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Measurements of the temperature-dependent ac magnetic susceptibility of superconducting films reveal reversible responses, i.e., irrespective of the magnetic and thermal history of the sample. This experimental fact is observed even in the presence of stochastic and certainly irreversible magnetic flux avalanches which, in principle, should randomly affect the results. In this work, we explain such an apparent contradiction by exploring the spatial resolution of magneto-optical imaging. To achieve this, we successfully compare standard frequency-independent first harmonic ac magnetic susceptibility results for a superconducting thin film with those obtained by ac-emulating magneto-optical imaging (acMOI). A quantitative analysis also provides information regarding flux avalanches, reveals the presence of a vortex-antivortex annihilation zone in the region in which a smooth flux front interacts with pre-established avalanches, and demonstrates that the major impact on the flux distribution within the superconductor happens during the first ac cycle. Our results establish acMOI as a reliable approach for studying frequency-independent ac field effects in superconducting thin films while capturing local aspects of flux dynamics, otherwise inaccessible via global magnetometry techniques., Comment: 15 pages, 10 figures

Ubiquitous in most superconducting materials and a common result of nanofabrication processes, weak-links are known for their limiting effects on the transport of electric currents. Still, they are at the root of key features of superconducting technology. By performing quantitative magneto-optical imaging experiments and thermomagnetic model simulations, we correlate the existence of local maxima in the magnetization loops of FIB-patterned Nb films to a magnetic field-induced weak-to-strong-link transformation increasing their critical current. This phenomenon arises from the nanoscale interaction between quantized magnetic flux lines and FIB-induced modifications of the device microstructure. Under an ac drive field, this leads to a rectified vortex motion along the weak-link. The reported tunable effect can be exploited in the development of new superconducting electronic devices, such as flux pumps and valves, to attenuate or amplify the supercurrent through a circuit element, and as a strategy to enhance the critical current in weak-link-bearing devices., Comment: 11 pages and 8 figures

Thickness uniformity is regarded as an important parameter in designing thin film devices. However, some applications based on films with non-uniform thickness have recently emerged, such as gas sensors and optimized materials based on the gradual change of film composition. This work deals with superconducting Pb thin films with a thickness gradient prepared with the aid of a diffuse stencil mask. Atomic Force Microscopy and Energy-Dispersive X-ray Spectroscopy show variations ranging from 90~nm to 154~nm. Quantitative magneto-optical images reveal interesting features during both the abrupt and the smooth penetration regimes of magnetic flux, as well as the thickness-dependent critical current density ($J_c$). In addition, we observe a gradual superconducting transition as the upper critical field is progressively reached for certain thicknesses. Furthermore, the hysteresis observed for triggering flux avalanches when increasing and decreasing magnetic fields is also accounted for by the $J_c$ profile evolution along the thickness gradient. Numerical simulations based on the Thermomagnetic Model are in fair agreement with the experimental data. These findings demonstrate that wedge-shaped films are a viable approach to investigate, in a continuous fashion, thickness-dependent properties of a superconducting materials.

Quantitative magneto-optical imaging of a type-II superconductor thin film cooled under zero, homogeneous, and inhomogeneous applied magnetic fields, indicates that the latter procedure leads to an enhancement of the screening capacity. Such an observation is corroborated by both B-independent and B-dependent critical state model analyses. Furthermore, repulsive (attractive) vortex-(anti)vortex interactions were found to have a decisive role in the shielding ability, with initial states prepared with vortices resulting in a shorter magnetic flux front penetration depth than those prepared with antivortices. The proposed strategy could be implemented to boost the performance of thin superconducting devices., Comment: 6 pages and 5 figures

A method to measure the electrical connectivity between square superconducting plates joined by weak link interfaces is presented. It is based on observation of lines where the flow of critical current abruptly changes direction due to the presence of weak links, and the confinement created by the shape of the sample. The method is demonstrated using magneto-optical imaging (MOI) of systems consisting of up to 2 X 2 plates joined to form a larger square. Common features are found in the current flow patterns, which allow to measure the electrical connectivity between the plates by observing an angle between pairs of lines indicating where the current abruptly changes flow direction, so-called discontinuity, or d-lines. The samples used in this study are Nb films with weak links created by focused ion beam machining.

