Vortex Fluctuations Research Articles

Magnetic friction due to vortex fluctuation

We use Monte Carlo and molecular dynamics simulation to study a magnetic tip-sample interaction. Our interest is to understand the mechanism of heat dissipation when the forces involved in the system are magnetic in essence. We consider a magnetic crystalline substrate composed of several layers interacting magnetically with a tip. The set is put thermally in equilibrium at temperature T by using a numerical Monte Carlo technique. By using that configuration we study its dynamical evolution by integrating numerically the equations of motion. Our results suggest that the heat dissipation in this system is closed related to the appearing of vortices in the sample.

Superconducting Properties of Iodine-Intercalated Bi2Sr2Ca2Cu3O10+x

The superconducting properties of iodine-intercalated high-temperature superconducting Bi2Sr2Ca2Cu3O10+x phase (Bi-2223) were systematically studied. It was found that for samples containing a significant amount of Bi2Sr2CaCu2O8+x, iodine intercalation results in the dramatic decrease of the inter-granular critical current density, as well as a significant decrease of the critical temperature (Tc), the critical current density in the grains (Jcg), and of the amount of Bi-2223. For samples with a large amount of Bi-2223, Tc changes insignificantly, whereas Jcg can even increase. We argue that the different behavior of the superconducting parameters is the result of various oxygen concentrations, and we explain the effect of iodine intercalation based on the parabolic dependence between Tc and the number of holes per CuO2 layer. The H(T) curves (determined from the peak position in the loss signal of ac susceptibility) for intercalated samples deviate significantly from the quasi 2D-like behavior, pointing toward an enhancement of the 3D fluctuations of vortices. For the change in the values and dimensionality of the flux pinning in the process of the intercalation, we attempted a qualitative explanation based on the models proposed in literature.

Thermal Fluctuations of Vortex Matter in Trapped Bose-Einstein Condensates

We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He; the latter is relevant to a rotating trapped Bose-Einstein condensate. In the former case, we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tensionless vortex tangle near the edge of the trap. At higher temperatures an intermediate tensionful vortex liquid located between the vortex solid and the vortex tangle may exist.

Slowing down the Josephson vortex lattice inBi2Sr2CaCu2O8+δwith pancake vortices

We study theoretically and experimentally the influence of pancake vortices on motion of the Josephson vortex lattice in layered high-temperature superconductors. Mobility of the Josephson vortices in layered superconductors is strongly suppressed by a small amount of pancake-vortex stacks. Moving Josephson vortex lattice forces oscillating zigzag deformation of the pancake-vortex stacks contributing to damping. The salient feature of this contribution is its nonmonotonic dependence on the lattice velocity and the corresponding voltage. Maximum pancake effect is realized when the Josephson frequency matches the relaxation frequency of the stacks. The pancake-vortex damping is strongly suppressed by thermal fluctuations of the pancake vortices. This theoretical picture was qualitatively confirmed by experiments on two mesas prepared out of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ whiskers. We found that the Josephson-vortex flux-flow voltage is very sensitive to small $c$-axis magnetic field. The pancake-vortex contribution to the current indeed nonmonotonically depends on voltage and decreases with increasing temperature and in-plane magnetic field. We also found that irradiation with heavy ions has no noticeable direct influence on motion of the Josephson vortices but dramatically reduces the pancake-vortex contribution to the damping of the Josephson vortex lattice at low temperatures.

Three-dimensional and two-dimensional high field vortex fluctuations in deoxygenated YBa 2Cu 3O 7− x depending on the vicinity of Tc( H)

We analyzed reversible magnetization data, M versus T curves, of three single crystals of YBa 2Cu 3O 7− x (Y123), with superconducting transition temperatures T c = 62.5 ( x = 0.35), 52 ( x = 0.5), and 41 K ( x = 0.6). M versus T curves of each sample exhibited a field independent crossing point, M( T ∗), occurring close to the superconductor critical temperature. These crossing points were shown to be due to fluctuations of vortices. Besides the reversible data of each sample were shown to obey a two-dimensional diamagnetic lowest-Landau-level (LLL) fluctuation theory, it is shown here that the data, within a temperature region where the crossing points occur for two samples (62.5 K and 52 K), are also explained by a three-dimensional version of this fluctuation theory. Since the crossing points for these two samples occur close to T c, these are interpreted as been due to three-dimensional vortex fluctuations instead two-dimensional ones. An expression for the field independent magnetization, M( T ∗), which is expected to occur at the crossing point of the various M versus T curves, is obtained for the case of three-dimensional vortex fluctuations, and compared to the experimental values of M( T ∗). This comparison produced consistent values for the coherence length along the c-axis of the samples with T c = 62.5 and 52 K, solving an inconsistent result previously published, when experimental values of M( T ∗) were compared with an expression obtained from two-dimensional vortex-fluctuations. The results of the present work show that, despite the fact that two-dimensional LLL fluctuations scaling is obeyed in a much wider temperature range for two studied samples ( T c = 52 ( x = 0.5), and 62.5 K ( x = 0.35)) when compared to the 3D-LLL scaling form, these systems behave as three-dimensional for temperatures close to T c( H).

