Vortex Bundles Research Articles

Current-driven vortex dynamics in untwinned superconducting single crystals

Current-driven vortex dynamics of type-II superconductors in the weak-pinning limit is investigated by quantitatively studying the current-dependent vortex dissipation of an untwinned single crystal. For applied current densities (J) substantially larger than the critical current density , non-linear resistive peaks appear below the thermodynamic first-order vortex-lattice melting transition temperature , in contrast to the resistive hysteresis in the low-current limit . These resistive peaks are quantitatively analysed in terms of the current-driven coherent and plastic motion of vortex bundles in the vortex-solid phase, and the non-linear current - voltage characteristics are found to be consistent with the collective flux-creep model. The effects of high-density random point defects on the vortex dynamics are also investigated via proton irradiation of the same single crystal. Neither resistive hysteresis at low currents nor peak effects at high currents are found after the irradiation. Furthermore, the current - voltage characteristics within the instrumental resolution become completely ohmic over a wide range of currents and temperatures, despite theoretical predictions of much larger -values for the given experimental variables. This finding suggests that the vortex-glass phase, a theoretically proposed low-temperature vortex state which is stabilized by point disorder and has a vanishing resistivity, may become unstable under applied currents significantly smaller than the theoretically predicted . More investigation appears necessary in order to resolve this puzzling issue.

Superfluid vortex lines in a model of turbulent flow

Recent experiments have shown that the high Reynolds number turbulent flow of superfluid helium is similar to classical turbulence. To understand this evidence we have developed an idealized model of normal fluid turbulence which is based on vorticity tubes and we have studied numerically the behavior of superfluid quantized vortex lines in this model of turbulent normal flow. We have found that the vortex lines form ordered superfluid vortex bundles in regions of high normal fluid vorticity. A vortex wave instability and mutual friction are responsible for generating a high density of vortex lines such that the resulting macroscopic superfluid vorticity and the driving normal fluid vorticity patterns match. The results are discussed from the point of view of the idea, put forward to explain experiments, that in the isothermal, turbulent flow of He II a high density of vortex lines locks the two fluid components together and the resulting turbulent flow is that of a classical Navier–Stokes fluid.

Dependence of flux-creep activation energy upon current density in HgBa 2Ca 2Cu 3O y

We have investigated the magnetic relaxation on a HgBa 2Ca 2Cu 3O y superconductor over the range 4.2–60 K. Using a linear relation between U( J) and kT ln(1 + t/ t 0), we extracted the effective activation energy and the time-window constant t 0. A nonlinear dependence of U eff on J, U eff∝ J − μ , was found. μ is about 0.98 in the temperature range 4.2–60 K, close to the value of 7 9 in the regime of flux creep in large vortex bundles predicted by the three-dimensional collective-creep theory. The time scale t 0 depends exponentially on the initial conditions. The relationship between U( J) and the magnetic relaxation curve is discussed. With logarithmic accuracy one can construct the U( J) curve simply using several long-time relaxation curves at different temperatures.

Real-time scanning Hall probe microscopy

We describe a low-noise scanning Hall probe microscope having unprecedented magnetic field sensitivity (∼2.9×10−8 T/√Hz at 77 K), high spatial resolution, (∼0.85 μm), and operating in real-time (∼1 frame/s) for studying flux profiles at surfaces. A submicron Hall probe manufactured in a GaAs/AlGaAs two-dimensional electron gas (2DEG) is scanned over the sample to measure the surface magnetic fields using conventional scanning tunneling microscopy positioning techniques. Flux penetration into a high Tc YBa2Cu3O7−δ thin film has been observed in real time at 85 K with single vortex resolution. Flux is seen to enter the film in the form of vortex bundles as well as single flux quanta, Φ0.

A neutron study of the flux lattice in the superconductor CeRu 2

Small-angle neutron diffraction measurements from the flux lattice in a single crystal of the cubic Laves' phase superconductor, CeRu 2, are reported. The mixed state is described in terms of aligned rigid bundles of vortices. The bundle diameters decrease above 1 2 H c2 (consistent with collective weak pinning theory) and become comparable with the penetration length at a field at which a ‘peak effect’ is seen in magnetisation measurements. A clear memory of field histories that pass through the ‘peak effect’ region is also found; however, some of the induced disorder can be removed by subsequently cycling the field.