Scaling behaviour of dynamically driven vortex avalanches in superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films deposited on tilted crystalline substrates has been observed using quantitative magneto-optical imaging. Two films with different tilt angles are characterized by the probability distributions of avalanche size in terms of the number of moving vortices. It is found in both samples that these distributions follow power-laws over up to three decades, and have exponents ranging between 1.0 and 1.4. The distributions also show clear finite-size scaling, when the system size is defined by the depth of the flux penetration front -- a signature of self-organized criticality. A scaling relation between the avalanche size exponent and the fractal dimension, previously derived theoretically from conservation of the number of magnetic vortices in the stationary state and shown in numerical simulations, is here shown to be satisfied also experimentally., Comment: 7 pages, 5 figures

A novel mathematical approach has been developed to complete the inversion of the Biot-Savart law in one- and two-dimensional cases from measurements of the perpendicular component of the magnetic field using the well-developed Magneto-Optical Imaging technique. Our approach, especially in the 2D case, is provided in great detail to allow a straightforward implementation as opposed to those found in the literature. Our new approach also refines our previous results for the 1D case [Johansen et al., Phys. Rev. B 54, 16264 (1996)], and streamlines the method developed by Jooss et al. [Physica C 299, 215 (1998)] deemed as the most accurate if compared to that of Roth et al. [J. Appl. Phys. 65, 361 (1989)]. We also verify and streamline the iterative technique, which was developed following Laviano et al. [Supercond. Sci. Technol. 16, 71 (2002)] to account for in-plane magnetic fields caused by the bending of the applied magnetic field due to the demagnetising effect. After testing on magneto-optical images of a high quality YBa2Cu3O7 superconducting thin film, we show that the procedure employed is effective.

Stability of the vortex matter -- magnetic flux lines penetrating into the material -- in type-II superconductor films is crucially important for their application. If some vortices get detached from pinning centres, the energy dissipated by their motion will facilitate further depinning, and may trigger an electromagnetic breakdown. In this paper, we review recent theoretical and experimental results on development of the above mentioned thermomagnetic instability. Starting from linear stability analysis for the initial critical-state flux distribution we then discuss a numerical procedure allowing to analyze developed flux avalanches. As an example of this approach we consider ultra-fast dendritic flux avalanches in thin superconducting disks. At the initial stage the flux front corresponding to the dendrite's trunk moves with velocity up to 100~km/s. At later stage the almost constant velocity leads to a specific propagation regime similar to ray optics. We discuss this regime observed in superconducting films coated by normal strips. Finally, we discuss dramatic enhancement of the anisotropy of the flux patterns due to specific dynamics. In this way we demonstrate that the combination of the linear stability analysis with the numerical approach provides an efficient framework for understanding the ultra-fast coupled non-local dynamics of electromagnetic fields and dissipation in superconductor films., Comment: 16 pages, 20 figures

Active triggering and manipulation of ultrafast flux dynamics in superconductors are demonstrated in films of Nb. Controlled amounts of magnetic flux were injected from a point along the edge of a square sample, which at 2.5 K responds by nucleation of a thermomagnetic avalanche. Magneto-optical imaging was used to show that when such films are cooled in the presence of in-plane magnetic fields they become anisotropic, and the morphology of the avalanches change systematically, both with the direction and magnitude of the field. The images reveal that the avalanching dendrites consistently bend towards the direction perpendicular to that of the in-plane field. The effect increases with the field magnitude, and at 1.5 kOe the triggered avalanche becomes quenched at the nucleation stage. The experimental results are explained based on a theoretical model for thermomagnetic avalanche nucleation in superconducting films, and by assuming that the frozen-in flux generates in-plane anisotropy in the film thermal conductance. The results demonstrate that applying in-plane magnetic fields to film superconductors can be a versatile external tool for controlling their ultrafast flux dynamics.

We report on magneto-optical imaging, magnetization, Hall effect and magneto-resistance experiments in Nb/Al_2O_3/Co thin film heterostructures. The magnetic field is applied perpendicularly to the plane of the film and gives rise to abrupt flux penetration of dendritic form. A magnetization texture is imprinted in the Co layer in perfect coincidence with these ramifications. The spin domains that mimic the vortex dendrites are stable upon the field removal. Moreover, the imprinted spin structure remains visible up to room temperature. Complementary magnetization, Hall effect and magneto-resistance experiments were performed in a similar sample where electrical contacts were placed on the Co layer. In the region of the field - temperature diagram where flux instabilities are known to occur in Nb films, irregular jumps are observed in the magnetic hysteresis and large amplitude noise is detected in the magneto-resistance and Hall resistivity data when measured as a function of the field., Comment: 13 pages, 8 figures

