Atle Jorstad Qviller

Scaling behaviour of dynamically driven vortex avalanches in superconducting YBa₂Cu₃O_7−δ 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.

Magneto-optical imaging is a powerful technique for studying qualitative features of magnetic flux distributions in superconductors and other magnetic samples. However, magneto-optical imaging does not automatically return two-dimensional maps with the actual values of the magnetic field, due to the non-linear response functions of magneto-optical indicator films and in practice also non-uniform illumination. A quantitative treatment is needed in order to achieve such a calibration. After calibration, one can proceed to deduce the corresponding two-dimensional maps of the current density distribution from inversion of the Biot-Savart law. While there has been published a large amount of work on quantitative magneto-optical imaging, the material is scattered and notation differs significantly between different authors. These notes originate from parts of the Ph. D. thesis of the author and collect the most important materials into a unified and updated treatment. Basic aspects of magnetic flux penetration in superconductors including the Bean model are reviewed briefly in chapter 1. In chapter 2, the method of magneto-optical imaging using the Faraday effect is introduced, together with practical aspects of magneto-optical experiments at low temperatures and the semi-qualitative technique of RGB addition for checking the reproducibility of flux patterns. The physics of magneto-optical indicator films and calibration of magneto-optical images into maps of magnetic field values are discussed in chapter 3. Next, in chapter 4 the Biot-Savart law and fast Fourier transformations are discussed before proceeding to inversion of magnetic field maps into current density maps. Finally, magnetometry with Faraday magneto-optical imaging is treated. MATLAB codes for several of the discussed concepts can be found at https://github.com/atlejq/Magneto-optics

A method for calculating stored magnetic energy in a thin superconducting film based on quantitative magneto-optical imaging is developed. Energy and magnetic moment are determined with these calculations for full hysteresis loops in a thin film of the superconductor NbN. Huge losses in energy are observed when dendritic avalanches occur. Magnetic energy, magnetic moment, sheet current and magnetic flux distributions, all extracted from the same calibrated magneto-optical images, are analyzed and discussed. Dissipated energy and the loss in moment when dendritic avalanches occur are related to each other. Calculating these losses for specific spatially-resolved flux avalanches is a great advantage, because of their unpredictable and non-reproducible nature. The relative losses in energy are much higher than the relative losses in moment.

Appearance of dendritic magnetic flux avalanches in superconducting films, which are associated with thermo-magnetic instability (TMI), very often indicates serious limitations for the ultimate performance of superconducting devices made of type-II superconducting thin films. We demonstrate that the stability can be controlled by a thorough adjustment of samples morphology at nano-scale, which affects internal material parameters. By this, the metal coating, commonly used as for stabilization, becomes redundant. Most importantly, we directly show by the mean of magneto-optical imaging that introduction of nano-scaled disorder dramatically changes the mode of magnetic flux propagation in the superconductors, from uniform motion of individual vortices to correlated jumps of relatively large vortex bundles, revealing the triggering mechanism of TMI.