# Scaling Behavior of Quasi-One-Dimensional Vortex Avalanches in Superconducting Films

## TL;DR

This paper investigates the scaling behavior of vortex avalanches in superconducting films, demonstrating power-law distributions, finite-size scaling, and confirming a theoretical scaling relation through experimental data.

## Contribution

It provides the first experimental validation of the theoretical scaling relation between avalanche size exponent and fractal dimension in vortex avalanches.

## Key findings

- Avalanche size distributions follow power-laws over three decades.
- Finite-size scaling indicates self-organized criticality.
- Experimental data confirms the theoretical scaling relation.

## Abstract

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.