The sub-microsecond dynamics of thermomagnetic avalanches in superconducting films with non-conducting holes (antidots) is considered. When such an avalanche reaches a hole, it is quickly filled with magnetic flux, and often its rim becomes unstable and a second avalanche is nucleated. In this work the time- and space-resolved behavior of such cascading avalanche behavior is determined using numerical simulations. Results are presented for films with holes of different shape. It is found that holes with sharp corners are those that most frequently create secondary avalanches, and they tend to nucleate in corners. Magneto-optical imaging of Nb films patterned with the same set of holes strongly supports the numerical results., Comment: 5 pages, 5 figures

Thermomagnetic avalanches in superconducting films propagating extremely fast while forming unpredictable patterns, represent a serious threat for the performance of devices based on such materials. It is shown here that a normal-metal frame surrounding a selected region inside the film area can provide efficient protection from the avalanches during their propagation stage. Protective behavior is confirmed by magneto-optical imaging experiments on NbN films equipped with Cu and Al frames, and also by performing numerical simulations. Experimentally, it is found that while conventional flux creep is not affected by the frames, the dendritic avalanches are partially or fully screened by them. The level of screening depends on the ratio of the sheet conductance of the metal and the superconductor in the resistive state, and for ratios much larger than unity the screening is very efficient., Comment: 5 pages, 5 figures

We have observed the occurrence of dendritic flux avalanches in an amorphous film of Mo$_{84}$Si$_{16}$. These events are understood to have a thermomagnetic origin and involve the abrupt penetration of bursts of magnetic flux taking place within a limited window of temperatures and magnetic fields. While dc-magnetometry allows one to determine the threshold fields for the occurrence of the thermomagnetic instabilities, magneto-optical imaging reveals the spatial distribution of magnetic flux throughout the sample. Conducting appropriate experiments, typical for this goal, avalanches were confirmed to be a characteristic of this material, ruling out the otherwise admissible possibility of an experimental artifact or a feature related to defects in the film. After the present observation, a-MoSi can be included in the gallery of superconducting materials exhibiting flux avalanches when in the form of thin films, a characteristic that must be carefully taken into consideration when one plans to employ films of those materials in applications., Comment: Presented on ASC 2014 and submitted to IEEE TRANSACTION ON APPLIED SUPERCONDUCTIVITY (Special Issue)

Experimental evidence of wave properties of dendritic flux avalanches in superconducting films is reported. Using magneto-optical imaging the propagation of dendrites across boundaries between a bare NbN film and areas coated by a Cu-layer was visualized, and it was found that the propagation is refracted in full quantitative agreement with Snell's law. For the studied film of 170 nm thickness and a 0.9 mkm thick metal layer, the refractive index was close to n=1.4. The origin of the refraction is believed to be caused by the dendrites propagating as an electromagnetic shock wave, similar to damped modes considered previously for normal metals. The analogy is justified by the large dissipation during the avalanches raising the local temperature significantly. Additional time-resolved measurements of voltage pulses generated by segments of the dendrites traversing an electrode confirm the consistency of the adapted physical picture., Comment: 4 pages, 4 figures

At low temperatures the critical state in superconducting films can be unstable with respect to thermomagnetic dendritic avalanches. By numerical simulations of disk-shaped superconductors, we consider how the dynamics and morphology of the avalanches depend on the disk thickness. We find that as the disks get thicker, the jumps in magnetic moment caused by the avalanches get larger and the threshold magnetic field for the appearance of the first avalanche increases. At the same time, the branches are straighter and the number of branches decreases. Comparison with theory suggests that strong spatial disorder to some extent cancels the stabilizing effects of the substrate kept at constant temperature., Comment: 8 pages, 4 figures

The penetration of transverse magnetic flux into a thin superconducting square film in the flux flow state is considered by numerical simulation. Due to the film self-field, the governing equations are nonlinear, and in combination with the finite viscosity of the moving vortices, this sets up a dynamical barrier for flux penetration into the sample. The corresponding magnetization loop is hysteric, with the peak in magnetization shifted from the zero position. The magnetic field in increasing applied field is found to form a well-defined front of propagation. Numerical estimates shows that the dynamical barrier should be measurable on films with low volume pinning., Comment: 4 pages, 2 figures