Low-field vortex dynamics over seven time decades in aBi2Sr2CaCu2O8+δsingle crystal for temperatures13<~T<~83K

Using a custom-made dc superconducting quantum interference device (dc-SQUID) magnetometer, we have measured the time relaxation of the remanent magnetization ${M}_{\mathrm{rem}}$ of a ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ single crystal from the fully critical state for temperatures $13 \mathrm{K}<~T<~83 \mathrm{K}$. The measurements cover a time window of seven decades ${10}^{\ensuremath{-}2} \mathrm{s}\ensuremath{\lesssim}t\ensuremath{\lesssim}{10}^{5} \mathrm{s}$, so that the current density $j$ can be studied from values very close to ${j}_{c}$ down to values considerably smaller than ${j}_{c}$. From the data we have obtained (i) the flux-creep activation barriers $U$ as a function of current density $j$, (ii) the current-voltage characteristics $E(j)$ in a typical range of ${10}^{\ensuremath{-}7}$-${10}^{\ensuremath{-}15}$ V/cm, and (iii) the critical current density ${j}_{c}(0)$ at $T=0$. Three different regimes of vortex dynamics are observed: For temperatures $T\ensuremath{\lesssim}20$ K the activation barrier $U(j)$ is logarithmic, no unique functional dependence $U(j)$ could be found for the intermediate-temperature interval $20 \mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}40 \mathrm{K}$, and finally for $T\ensuremath{\gtrsim}40$ K the activation barrier $U(j)$ follows a power-law behavior with an exponent $\ensuremath{\mu}\ensuremath{\simeq}0.6$. From the analysis of the data within the weak collective pinning theory for strongly layered superconductors, it is argued that for temperatures $T\ensuremath{\lesssim}20$ K pancake vortices are pinned individually, while for temperatures $T\ensuremath{\gtrsim}40$ K pinning involves large collectively pinned vortex bundles. A description of the vortex dynamics in the intermediate-temperature interval $20 \mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}40 \mathrm{K}$ is given on the basis of a qualitative low-field phase diagram of the vortex state in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$. Within this description a second peak in the magnetization loop should occur for temperatures between 20 and 40 K, as has been observed in several magnetization measurements in the literature.

Renormalization group analysis of weak collective pinning

The effect of impurity disorder on vortex lattices in type-II superconductors is studied within the framework of the weak collective pinning theory. Using a renormalization group approach, we calculate the sizeR c of collectively pinned vortex bundles in the regimea o <R c <λ (small bundles) for isotropic superconductors. We assume weak disorder and neglect thermal effects. Our findings quantitatively refine the lowest-order perturbation result,R c ∞\(\sqrt B \), obtained by Larkin and Ovchinnikov in 1979 (B is the magnetic induction). In particular, we find a different numerical constant in the exponential as well as a new algebraic prefactor. These improvements provide us with a more accurate functional dependence of the critical current on the magnetic field.

On the Rotation and Magnetic Field Evolution of Superconducting Strange Stars

Are pulsars made up of strange matter? The magnetic field decay of a pulsar may be able to give us an answer. Since Cooper pairing of quarks occurs inside a sufficiently cold strange star, the strange stellar core is superconducting. In order to compensate for the effect of rotation, different superconducting species inside a rotating strange star try to set up different values of London fields. Thus we have a frustrated system. Using Ginzburg-Landau formalism, I solved the problem of a rotating superconducting strange star: Instead of setting up a global London field, vortex bundles carrying localized magnetic fields are formed. Moreover, the number density of vortex bundles is directly proportional to the angular speed of the star. Since it is energetically favorable for the vortex bundles to pin to magnetic flux tubes, the rotational dynamics and magnetic evolution of a strange star are coupled together, leading to magnetic flux expulsion as the star slows down. I investigate this effect numerically and find that the characteristic field decay time is much less than 20 Myr in all reasonable parameter regions. On the other hand, the characteristic magnetic field decay time for pulsars is ≥20 Myr. Thus, my finding casts doubts on the hypothesis that pulsars are strange stars.

Nuclear spin relaxation due to random motion of vortex bundles.

The dependence of nuclear-spin-relaxation rate ${\mathit{T}}_{1}$ on NMR resonant frequency for a layered superconducting sample has been analyzed theoretically. In the considered arrangement the Zeeman field has been applied in the plane of superconducting layers while the relaxation was due to interactions between the spin systems and moving flux bundles, created by the transport current flowing along superconducting layers. It has been found that the functional form of a dependence of spin-relaxation rate on the Zeeman field has two components, a Lorentzian and an oscillatory one. The characteristic rolloff frequency of the Lorentzian component depends on the pinning properties of the sample. The period of oscillations of the oscillatory component is of the order of the inverse of interaction time of flowing flux bundles with a probe nucleus. \textcopyright{} 1996 The American Physical Society.

