Magneto-optic imaging was used for a detailed study of the flux and current distribution of a long thin strip of YBa 2 Cu 3 O 7Ϫ␦ placed in a perpendicular external magnetic field. The inverse magnetic problem, i.e., that of deriving from a field map the underlying current distribution, is formulated and solved for the strip geometry. Applying the inversion to the magneto-optically found field map we find on a model-independent basis the current distribution across the strip to be in remarkable agreement with the profile predicted by the Bean model. The paper also presents results on the behavior of the Bi-doped YIG film with in-plane anisotropy which we use as field indicator, explaining why previous measurements of flux density profiles have displayed surprisingly large deviations from the expected behavior. ͓S0163-1829͑96͒02046-2͔

Avalanche dynamics are found in many phenomena, from earthquakes to the evolution of species. They can also be found in vortex matter when a type-II superconductor is externally driven, for example, by an increasing 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 may provide an interesting test scenario for nonequilibrium dynamics theory. In contrast to the equilibrium phases of vortex matter in type-II superconductors, the corresponding dynamical phases-in which avalanches can play a role-are only beginning to be studied. This article reviews relevant experiments performed in the last decade or so, emphasizing the ability of different experimental techniques to establish the nature and statistical properties of avalanche behavior. CONTENTS

Following the discovery of superconductivity in polycrystalline magnesium diboride a tremendous effort is now focused on thin films of this material. Contrary to expectations, the penetration of magnetic flux in such films is found dominated by large dendritic structures abruptly created when small fields are applied. The dendritic instability, observed below 10 K using magneto-optical imaging, has a temperature dependent morphology ranging from quasi-1D dendrites to beautiful tree-like structures. This behavior is responsible for the anomalous noise in magnetization curves, and strongly suppresses the apparent critical current. Simulations of vortex dynamics incorporating local heating effect reproduce the observed dendritic scenario.The new superconductor, MgB 2 , discovered (1) in January this year has already proved to be a promising candidate for technological applications due to success in fabrication of thin films (2) and wires (3) with high current carrying capabilities. At the same time, such films and wires, as well as polycrystalline MgB 2 are reported to show exceptional magnetic behavior displaying numerous and "noise-like" jumps in the magnetization as a function of applied field (3-5). Magnetization jumps in type-II superconductors are usually associated with a thermo-magnetic instability of the quantized flux lines (vortices) penetrating the material. When the vortices move they leave a trail of elevated temperature facilitating motion of nearby vortices, which eventually leads to a large-scale avalanche invasion of depinned flux lines (6). This thermal runaway, where the magnetic energy stored in the superconductor suddenly converts to thermal energy, can cause instability of the superconducting properties and have catastrophic consequences for practical applications. To which extent the thermomagnetic instability will affect the technological potential of MgB 2 is today a vitally important question. In high temperature superconductors (HTSs) the flux jumps occur only in bulk materials, the first one at applied fields of typically one Tesla and then nearly periodically as the field increases. In MgB 2 the jumps are omnipresent, with the first one occurring already at a few milliTesla and subsequent jumps coming at random. Thus, MgB 2 appears not only far more susceptible to thermal runaways than HTSs, but the flux jumps exhibit also qualitatively new features. All this motivated the present study of MgB 2 films using magneto-optical (MO) imaging to visualize and characterize the nature of the magnetic instability.Thin films of MgB 2 were fabricated on (1  102) Al 2 O 3 substrates using pulsed laser deposition. An amorphous B film was first deposited, and then sintered at high temperature in a Mg atmosphere. Details of the preparation are reported elsewhere (2). Typical films had a sharp superconducting transition (∆T c ~ 0.7 K) at T c = 39 K, and a high degree of c-axis alignment perpendicular to the film plane.Magnetic characterization of the films was first done by measuring the magnetization...

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 thermomagnetic model published very recently [Phys. Rev. B 73, 014512 (2006)10.1103/PhysRevB.73.014512] gives an excellent quantitative description of key features like the stability 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.

We report that the ͑Ba, K͒Fe 2 As 2 crystal with T c = 32 K shows a pinning potential, U 0 , as high as 10 4 K, with U 0 showing very little field dependence. The ͑Ba, K͒Fe 2 As 2 single crystals become isotropic at low temperatures and high magnetic fields, resulting in a very rigid vortex lattice, even in fields very close to H c2 . The isotropic rigid vortices observed in the two-dimensional ͑2D͒ ͑Ba, K͒Fe 2 As 2 distinguish this compound from 2D high-T c cuprate superconductors with 2D vortices. The vortex avalanches were also observed at low temperatures in the ͑Ba, K͒Fe 2 As 2 crystal. It is proposed that it is the K substitution that induces both almost isotropic superconductivity and the very strong intrinsic pinning in the ͑Ba, K͒Fe 2 As 2 crystal.A high critical current density, J c , upper critical field, B c2 , and irreversibility field, B irr , a high superconducting transition temperature, T c , strong magnetic-flux pinning, good grain connectivity, and isotropic superconductivity are the major physical requirements for superconducting materials used in practical applications operating at low and, in particular, high magnetic fields. The conventional low-T c superconductors, where H c2 is also small, can only carry large J c at very low temperatures. The cuprate high-T c superconductors suffer from poor grain connectivity and easy melting of the vortex lattice, leading to small J c in high magnetic fields at relatively high temperatures. For MgB 2 superconductor with T c of 39 K, B irr is far below H c2 , and J c drops quickly with both field and temperature, preventing its use above 20 K. The newly discovered Fe-based superconductors 1-7 show T c as high as 55 K and B c2 above 200 T, in combination with a small anisotropy for REFeAsO 1−x F x ͑RE-1111 phase, with RE a rare-earth element͒ 8 and an almost isotropic superconductivity for ͑Ba, K͒Fe 2 As 2 ͑122 phase͒. 9 These properties make the Fe-based superconductors extremely promising candidates for high magnetic field applications at relatively high temperatures. The current carrying ability of these superconductors at high fields and temperatures is largely determined by the flux-pinning strength and the behavior of the vortex matter. Therefore, the determination of their intrinsic vortex pinning strength is a central issue from both an applied and a fundamental perspective. Both 1111 and 122 phase compounds have typical two-dimensional ͑2D͒ crystal structures. In RE-1111 phase, where RE is a rare-earth element, the FeAs superconducting layers are separated by insulating LaO layers 10 while in Ba͑K͒-122 phase, the FeAs layer is sandwiched between conductive Ba layers. 5 It is expected that the 122 phase containing two FeAs layers would have small anisotropy and thus higher intrinsic pinning compared to the single layer 1111 phase. Co-doped BaFe 2 As 2 single crystal shows an anisotropy of 1-3 and upper criticalfield values of B c2 ͑B ʈ ab͒ = 20 T and B c2 ͑B ʈ c͒ = 10 T at 20 K, with dB c2 / dT Ϸ 5 T/ K. 11 For single crystals of the optimally do...