The stability of superconducting films with respect to oscillatory precursor modes for thermomag- netic avalanches is investigated theoretically. The results for the onset threshold show that previous treatments of non-oscillatory modes have predicted much higher thresholds. Thus, in film supercon- ductors, oscillatory modes are far more likely to cause thermomagnetic breakdown. This explains the experimental fact that flux avalanches in film superconductors can occur even at very small ramping rates of the applied magnetic field. Closed expressions for the threshold magnetic field and temperature, as well oscillation frequency, are derived for different regimes of the oscillatory thermomagnetic instability., Comment: 5 pages, 5 figures

We report on the observation of dendritic flux avalanches in a large Niobium single crystal. In contrast to avalanches observed in thin films, they appear only in a very narrow temperature interval of about a tenth of a Kelvin near the critical temperature of Nb. At a fixed temperature, we find two sets of dendritic structures, which differ by the magnetic field required for their formation and by the maximum distance the dendrites penetrate into the sample. The effect is caused by dendritic flux penetration into thin superconducting surface layers formed in the single crystal close to the critical temperature.

Electrically conducting films in a time-varying transverse applied magnetic field are considered. Their behavior is strongly influenced by the self-field of the induced currents, making the electrodynamics nonlocal, and consequently difficult to analyze both numerically and analytically. We present a formalism which allows many phenomena related to superconducting and Ohmic films to be modelled and analyzed. The formalism is based on the Maxwell equations, and a material current-voltage characteristics, linear for normal metals, and nonlinear for superconductors, plus a careful account of the boundary conditions. For Ohmic films, we consider the response to a delta function source-field turned on instantly. As one of few problems in nonlocal electrodynamics, this has an analytical solution, which we obtain, in both Fourier and real space. Next, the dynamical behaviour of a square superconductor film during ramping up of the field, and subsequently returning to zero, is treated numerically. Then, this remanent state is used as initial condition for triggering thermomagnetic avalanches. The avalanches tend to invade the central part where the density of trapped flux is largest, forming dendritic patterns in excellent agreement with magneto-optical images. Detailed profiles of current and flux density are presented and discussed. Finally, the formalism is extended to multiply connected samples, and numerical results for a patterned superconducting film, a ring with a square lattice of antidots, are presented and discussed., Comment: 25 pages, 10 figures

Dendritic flux avalanches is a frequently encountered consequence of the thermomagnetic instability in type-II superconducting films. The avalanches, potentially harmful for superconductor-based devices, can be suppressed by an adjacent normal metal layer, even when the two layers are not in thermal contact. The suppression of the avalanches in this case is due to so-called magnetic braking, caused by eddy currents generated in the metal layer by propagating magnetic flux. We develop a theory of magnetic braking by analyzing coupled electrodynamics and heat flow in a superconductor-normal metal bilayer. The equations are solved by linearization and by numerical simulation of the avalanche dynamics. We find that in an uncoated superconductor, even a uniform thermomagnetic instability can develop into a dendritic flux avalanche. The mechanism is that a small non-uniformity caused by the electromagnetic non-locality induces a flux-flow hot spot at a random position. The hot spot quickly develops into a finger, which at high speeds penetrates into the superconductor, forming a branching structure. Magnetic braking slows the avalanches, and if the normal metal conductivity is sufficiently high, it can suppress the formation of the dendritic structure. During avalanches, the braking by the normal metal layer prevents the temperature from exceeding the transition temperature of the superconductor. Analytical criteria for the instability threshold are developed using the linear stability analysis. The criteria are found to match quantitatively the instability onsets obtained in simulation., Comment: 14 pages, 9 figures

A graded distribution of pinning centers (antidots) in superconducting MoGe thin films has been investigated by magnetization and magneto-optical imaging. The pinning landscape has maximum density at the border, decreasing progressively towards the center. At high temperatures and low fields, where this landscape mimics the vortex distribution predicted by the Bean model, an increase of the critical current is observed. At low temperatures and fields, the superconducting performance of the non-uniform sample is also improved due to suppression of thermomagnetic avalanches. These findings emphasize the relevance of non-uniform pinning landscapes, so far experimentally unexplored, on the enhancement of pinning efficiency., Comment: 5 pages and 3 figures

