  We provide the first quantitative comparison between Barkhausen-noise
experiments and recent predictions from the theory of avalanches for pinned
interfaces, both in and beyond mean-field. We study different classes of soft
magnetic materials: polycrystals and amorphous samples, characterized by
long-range and short-range elasticity, respectively; both for thick and thin
samples, i.e. with and without eddy currents. The temporal avalanche shape at
fixed size, and observables related to the joint distribution of sizes and
durations are analyzed in detail. Both long-range and short-range samples with
no eddy currents are fitted extremely well by the theoretical predictions. In
particular, the short-range samples provide the first reliable test of the
theory beyond mean field. The thick samples show systematic deviations from the
scaling theory, providing unambiguous signatures for the presence of eddy
currents.
