries (TB) on the flux-line-lattice (FLL) structure was investigated by small-angle neutron scattering (SANS). $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystals possessing different TB densities were studied. The SANS experiments show that the TB strongly modify the structure of the FLL. The flux lines meander as soon as the magnetic field makes an angle with the TB direction. According to the value of this angle but also to the ratio of the flux lines density over the TB density, one observes that the FLL exhibits two different unit cells in the plane perpendicular to the magnetic field. One is the classical hexagonal and anisotropic cell while the other is affected by an additional deformation induced by the TB. We discuss a possible relation between this deformation and the increase of the critical current usually observed in heavily twinned samples.

Displacement profile of charge density waves and domain walls at critical depinning.

The influence of a strong surface potential on the critical depinning of an elastic system driven in a random medium is considered. If the surface potential prevents depinning completely the curvature C of the displacement profile exhibits at zero temperature a pronounced rhombic hysteresis curve of width 2f(c) with the bulk depinning threshold f(c). The hysteresis disappears at nonzero temperatures if the driving force is changed adiabatically. If the surface depins by the applied force or thermal creep, C is reduced with increasing velocity. The results apply, e.g., to driven magnetic domain walls, fluxline lattices, and charge-density waves.

Phase transition between two kinds of flux-line lattice in high- Tc superconductors in a tilted field

Structures of flux-line lattices (FLL) in vortex states of high- T c superconductors in a tilted field are directly studied by Monte Carlo simulations of the three-dimensional anisotropic XY model, where only Josephson couplings are considered between superconducting layers. A nontrivial structural transition between the Josephson-dominant and Abrikosov-dominant FLL phases occurs as the tilting angle of the external field is increased at low enough temperatures. A similar phase transition is observed by varying the anisotropy parameter with a fixed external field. A finite latent heat at the transition point indicates that this phase transition is of first order.

AC-susceptibility of superconducting films with a periodic pinning array

We use AC-susceptibility measurements to study the dynamic response of vortices in a Pb thin film with a periodic array of antidots. In the linear regime, from the field dependence of the AC-penetration depth λ we determine the curvature of the pinning potential well α for different matching fields. For applied fields H below the first matching field H 1, α reaches its highest value due to the strong vortex localization at the pinning sites. For H 1< H< H 2, the metallic-like behavior of interstitial vortices gives rise to a reduction of α and a further decrease of the pinning strength is observed for H 2< H< H 3. However, for H 3< H< H 4, a reentrance in the pinning strength appears, due to a specific configuration of the flux line lattice which strongly restricts the mobility of vortices.

Some properties of the ideal Ginzburg–Landau vortex lattice

Some features of the vortex lattice in ideal type-II superconductors are calculated from Ginzburg–Landau theory for the entire ranges of applied magnetic fields H c2⩽ H⩽ H c2 or induction 0⩽ B⩽ μ 0 H c2 and Ginzburg–Landau parameters κ⩾2 −1/2. Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field B( x, y) and magnetization M( H, κ) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting and fitting expressions are presented.

The effect of chemical inhomogeneities on the pinning properties of Bi2212 singlecrystals

We have carried out a detailed characterization of chemical inhomogeneities in Bi2212 singlecrystals grown by a floating zone method. According to the chemical analyses using WDS,there are two types of inhomogeneities; one with linear structures extending toward thea-axis, and another with sheet-like structures that lying along thea-axis.The line defects relate to compositional inhomogeneities, such as Ca-enriched or Ca-deficientregions, with widths ranging from a few nanometres to micrometres and lie parallel to the crystala-axis. From the observation of local flux line arrangement using a Bitter decorationtechnique and a magneto-optical imaging technique, the flux line arrangement atthe defect region is largely affected by the type of nonstoichiometry involved.We found that the flux-line lattice at the Ca-enriched region has a hexagonalorder with small scattering, while that at the Ca-deficient region is amorphous.On the other hand, the crystal with sheet-like inhomogeneities showed a ‘zebra-like’ fluxpenetration and trapping behaviour. This result suggests that the samples arecomposed of two kinds of regions with completely different pinning properties.

Effect of varying material anisotropy on critical current anisotropy in vicinal YBa2Cu3O7−δ thin films

The high Tc cuprate superconductors are noted for their anisotropic layered structure, certain of these materials indeed tend toward the limit of a Lawrence–Doniach superconductor. However, YBa2Cu3O7−δ has a smaller anisotropy than would be expected from its interlayer spacing. This is due to the cuprate chains in the structure. To investigate the influence of the chain oxygen on transport properties critical current versus applied field angle measurements were performed on fully oxygenated and deoxygenated YBa2Cu3O7−δ thin films and optimally oxygenated Y0.75Ca0.25Ba2Cu3O7−δ thin films. The films were grown on 10° miscut SrTiO3 substrates to enable the intrinsic vortex channeling effect to be observed. The form of the vortex channeling minimum observed in field angle dependent critical current studies on the films was seen to depend on film oxygenation. The vortex channeling effect is dependent on a angular dependent crossover to a string-pancake flux line lattice. The results obtained appear to be consistent with the prediction of [G. Blatter, M. V. Feigelman, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994)] that increased superconducting anisotropy leads to the kinked string-pancake lattice existing over a smaller angular range.

Magnetoacoustic measurements on pure and Zn doped YBCO crystals

Abstract Investigations on the temperature dependence in the range from 4 to 100 K of the ultrasonic attenuation α ( T , B ) and the relative change Δ v ( T , B )/ v of the sound velocity for various applied magnetic fields have been made. The ultrasonic attenuation α was measured by the pulse-echo technique and the relative change of the sound velocity Δ v / v by a phase-comparison method. The measurements serve for the examination of the elastic behaviour of the flux line lattice (FLL) of pure and Zn doped YBCO crystals and YBCO/Ag composites. These crystals are important for applications as permanent magnets. In the framework of the thermally assisted flux flow model (TAFF) the activation energies U ( B ) were deduced from the ultrasonic data.

Observation of the flux line lattice and crystal defects in Bi–Sr–Ca–Cu–O single crystals

Abstract We have observed flux line lattice (FLL) structure in two different types of Bi 2 Sr 2 CaCu 2 O 8+ δ (Bi-2212) single crystals with different pinning by using a Bitter decoration technique. We have also observed the microstructure and analyzed local chemical composition with wave dispersive spectroscopic analyses. In a low J c sample, we found two types of line defects, one with Ca-rich and the other with Ca-deficient. These defects extended almost parallel to the growth direction, which caused a distortion in the FLL structure. In contrast, no such defects were observed in the matrix in a high- J c sample, and a relatively ordered FLL was observed.