  The field-driven magnetisation reversal processes in disordered systems
exhibit a collective behaviour that is manifested in the scale-invariance of
avalanches, closely related to underlying dynamical mechanisms. Using the
multifractal time series analysis, we study the structure of fluctuations at
different scales in the accompanying Barkhausen noise. The stochastic signal
represents the magnetisation discontinuities along the hysteresis loop of a
3-dimensional random field Ising model simulated for varied disorder strength
and driving rates. The analysis of the spectrum of the generalised Hurst
exponents reveals that the segments of the signal with large fluctuations
represent two distinct classes of stochastic processes in weak and strong
pinning regimes. Furthermore, increased driving rates have a profound effect on
the small fluctuation segments and broadening of the spectrum. The study of the
temporal correlations, sequences of avalanches, and their scaling features
complements the quantitative measures of the collective dynamics at the
hysteresis loop. The multifractal properties of Barkhausen noise describe the
dynamical state of domains and precisely discriminate the weak pinning,
permitting the motion of individual walls, from the mechanisms occurring in
strongly disordered systems. The multifractal nature of the reversal processes
is particularly relevant for currently investigated memory devices that utilize
a controlled motion of individual domain walls.