Vortex fluctuations and freezing of dipolar-coupled granular moments in thin ferromagnetic films

Below the Curie temperature T_c of a Heusler-alloy film, consisting of densely packed, but exchange-decoupled nanograins, the spontaneous magnetization M_s(T) and static in-plane susceptibility \chi_{||}(T) increase very slowly signalizing a suppression of magnetization fluctuations. The unpredicted variation \chi_{||}(T) ~ G_d^2(T), where G_d ~ M_s^2 is the intergranular dipolar coupling, and also the magnetic freezing observed in the dynamic susceptibility at lower temperatures is quantitatively reproduced by Monte Carlo (MC) simulations with 10^4 dipolar-coupled moments on a disordered triangular lattice. At high temperatures, the MC spin configurations clearly reveal a dense gas of local vortex structures, which at low temperatures condense in regions with stronger disorder. This vortex depletion upon decreasing temperature seems to be responsible for the observed \textit{increase} of the magnetic relaxation time. For weak disorder, the temperature dependence of the MC vorticity and a singularity of the specific heat at T_v=1/2 G_d(T_v)/k_B indicate a thermal transition from a vortex gas to a state with a single vortex center plus linear vortex structures.

Dimensional Crossover in the Fluctuation Magnetization in YBa2Cu3O7- x and its Evolution with the Content of Oxygen

We have studied the field-induced dimensional crossover in the fluctuation magnetization of three single crystals of $YBa_2Cu_3O_{7-x}$, with superconducting transition temperatures, $T_c$= 62.5, 52, and 41 K. The dimensional crossover is observed by studying the diamagnetic vortex fluctuations of the lowest-Landau-level type which occur in isochamps magnetization curves, $MvsT$, for temperatures close to the transition temperature $T_{c}(H)$. The study was accomplished by obtaining isochamps magnetization curves as a function of temperature for fields in the range of 0.4 T to 5 T. Magnetization curves for each sample when plotted together show two distinct well resolved crossing points, one formed by low field curves and located at a higher temperature than the other formed by high field curves. A lowest-Landau-level scaling analysis is applied to the curves forming the crossing points and it is verified that lower field curves obey the three-dimensional form of this scaling while the higher field curves obey the two-dimensional form. The results allow to observe the evolution of the dimensional crossover field $H_{cross}$, 3D-2D, with the content of oxygen in $YBa_2Cu_3O_{7-x}$. It is observed that the evolution of the field $H_{cross}$ with the content of oxygen in each sample qualitatively agrees with theoretical predictions and allow us to estimate the ratio of the anisotropy among the studied samples. \\pacs{74.40.+k}

Hole concentration dependence of penetration depth and upper critical field inBi2Sr2(Ca,Y)Cu2O8+δextracted from reversible magnetization

We have measured the reversible magnetization of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (Bi-2212) with different hole concentrations as a function of temperature and magnetic field. By employing the vortex fluctuation model, the values of the penetration depth and the upper critical field are obtained. As the hole concentration decreases, fluctuation effects become more remarkable due to the decrease in superfluid density. The upper critical field has a maximum value when the hole concentration is around 0.19.

