Multifractal structure of Barkhausen noise: A signature of collective dynamics at hysteresis loop

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.