The variety of morphologies in flux patterns created by thermomagnetic dendritic avalanches in type-II superconducting films is investigated using numerical simulations. The avalanches are triggered by introducing a hot spot at the edge of a strip-shaped sample, which is initially prepared in a partially penetrated Bean critical state by slowly ramping the transversely applied magnetic field. The simulation scheme is based on a model accounting for the nonlinear and nonlocal electrodynamics of superconductors in the transverse geometry. By systematically varying the parameters representing the Joule heating, heat conduction in the film, and heat transfer to the substrate, a wide variety of avalanche patterns is formed, and quantitative characterization of areal extension, branch width etc. is made. The results show that branching is suppressed by the lateral heat diffusion, while large Joule heating gives many branches, and heat removal into the substrate limits the areal size. The morphology shows significant dependence also on the initial flux penetration depth., Comment: 6 pages, 6 figures

Thermo-magnetic instability (TMI) in superconductors is known to destroy the critical state via magnetic flux avalanches, and hence it deteriorates the ability of the superconductors to shield external magnetic field. In this work, we quantify to what extent the shielding current is affected by TMI. We recover the critical state in one half of a thermo-magnetically unstable NbN film by coating it with a thin layer of Cu. Suppression of the instability in the metal coated part is confirmed by the results of a direct real time magneto-optical imaging. A pattern of discontinuity lines in the observed flux distribution indicates that only one quarter of the shielding current flows through the whole sample, including the unstable uncoated part, while three quarters flow in loops within the stable Cu-coated part., Comment: 5 pages, 5 figures

Dendritic flux avalanches is a frequently encountered instability in the vortex matter of type II superconducting films at low temperatures. Previously, linear stability analysis has shown that such avalanches should be nucleated where the flux penetration is deepest. To check this prediction we do numerical simulations on a superconducting rectangle. We find that at low substrate temperature the first avalanches appear exactly in the middle of the long edges, in agreement with the predictions. At higher substrate temperature, where there are no clear predictions from the theory, we find that the location of the first avalanche is decided by fluctuations due to the randomly distributed disorder., Comment: 3 pages, 2 figures

We consider magnetic flux penetration in a superconducting film with a concave corner. Unlike convex corners, where the current flow pattern is easily constructed from Bean's critical state model, the current flow pattern at a concave corner is highly nontrivial. To address the problem, we do a numerical flux creep simulation, where particular attention is paid to efficient handling of the non-local electrodynamics, characteristic of superconducting films in the transverse geometry. We find that the current stream lines at the concave corner are close to circular, but the small deviation from exact circles ensure that the electric field is finite and continuous. Yet, the electric field is, as expected, very high at the concave corner. At low fields, the critical state penetration is deeper from the concave corner than from the straight edges, which is a consequence of the electrodynamic non-locality. A magneto-optical experiment on a YBCO displays an almost perfect match with the magnetic flux distribution from the simulation, hence verifying the necessity of including electrodynamic non-locality in the modelling of superconducting thin films., Comment: 7 pages, 7 figures

A study of magnetic flux penetration in a superconducting film patterned with arrays of micron sized antidots (microholes) is reported. Magneto-optical imaging (MOI) of a YBCO film shaped as a long strip with perpendicular antidot arrays revealed both strong guidance of flux, and at the same time large perturbations of the overall flux penetration and flow of current. These results are compared with a numerical flux creep simulation of a thin superconductor with the same antidot pattern. To perform calculations on such a complex geometry, an efficient numerical scheme for handling the boundary conditions of the antidots and the nonlocal electrodynamics was developed. The simulations reproduce essentially all features of the MOI results. In addition, the numerical results give insight into all other key quantities, e.g., the electrical field, which becomes extremely large in the narrow channels connecting the antidots., Comment: 8 pages, 7 figures

We have employed magneto-optical imaging to visualize the occurrence of flux avalanches in a superconducting film of a-MoGe. The specimen was decorated with square antidots arranged in a square lattice. We observed avalanches with the anomalous habit of forming trees where the trunk is perpendicular to the main axis of the square lattice, whereas the branches form angles of 45 degrees. The overall features of the avalanches, and in particular the 45 degree direction of the branches, were confirmed by numerical simulations., Comment: 3 pages, 3 figures