Voltage noise due to randomly interrupted motion of vortices

The voltage noise generated by an randomly interrupted flow of flux vortices across thin film superconducting strips is discussed. It is demonstrated that processes of vortex pinning and depinning, as well as motion of vortex-density fluctuations contribute to the noise spectra. Random switching of vortices between the state of pinning and flow results in random telegraph noise-like behavior at high frequencies. The flow of spatially non-correlated vortices, or vortex bundles, results in oscillatory peaks in the power spectra. The difference in frequency between two peaks is related to the inverse of the average time the vortices need to cross the sample. The shape of the voltage noise spectrum dramatically depends on the ratio of average lifetimes of vortices in the pinned and in the flow state. Spectral oscillations are attenuated and disappear with increasing pinning strength. It is demonstrated that the physical picture depends on the type of geometrical resolution function chosen for the calculations.

Spatial distributions of vortices in sintered YBa 2Cu 3O 7 studied by neutron depolarization

The spatial distributions of vortices in equilibrium (the critical state) in a sintered YBa 2Cu 3O 7 sample are studied by three-dimensional neutron depolarization (3DND), in field and for remanent states. Neutron depolarization provides the magnetization, the length of vortex straightness and the direction cosine of vortex bundles in the sample. By scanning a neutron beam through the sample, the position dependence of these vortex-distribution parameters are determined. From the length of vortex straightness and the position dependence of the magnetization it is found that vortices penetrate between the clusters of grains in small applied field and are pinned in the grain clusters in remanence after a field pulse.

Influence of oxygen stoichiometry on the irreversible magnetization and flux creep in RBa2Cu3O7- delta (R=Y,Tm) single crystals.

The influence of the oxygen stoichiometry on magnetization and relaxation of R${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (R=Y,Tm) single crystals was studied for 0\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}0.55. The field dependences of the shielding currents ${\mathit{j}}_{\mathit{s}}$(H) and flux creep rates S(H) were analyzed. Three different kinds of ${\mathit{j}}_{\mathit{s}}$(H) and S(H) behavior can be seen in highly oxygenated samples (\ensuremath{\delta}0.1). (i) At high temperatures, ${\mathit{j}}_{\mathit{s}}$(H) shows a common fishtail peak, which is present for all oxygen contents. The field position and height of the ${\mathit{j}}_{\mathit{s}}$ peak increase rapidly with decreasing \ensuremath{\delta}. Approaching the stoichiometric state \ensuremath{\delta}=0, the value of the current starts to decrease with lower oxygen deficiency, in contrast to the still increasing irreversibility field ${\mathit{B}}_{\mathrm{irr}}$. This points to the importance of oxygen disorder for the pinning and stresses the melting nature of the irreversibility line. The peak position ${\mathit{B}}_{\mathrm{max}}$ is found to correlate with ${\mathit{B}}_{\mathrm{irr}}$. A possible relation of the fishtail with a synchronization effect and with the vanishing of ${\mathrm{C}}_{66}$ at the melting transition is proposed. (ii) In the intermediate-temperature region, some of the samples showed a new second peak with weak temperature and \ensuremath{\delta} dependence. The probable origin of this feature is matching with twin structure. This peak disappears for \ensuremath{\delta}g0.1, when the fishtail position shifts below the matching field. (iii) The low-temperature region is characterized by a monotonic decrease of ${\mathit{j}}_{\mathit{s}}$(B). This region becomes narrower with larger \ensuremath{\delta} and disappears for \ensuremath{\delta}g0.3. Thus in highly deoxygenated samples, the fishtail feature is observed for practically all temperatures. The possible connection of the low-temperature region with the pinning of the small vortex bundles or with the slipping of vortices along the twin planes is considered.

Observation and manipulation of vortices in a YBa 2Cu 3O 7 thin film with a low temperature magnetic force microscope

A low temperature magnetic force microscope has been applied to spatially resolve single vortices in an epitaxially grown YBa 2Cu 3O 7 thin film at 77 K. A disordered vortex arrangement is observed. Further the magnetic stray field of the magnetic force microscope tip is used to locally nucleate vortex bundles.

Collective creep of vortex bundles in YBa2Cu3O7 crystals.