VORTEX FLUCTUATIONS IN WEAK MAGNETIC FIELDS

Flux-noise and ac susceptibility measurements have been performed on epitaxial films of YBa 2 Cu 3 O 7. The validity of the fluctuation-dissipation-theorem is verified by the proportionality between flux noise and ac susceptibility results. The nominal zero-field flux-noise spectrum (Sϕ(f)) can be characterized as follows: Below a temperature dependent frequency f0(T), the flux-noise spectrum is frequency independent. For frequencies f>f0(T), the flux-noise spectrum follows f-x, with x≈1.7-1.8. f0 decreases by 4 orders of magnitude in a temperature interval of ΔT≈0.5 K . Moreover, the flux-noise spectrum scales as fSϕ=g(f/f0(T)), where g(·) is a scaling function. The influence of weak perturbing magnetic fields was investigated. While the general characteristics of the flux-noise spectrum remain, the characteristic frequency f0 increases by 3-4 orders of magnitude increasing the field from zero to 1 Oe. Flux-noise measurements performed using a compensating field to reduce the residual field in the experimental setup reveal new features of the measured noise spectra. The flux-noise is dominated by thermally generated vortex-antivortex pair fluctuations at temperatures below the mean-field transition temperature, while with decreasing temperature there is a transition to vortex fluctuations being dominated by field generated vortices.

11B NMR study of vortex motion in magnesium-diboride

We have performed 11B nuclear magnetic resonance (NMR) measurements to investigate vortex dynamics in the polycrystalline MgB 2 superconductor. 11B NMR spectrum, shift and transverse relaxation rate 1 / T 2 were measured down to 4.3 K at ∼ 1.8 T . The spectrum below T c exhibits a typical local field distribution for a vortex lattice under magnetic field. The peak point of the spectrum shifts toward low magnetic field due to incomplete field penetration. Below the irreversibility temperature T irr , 1 / T 2 data, probing the slow motion of vortices, shows a single peak with a small change of the rate, contrary to the results of nickel borocarbides. Also, the relaxation profile changes from Lorentzian decay below T c to Gaussian decay at lower temperature. It strongly suggests that thermal fluctuation of vortices is reduced at low temperature and the vortex motion is much weaker compared with nickel borocarbides.

Microscopic analysis of low-frequency flux noise in YBa2Cu3O7 direct current superconducting quantum interference devices

We use low-temperature scanning electron microscopy combined with superconducting quantum interference device (SQUID) detection of magnetic flux to image vortices and to investigate low-frequency flux noise in YBa2Cu3O7 thin film SQUIDs. The low-frequency flux noise shows a nonlinear increase with magnetic cooling field up to 60μT. This effect is explained by the surface potential barrier at the SQUID hole. By correlating flux noise data with the spatial distribution of vortices, we obtain information on spatial fluctuations of vortices on a microscopic scale, e.g., an average vortex hopping length of ∼10nm.

Numerical study of vortex system quantum melting

We report a numerical study of the vortex system in the two-dimensional II-type superconductors. We have proposed a phenomenological model that takes into account quantum fluctuations of Abrikosov's vortices. The results of the quantum Monte Carlo simulations by the SSE algorithm show that the thermal fluctuations are dominated by quantum fluctuations at low temperatures. In particular, we demonstrate the possibility of the quantum melting transition for vortex system in the temperature region where thermal melting transition is improbable.

Finite-temperature superfluid density in very underdoped cuprates

The combination of a large superconducting gap, low transition temperature, and quasi two-dimensionality in strongly underdoped high temperature superconductors severely constrains the behavior of the ab-plane superfluid density \rho with temperature T. In particular, we argue that the contribution of nodal quasiparticles to \rho(T) is essential to account both for the amplitude of, and the recently observed deviations from, the Uemura scaling. A relation between T_c and \rho(0) which combines the effects of quasiparticle excitations at low temperatures and of vortex fluctuations near the critical temperature is proposed and discussed in light of recent experiments.

Angular dependence of high field magnetization fluctuation of two-dimensional Bi 2Sr 2CaCu 2O 8 single crystals

We report reversible magnetization data and the scaling for the magnetization obtained for magnetic fields ( H) applied at various tilt angles θ of the dc magnetic field with respect to the c axis in a single crystal of Bi 2Sr 2CaCu 2O 8. Our data show the crossover of the magnetization below the superconducting onset temperature, which indicates a dominant vortex fluctuation.

Thermodynamic properties of excess-oxygen-dopedLa2CuO4.11near a simultaneous transition to superconductivity and long-range magnetic order

We have measured the specific heat and magnetization versus temperature in a single crystal sample of superconducting ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4.11}$ and in a sample of the same material after removing the excess oxygen, in magnetic fields up to 15 T. Using the deoxygenated sample to subtract the phonon contribution, we find a broad peak in the specific heat, centered at 50 K. This excess specific heat is attributed to fluctuations of the Cu spins possibly enhanced by an interplay with the charge degrees of freedom, and appears to be independent of magnetic field, up to 15 T. Near the superconducting transition ${T}_{c}(H=0)=43\mathrm{K},$ we find a sharp feature that is strongly suppressed when the magnetic field is applied parallel to the crystallographic c axis. A model for three-dimensional vortex fluctuations is used to scale magnetization measured at several magnetic fields. When the magnetic field is applied perpendicular to the c axis, the only observed effect is a slight shift in the superconducting transition temperature.