Electrical conductivity, Hall effect and magnetoresistance of In$_2$O$_3$:Sn thin films deposited on a glass substrates at different temperatures and oxygen pressures, as well as the films treated in a hydrogen plasma, have been investigated in the temperature range 1.5-300 K. The observed temperature dependences of resistivity were typical for metallic transport of electrons except temperature dependence of resistivity of the In$_2$O$_3$:Sn film deposited in the oxygen deficient atmosphere. The electron concentration and mobility for the film deposited at 230$^\circ$C was larger than that for the film deposited nominally at room temperature. Short (5 minutes) treatment of the films in hydrogen plasma leads to the enhancement of electrical conductivity while longer (30 minute) treatment has the opposite effect. The electrical measurements were accompanied by AFM and SEM studies of structural properties, as well as by XPS analysis. Basic on structural and electrical measurements we conclude the reduction process initiated by the hydrogen plasma provides essential modification of the ITO films surface. At the same time, electrical properties of the remaining (located beneath the surface layer) parts of the ITO films remain mostly unchangeable. XPS analysis shows that grown in situ oxygen deficient ITO films have enhanced DOS between the Fermi level and the valence band edge. The extra localized states behave as acceptors leading to a compensation of $n$-type ITO. That can explain lower $n$-type conductivity in this material crossing over to a Mott-type hopping., Comment: Submitted to the Journal of Applied Physics

We develop a fast numerical procedure for analysis of nonlinear and nonlocal electrodynamics of type-II superconducting films in transverse magnetic fields taking into account realistic boundary conditions. Using this procedure we explore stability of such films with respect to dendritic flux avalanches. The calculated flux patterns are very similar to experimental magneto-optical images of MgB2 and other superconductors, where the avalanche size and morphology change dramatically with temperature. We also find a threshold magnetic field, which agrees with both experiments and linear stability analysis. The simulations predict the temperature rise during an avalanche, where for a sub-microsecond time T ~ 1.5 Tc, and a precursor stage with large thermal fluctuations., Comment: 7 pages 7 figures

We report that single crystals of (Ba,K)Fe2As2 with Tc = 32 K have a pinning potential, U0, as high as 10^4 K, with U0 showing very little field depend-ence. In addition, the (Ba,K)Fe2As2 single crystals become isotropic at low temperatures and high magnetic fields, resulting in a very rigid vortex lattice, even in fields very close to Hc2. The rigid vortices in the two dimensional (Ba,K)Fe2As2 distinguish this compound from 2D high Tc cuprate superconductors with 2D vortices, and make it being capable of cearrying very high critical current.Flux jumping due to high Jc was also observed in large samples at low temperatures., Comment: 4 pages, 7 figures. submitted

Using fluorescent microthermal imaging we have investigated the origin of "two-step" behavior in I-V curves for a current-carrying YBa_2Cu_3O_x superconducting bridge. High resolution temperature maps reveal that as the applied current increases the first step in the voltage corresponds to local dissipation (hot spot), whereas the second step is associated with onset of global dissipation throughout the entire bridge. A quantitative explanation of the experimental results is provided by a simple model for an inhomogeneous superconductor, assuming that the hot spot nucleates at a location with slightly depressed superconducting properties., Comment: 4 pages, 4 figures

Flux penetration into type-II superconducing films is simulated for transverse applied magnetic field and flux creep dynamics. The films contain macroscopic, non-conducting holes and we suggest a new method to introduce the holes in the simulation formalism. The method implies reconstruction of the magnetic field change inside the hole. We find that in the region between the hole and the edge the current density is compressed so that the flux density is slightly reduced, but the traffic of flux is significantly increased. The results are in good agreement with magneto-optical studies of flux distributions in YBCO films., Comment: 7 pages, 7 figures (low resolution)

The distributions of electrical current and magnetic field in a thin-film superconductor ring is calculated by solving the London equation. The maximum amount of flux trapped by the hole, the fluxoid saturation number, is obtained by limiting the current density by the depairing current. The results are compare it with similar results derived for the bulk case of a long hollow cylinder [Nordborg & Vinokur, Phys. Rev. B 62, 12408 (2000)]. In the limit of small holes our result reduces to the Pearl solution for an isolated vortex in a thin film. For large hole radius, the ratio between saturation numbers in bulk and film superconductors is proportional to the square root of the hole size., Comment: 4 pages, 4 figures

The flux penetration near a semicircular indentation at the edge of a thin superconducting strip placed in a transverse magnetic field is investigated. The flux front distortion due to the indentation is calculated numerically by solving the Maxwell equations with a highly nonlinear $E(j)$ law. We find that the excess penetration, $\Delta$, can be significantly ($\sim$ 50%) larger than the indentation radius $r_0$, in contrast to a bulk supercondutor in the critical state where $\Delta=r_0$. It is also shown that the flux creep tends to smoothen the flux front, i.e. reduce $\Delta$. The results are in very good agreement with magneto-optical studies of flux penetration into an YBa$_2$Cu$_3$O$_x$ film having an edge defect., Comment: 5 pages, 7 figures

We propose a mechanism responsible for the abrupt vanishing of the dendritic flux instability found in many superconducting films when an increasing magnetic field is applied. The onset of flux avalanches and the subsequent reentrance of stability in NbN films was investigated using magneto-optical imaging, and the threshold fields were measured as functions of critical current density, $j_c$. The results are explained with excellent quantitative agreement by a thermomagnetic model published recently, Phys. Rev. B73, 014512 (2006), showing that the reentrant stability is a direct consequence of a monotonously decreasing $j_c$ versus field.