We present evidence for the crossover between creep of individual vortices and collective creep of vortex bundles from measurements of the relaxation of the persistent currents in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ single crystals over long periods of time. In the single-vortex regime at low fields the relaxation is fast and is characterized by an exponent \ensuremath{\mu}\ensuremath{\simeq}0.16, as predicted in the collective-creep scenario. With increasing field, collective bundling of vortices induces a slowdown of the relaxation, with a maximum \ensuremath{\mu}\ensuremath{\simeq}1.4. At even higher fields, \ensuremath{\mu} decreases again to about 1 as the size of the bundles grows.

Observed regimes of collective flux creep in proton-irradiated, single-crystal Y-Ba-Cu-O: Dependence on current density

Flux-creep studies have quantified the time decay of supercurrents in a proton-irradiated ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ crystal. We determine the dependence of the characteristic exponent \ensuremath{\mu} (which governs current decay) on current density and magnetic field. The results are compared with collective-creep theory for the case of random pointlike disorder. Observed are predicted regimes of creep with small and large bundles of vortices, indications of single vortex motion, crossovers in current density, and other qualitative consistencies.

Diffusion and dynamical randomness of the flux flow state in high temperature superconductors

In strongly layered superconductors, the dynamical system of vortex lattice is a disordered state with large energy of the vortex bundle for small driving currents. We provide an evidence that broadening of the resistive transitions in HTSC measured under magnetic field is due to random diffusion and fast relaxational hopping of flux lines between different metastable configurations. A model is presented in which the dynamics of the two-dimensional vortex lattice are characterized by a diffusive transfer rather than distinct movements of the vortices. The predictions of the model are consistent with large scale numerical simulation on two-dimensional vortex lattice using molecular dynamics' methods. In addition, excellent agreements were established between the model calculations and the measured resistive transitions in twined (YBaCuO) single crystal high temperature superconductors (HTSC).

"Phase diagram" of the vortex-solid phase in Y-Ba-Cu-O crystals: A crossover from single-vortex (1D) to collective (3D) pinning regimes.

We construct a ``phase diagram'' of the vortex-solid phase of Y-Ba-Cu-O single crystals by making a first overall connection of the shape of the magnetic hysteresis M(H,T) with the single-vortex (1D) and collective (3D) pinning regimes. The crossovers between different regimes are visualized by drawing contours of constant critical current density ${\mathit{J}}_{\mathit{c}}$ in the H-T plane. We identify the transition from 1D to 3D pinning, and from the nonlocal into a local behavior of vortex bundles in the collective pinning regime. A direct correlation between the shape of M(H) and the field-dependent thermal relaxation rate is demonstrated. We also identify a signature of the thermal softening boundary at which thermal fluctuations on the scale of the coherence length \ensuremath{\xi} are relevant.

Collective effects in vortex movements in type-II superconductors observed by a method for the registration of individual vortices.

A method for the registration of Abrikosov vortices in type-II superconductors has been employed for studying magnetic-flux propagation through a superconducting film. This method is based on measurements of the vortex-induced magnetoresistance in normal-metal microprobes placed in the immediate vicinity of a superconductor surface. The sensitivity of such probes provides a registration of individual vortex movements in a submicrometer area of the superconductor. With use of this technique, it is demonstrated that both the penetration of magnetic flux into the superconductor and its withdrawal are accomplished not by individual vortex movements but by the hopping of vortex bundles. The size of the hopping bundles appears to be much larger than the correlation volume in the vortex lattice. A description of flux penetration based on the critical-state model, which assumes a smooth gradient of the vortex concentration across the sample, has been found to break down on the microscopic scale.

Flux creep in high temperature superconductors

Magnetic studies of flux creep in high temperature superconductors show many features unexpected in the conventional Anderson-Kim theory, which assumes a thermal activation mechanism and uncorrelated motion of vortex bundles. An alternative phenomenology is provided by the more recent collective pinning theories. Experiments probing this new phenomenology are reviewed, including long-time relaxation, flux-creep annealing and studies near T c.

Quantum collective creep.

We study the phenomenon of quantum creep in bulk superconductors within the framework of weak-collective-pinning theory. Single-vortex pinning at moderate magnetic fields as well as creep of vortex bundles at high fields are discussed for the case of current densities near critical. In the limit of strong dissipation and for moderate fields the basic parameter determining the tunneling rate is the ratio {rho}{sub {ital n}}/{xi} ({rho}{sub {ital n}}=normal-state resistivity, {xi}=coherent length), with strong tunneling realized for {rho}{sub {ital h}}/{xi}{approx gt}1 k{Omega}.