Vortex fluctuations in the critical Casimir effect of superfluid and superconducting films.

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when the size of the thermal vortex loops is comparable to the film thickness, and the results for T<T(c) are found to match very well with perturbative renormalization theories that have been carried out only for T>T(c). When applied to a high-T(c) superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and the bulk, and estimates show that this may be readily measurable.

The effects of vortex characteristics on performance of coiled wire turbulators used for heat transfer augmentation

The augmentation of the heat transfer by inserting different type turbulators into the channels is the conventional passive enhancement method. The coiled wire is one of the common heat transfer enhancement devices. These turbulators generate almost-periodic vortices into the flow while increasing the heat transfer rate. In this study, the properties of these vortices (i.e. the vortex shedding frequency and amplitudes of the pressure fluctuations of the vortices), flow (vortex)-acoustic coupling and the relation between entropy generation and vortex characteristics were investigated experimentally. Strouhal– Re– N s,a and P rms– Re– N s,a variations were presented graphically. It was observed that as the pitch increases, the vortex shedding frequencies decrease and the maximum amplitudes of pressure fluctuation of vortices produced by coiled wire turbulators occur with small pitches. In addition, the effects of the turbulators on the heat transfer, friction factor and performance characteristics were investigated. The coiled wires were thermodynamically advantageous ( N s,a<1) up to 13,000 Reynolds number.

Single-vortex fluctuations in layered superconductors: Electromagnetic coupling and crossover to strong pinning

Positional fluctuations of single vortices induced by thermal fluctuations and random point pinning are considered in detail for all length scales fully taking into account the competing effects of Josephson and electromagnetic coupling between vortex elements. The electromagnetic coupling gives rise to a pronounced dispersion of the line stiffness and soft short-wavelength modes which modify the displacement fluctuations of the pinned vortex over a wide range of length scales. Furthermore, we present a detailed analysis of strongly pinned individual pancake vortices in a layered superconductor and study the crossover to the collectively pinned single-vortex line. The line stiffness dispersion leads to sharp increases in the pinning length at characteristic temperatures both for weak and strong pinning and two crossover scales. We calculate as well the corresponding increase in the characteristic pinning energy and the pronounced drop of the critical current at these characteristic temperatures. We predict distinct features in the current-voltage characteristics due to the effects of strong pinning and vortex line tension dispersion.

Vortex fluctuation measurements inhigh-Tc SQUIDs

The correlation of the outputs of two dc-SQUIDs connected to the same solid washer wasstudied. A dedicated electronic system was used in order to operate both SQUIDs at thesame time. It was found that the temporal correlation of the SQUID outputs isstrongly dependent on the geometry of the SQUID loop. For a solid washer, theflux noise is mainly due to vortices located close to the SQUIDs. However, bysurrounding the SQUID loop with a hole patterned in the superconducting solidwasher, it is possible to drastically reduce the flux penetration around the loop. Theresulting flux noise becomes dominated by vortices located inside the washer farfrom the SQUIDs. Magneto-optical images were also used to visualize the fluxpenetration inside the washer around the slit of such SQUIDs. These confirm previousdescriptions of vortex penetration deduced from the electrical measurements.

NMR study of vortex dynamics in LuNi 2B 2C

11 B - and 13 C -pulsed nuclear magnetic resonance (NMR) measurements have been performed on two single crystals of LuNi 2B 2C and LuNi 2B 2 13C superconductors to investigate the vortex dynamics. 11 B NMR for the unenriched crystal, LuNi 2B 2C, shows a single peak. All data of 11 B NMR exhibit significant features characteristic of vortex lattice and fluctuation. On the other hand, 13 C NMR for the enriched crystal, LuNi 2B 2 13C, evolves to double peaks below T c. All NMR data for the broad peak of 13 C NMR are consistent with those of 11 B NMR indicating that this part comes from a superconducting phase. On the contrary, the narrow peak of 13 C NMR is found to originate from an impure phase. This suggests that crystallinity is deteriorated during 13 C enrichment into the crystal.