An increase in the critical current and suppression of AC losses in superconducting wires and tapes with soft magnetic sheath have been predicted theoretically and confirmed experimentally. In this work we present the results of magneto-optical investigations on a series of Ag-sheathed Bi-2223 tapes with Ni coating. We visualize distributions of magnetic field at increasing external field and different temperatures, demonstrating a difference between the flux propagation in the superconductor with Ni rims and a reference sample without Ni coating., Comment: 2 pages

Anisotropic penetration of magnetic flux in MgB2 films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate {\em perpendicular} to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest-pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability., Comment: 4 pages, 5 figures

Interaction between a Bloch wall in a ferrite-garnet film and a vortex in a superconductor is analyzed in the London approximation. Equilibrium distribution of vortices formed around the Bloch wall is calculated. The results agree quantitatively with magneto-optical experiment where an in-plane magnetized ferrite-garnet film placed on top of NbSe2 superconductor allows observation of individual vortices. In particular, our model can reproduce a counter-intuitive attraction observed between vortices and a Bloch wall having the opposite polarity. It is explained by magnetic charges appearing due to discontinuity of the in-plane magnetization across the wall., Comment: 4 pages, 5 figures

We report a detailed comparison of experimental data and theoretical predictions for the dendritic flux instability, believed to be a generic behavior of type-II superconducting films. It is shown that a thermo-magnetic model published very recently [Phys. Rev. B 73, 014512 (2006)] gives an excellent quantitative description of key features like the instability onset (first dendrite appearance) magnetic field, and how the onset field depends on both temperature and sample size. The measurements were made using magneto-optical imaging on a series of different strip-shaped samples of MgB2. Excellent agreement is also obtained by reanalyzing data previously published for Nb., Comment: 4 pages, 5 figures

The determination of inter- and intra-filament transport characteristics in superconducting composites such as BSCCO-Ag tapes is of great importance for material evaluation towards applications. Most attempts to separate the two contributions have relied on indirect methods based on magnetic measurements such as SQUID or magneto-optic imaging techniques. Here we show that laser patterning of superconducting BSCCO-Ag tapes constitutes a simple approach to measure local transport properties in a direct way, even able to separate inter- and intra-filament contributions to the overall transport behavior of the sample. Our technique is potentially useful for sub-millimeter devices based on superconducting tapes., Comment: 14 pages, 5 figures

Superconducting YBaCuO thin films were equipped with a special arrangement of antidots (holes) of 1 micron radius in order to guide the stream of magnetic flux moving in (or out of) the sample. The flux distribution and its dynamics were visualized using real-time magneto-optical imaging. It is clearly demonstrated that one-dimensional antidot arrays strongly facilitate propagation of magnetic flux. We also demonstrate a possibility to alter the direction of flux motion in a controlled way by special arrangement of intercepting antidot arrays. Our resolution was sufficient for observation of flux in particular antidots, which allows a more detailed dynamic analysis of such systems., Comment: 4 pages, 5 figures, submitted to Physica C, Proc. of VORTEX-IV Workshop on Crete-2005

Recent theoretical analysis of spatially-nonuniform modes of the thermomagnetic instability in superconductors [Phys. Rev. B 70, 224502 (2004)] is generalized to the case of a thin film in a perpendicular applied field. We solve the thermal diffusion and Maxwell equations taking into account nonlocal electrodynamics in the film and its thermal coupling to the substrate. The instability is found to develop in a nonuniform, fingering pattern if the background electric field, E, is high and the heat transfer coefficient to the substrate, h0, is small. Otherwise, the instability develops in a uniform manner. We find the threshold magnetic field, H_fing(E,h0), the characteristic finger width, and the instability build-up time. Thin films are found to be much more unstable than bulk superconductors, and have a stronger tendency for formation of dendritic pattern., Comment: 13 pages, 7 figures

