M.S. Welling

Dendritic flux avalanches and nonlocal electrodynamics in thin superconducting films.

We report a mechanism of nonisothermal dendritic flux penetration in superconducting films. Our numerical and analytical analysis of coupled nonlinear Maxwell and thermal diffusion equations shows that dendritic flux pattern formation results from spontaneous branching of propagating flux filaments due to nonlocal magnetic flux diffusion and positive feedback between flux motion and Joule heating. The branching is triggered by a thermomagnetic edge instability, which causes stratification of the critical state. The resulting distribution of thermomagnetic microavalanches is not universal, because it depends on a spatial distribution of defects. Our results are in good agreement with experiments on Nb films.

Fast imaging polarimeter for magneto-optical investigations

~typically, 0.5‐2.0 mm! is in direct contact with the superconductor and rotates the polarization vector of the incident linear polarized light over an angle f proportional to the local magnetic field B according to f5VlB. Between the crossed polarizers of a polarization microscope the square of the local magnetic field is thus imaged as an intensity map. Unfortunately, this type of setup has three main disadvantages: ~i! the sign of the rotation angle of the polarization vector and, hence, of the magnetic field, cannot be determined; ~ii! the setup is very insensitive for small magnetic fields/angles; and ~iii! the measured intensity distribution is strongly influenced by the inhomogeneous illumination. In this article, we report on a new method which circumvents all these problems. The transmitted intensity in a polarization microscope with a sample placed between the polarizer and analyzer is I5L sin 2 ~a1f!.L~a1f! 2 , where f is the rotation angle due to the sample, ~90°2a! is the angle between the polarizer and analyzer, and L is the incident intensity. For a50, i.e., with perfectly crossed polarizer and analyzer, the intensity depends quadratically on f for small f. This results in poor sensitivity close to f50 while the method gives no information on the sign of f .T o increase the sensitivity close to f50, sometimes a is set to a small nonzero value. We expand this idea by modulating the incident polarization direction. Since the sinusoidal modulation used for nonimaging Kerr measurements has the disadvantage that a lot of processing is needed to determine f and also has a response time lower than the modulation frequency ~which due to Nyquist’s 4 sampling theorem must be much lower than the image acquisition rate!, we use a modulation with only three fixed values of a. This is justified since, even if we take into account that there may be an intensity offset K ~due to camera noise, readout offset, or stray light! resulting in a measured intensity I.K1L~a1f! 2 , ~1! only three measurements suffice to determine K, L, and f. We choose to measure at a52a 0 , 0, and 1a 0 , where a 0 is typically of the order of the maximum rotation due to the sample ~a few degrees!; the corresponding intensities are denoted by I 2 , I 0 , and I 1 . It is easily verified that L and f can be found from such a measurement using

Ultra-sensitive field sensors - an alternative to SQUIDs

Very low magnetic fields are detected up to now using SQUID-based devices. In the femtotesla range, only low-T/sub c/ SQUIDs have a sufficiently low level of noise to measure extremely low signals, as for instance induced fields of the neural activity of the brain, for magneto-encephalography (MEG). An alternative to SQUIDs is to combine a superconducting flux-to-field transformer with a high-sensitivity giant magnetoresistive sensor (GMR). We have fabricated and performed experiments on such an integrated YBCO-based mixed sensor. It is comprised of a GMR stack separated from a YBCO thin film by an insulating layer. The induced supercurrent in the YBCO is forced through a narrow constriction, thereby creating a local field much larger than the external field. This large local field is detected by the GMR. Effective noise levels are down to 30 fT/sqrtHz, which is in the range of high-Tc Squids. Performance of this device is shown from liquid helium temperature (4.2 K) up to liquid nitrogen temperature (77K). By replacing the GMR by a Tunneling Magneto Resistance (TMR) or a Colossal Magneto Resistance (CMR) sensor, and by adjusting the dimensions to optimize the local enhancement effect, the sensitivity should reach the subfemtotesla range at low frequency. A large number of applications could be investigated by this sensor, especially in the biomagnetism area, as well as in various other fields, from earth mapping to fundamental physics (vortex motion in superconductors, magnetic interactions...).

