as well as the bursty propagation of cracks in disordered solids, but similar phenomena can be observed in a wide range of contexts beyond the traditional realm of physics, ranging from neuronal avalanches in the brain to volatility clustering in financial markets.
I will start by presenting an overview of Barkhausen noise from the perspective of a statistical physicist. Typically, one starts from the rather well-established assumption that the noise originates from the jerky field-driven motion of domain walls interacting with various impurities and imperfections in the magnet, something that is often modelled by considering domain walls as driven elastic interfaces in random media. This then leads one to study the depinning transition of domain walls, and how the statistical properties of Barkhausen noise reflect the universality class of the transition, governed by things like the range of interactions and the spatial dimensionality of the system.
Then, I will briefly discuss our recent modelling efforts focusing especially on the problem of Barkhausen noise in thin film geometry. First, I will discuss modelling Barkhausen noise in thin films with uniaxial in-plane anisotropy, where the competition between the domain-wall surface tension and dipolar interactions induces a crossover between a rough domain-wall phase at short length scales and a large-scale phase where the walls display a zigzag morphology . The two phases are characterized by different critical exponents for Barkhausen avalanche dynamics that are in quantitative agreement with experimental measurements on MnAs thin films. Finally, I discuss modelling of Barkhausen noise in disordered Pt/Co/Pt thin films with PMA due to precessional motion of domain walls using full micromagnetic simulations, allowing for a detailed description of the domain wall internal structure . In this regime the domain walls contain topological defects known as Bloch lines which repeatedly nucleate, propagate, and annihilate within the domain wall during the Barkhausen jumps. In addition to bursts of domain wall propagation, the in-plane Bloch line dynamics within the domain wall exhibits crackling noise and constitutes the majority of the overall spin rotation activity.
 L. Laurson, G. Durin, and S. Zapperi, Universality classes and crossover scaling of Barkhausen noise in thin films, Phys. Rev. B 89, 104402 (2014).
 T. Herranen and L. Laurson, Barkhausen noise from precessional domain wall motion, Phys. Rev. Lett. 122, 117205 (2019).