We report a simple and easily controllable method where a nano-undulated surface morphology of Nd1/3Eu1/3Gd1/3Ba2Cu3Ox (NEG) films leads to a substantial increase in the critical current density in superconducting YBa2Cu3Ox (YBCO) films deposited by pulsed laser deposition on such NEG layers. The enhancement is observed over a wide range of fields and temperatures. Transmission electron microscopy shows that such YBCO films possess a high density of localized areas, typically 20 x 20 nm2 in size, where distortion of atomic planes give rotational (2 to 5 degrees) moire patterns. Their distribution is random and uniform, and expected to be the origin of the enhanced flux pinning. Magneto-optical imaging shows that these films have excellent macroscopic magnetic uniformity., Comment: 4 pages, 4 figures

Magneto-optical imaging is used to visualize vortex avalanches in MgB2 films at 4K. Avalanches ranging from 50 to 50000 vortices were detected. The size distribution function has a clear peak whose position moves towards larger sizes as the applied field increases. This field dependence as well as variation of flux density profile during an avalanche are well described by a proposed model assuming a thermal origin of the avalanches. The model is based on the adiabatic approach and takes into account nonlocal electrodynamics in thin superconductors. The threshold field for thermal avalanches is predicted to be much smaller than that for thick superconductors, in agreement with the experiment., Comment: 8 pages, 10 figures, submitted to PRB

From the magneto optics images (MOI), the dendritic magnetic avalanche is known to appear dominantly for thin films of the newly discovered MgB$_2$. To clarify the origin of this phenomenon, we studied in detail the MOI of carbon-free MgB$_2$ thin films with and without a deposited gold layer. The MOI indicated carbon contamination was not the main source of the avalanche. The MOI clearly showed that the deposition of metallic gold deposition on top of a MgB$_2$ thin film improved its thermal stability and suppressed the sudden appearance of the dendritic flux avalanche. This is consistent with the previous observation of flux noise in the magnetization., Comment: 9 pages, 4 figeures

Flux distributions in thin superconducting NbN films placed in a perpendicular magnetic field have been studied using magneto-optical imaging. Below 5.5 K the flux penetrates in the form of abrupt avalanches resulting in dendritic structures. Magnetization curves in this regime exhibit extremely noisy behavior. Stability is restored both above a threshold temperature T* and applied field H*, where H* is smaller for increasing field than during descent. The dendrite size and morphology are strongly T dependent, and fractal analysis of the first dendrites entering into a virgin film shows that dendrites formed at higher T have larger fractal dimension., Comment: 3 pages, 5 figures

A linear analysis of thermal diffusion and Maxwell equations is applied to study the thermomagnetic instability in a type-II superconducting slab. It is shown that the instability can lead to formation of spatially nonuniform distributions of magnetic field and temperature. The distributions acquire a finger structure with fingers perpendicular to the screening current direction. We derive the criterion for the instability, and estimate its build-up time and characteristic finger width. The fingering instability emerges when the background electric field is larger than a threshold field, $E>E_c$, and the applied magnetic field exceeds a value $H_fing \propto 1/\sqrt{E}$. Numerical simulations support the analytical results, and allow to follow the development of the fingering instability beyond the linear regime. The fingering instability may be responsible for the nucleation of dendritic flux patterns observed in superconducting films using magneto-optical imaging., Comment: 8 pages, 6 figures, accepted to Phys. Rev. B; (new version: minor changes)

Avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. It can be also found in vortex matter when a type II superconductor is externally driven, for example, by increasing the magnetic field. Vortex avalanches associated with thermal instabilities can be an undesirable effect for applications, but "dynamically driven" avalanches emerging from the competition between intervortex interactions and quenched disorder constitute an interesting scenario to test theoretical ideas related with non-equilibrium dynamics. However, differently from the equilibrium phases of vortex matter in type II superconductors, the study of the corresponding dynamical phases - in which avalanches can play a role - is still in its infancy. In this paper we critically review relevant experiments performed in the last decade or so, emphasizing the ability of different experimental techniques to establish the nature and statistical properties of the observed avalanche behavior., Comment: To be published in Reviews of Modern Physics April 2004. 17 pages

We observe single vortices as they penetrate the edge of a superconductor using a high-sensitivity magneto-optical microscope. The vortices leap across a gap near the edge, a distance that decreases with increasing applied field and sample thickness. This behaviour can be explained by the combined effect of the geometrical barrier and bulk pinning., Comment: 2 pages, 1 figure, M2S-Rio proceedings