Self-organized criticality induced by quenched disorder: Experiments on flux avalanches in NbHx films

We present an experimental study of the influence of quenched disorder on the distribution of flux avalanches in type-II superconductors. In the presence of much quenched disorder, the avalanche sizes are powerlaw distributed and show finite-size scaling, as expected from self-organized criticality sSOCd. Furthermore, the shape of the avalanches is observed to be fractal. In the absence of quenched disorder, a preferred size of avalanches is observed and avalanches are smooth. These observations indicate that a certain minimum amount of disorder is necessary for SOC behavior. We relate these findings to the appearance or nonappearance of SOC in other experimental systems, particularly piles of sand.

Dynamic roughening of the magnetic flux landscape in YBa2Cu3O7-xYBa2Cu3O7-x

We study the magnetic flux landscape in YBa2Cu3O7-xYBa2Cu3O7-x thin films as a two dimensional rough surface. The vortex density in the superconductor forms a self-affine structure in both space and time. It is characterized by a roughness exponent α=0.76(3)α=0.76(3) and a growth exponent β=0.57(6)β=0.57(6). The roughening is caused by flux avalanches in a self-organized critical state, which is formed in the vortex matter of the superconductor. We discuss our results in the context of other roughening systems in the presence of quenched disorder.

Dynamic roughening of the magnetic flux landscape in

We study the magnetic flux landscape in YBa2Cu3O7-xYBa2Cu3O7-x thin films as a two dimensional rough surface. The vortex density in the superconductor forms a self-affine structure in both space and time. It is characterized by a roughness exponent α=0.76(3)α=0.76(3) and a growth exponent β=0.57(6)β=0.57(6). The roughening is caused by flux avalanches in a self-organized critical state, which is formed in the vortex matter of the superconductor. We discuss our results in the context of other roughening systems in the presence of quenched disorder.

Experimental study of self organized criticality on a three dimensional pile of rice

The dynamics of a driven, three dimensional rice‐pile is studied. When the pile is fully grown, its activity takes place in power‐law distributed avalanches. The observation of finite‐size scaling in the observed cut‐off size indicates that the pile is in a true critical state, as is demanded by self‐organized criticality. Before the stationary state is reached, the maximum slope of the pile is increasing towards a critical value, where the critical state is reached asymptotically. The exponent governing this approach to the critical state is related to the exponents determined in the critical state for the avalanche dimension and distribution. This is in good accord with an analytical theory of self‐organized criticality. based on extremal dynamics.

EFFECT OF SUBSTRATE ORIENTATION AND HYDROGEN IMPURITIES ON FLUX PENETRATION IN Nb THIN FILMS

Very different kinds of magnetic flux penetration patterns have been reported in the type-II superconductor Nb. Using our advanced magneto-optical setup we investigate the flux penetration in Nb thin films. We find that depending on the sapphire substrate orientation (either A-plane or R-plane) qualitatively different structures are observed. In particular, for the A-plane orientation we find fingering and branching, whereas for R-plane samples a rough but continuous flux front is observed. Since Nb easily accepts hydrogen atoms as interstitial impurities, the influence of static pinning centers on the flux penetration process can be investigated. We find that the flux penetration drastically changes, becoming more irregular. The possibility to add a well- controlled amount of disorder makes NbHx an ideal system to study the influence of quenched noise on roughening phenomena.

Magneto-Optical Imaging of Pattern Formation in the Vortex Landscape

Due to the occurrence of punctuations or avalanches, flux penetration in superconductors is not the smooth process that is described in many textbooks. We investigate the relationship between spatial fluctuations of the vortex density map and vortex avalanches. For the experiment, we use a magneto-optical image lock-in amplifier. The optimization of this apparatus, in particular with respect to noise reduction is discussed.