Multifractal analysis of Barkhausen noise reveals the dynamic nature of criticality at hysteresis loop

Abstract

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 three-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 dominant segments of the signal with large fluctuations represent two distinct classes of stochastic processes in weak and strong pinning regimes. Furthermore, in the weak pinning regime, the part of the signal originating from the beginning of the hysteresis loop has a different multifractal spectrum than the signal near the coercive field. The enhanced fluctuations (primarily in the central part of the hysteresis loop) for increased driving rate and larger system size, lead to a further broadening of the spectrum. The analysed Barkhausen signals are also shown to exhibit temporal correlations and power-law distributions of the magnetisation discontinuity and avalanche sizes, in agreement with previous studies. 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.