arXiv:1511.06118v2 [cond-mat.dis-nn] 7 Feb 2016 Multifractal analysis of Barkhausen noise reveals the dynamic nature of criticality at hysteresis loop Bosiljka Tadi´ c Department for Theoretical Physics; Jožef Stefan Institute; P.O. Box 3000; SI-1001 Ljubljana; Slovenia 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 accompa- nying 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. Further- more, 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 comple- ments 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, per- mitting 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. I. INTRODUCTION In driven disordered spin systems, the form of hysteresis loop reflects the existence of the domain structure, which re- sponds to the external magnetic field by a motion of the do- main walls. In particular, an increase of the domains aligned with the field occurs while the opposite magnetisation do- mains shrink. Thus, the magnetisation reversal processes in these systems involve a complex interplay between the mo- tion of the domain walls and their pinning by the magnetic and structural disorder centers. Driven by a slow field ramping along the hysteresis loop, the magnetisation reversal exhibits avalanches of aligned spins when the domain wall moves to a new position. The resulting burst events of magnetisation jumps is known as Barkhausen noise. These avalanches ex- hibit scaling features that depend on the strength of pinning and the driving rate, closely reflecting the underlying dynam- ical mechanism. In this work, we use the multifractal analysis of the Barkhausen noise to investigate the nature of fluctua- tions at all scales, which characterise the active mechanisms in different pinning regimes. Ferromagnetic alloys and metallic glasses exhibiting Barkhausen effect [1–4] represent strongly disordered sys- tems with domain structure grafted by the fabrication. Similar phenomena occur in relaxor ferroelectrics [5], stress-induced martensites [6], porous media [7] and other systems with a hysteresis. These phenomena represent a fascinating physics problem. Besides, the occurrence of hysteresis loop and the magnetisation reversal processes provide the basis for nonin- vasive structural analysis of materials [8] and technological applications. Prominent examples are the magnetic memory and, connected with charge transport, spin electronics in data storage [9]. Recently proposed memory devices are based on the controlled manipulation of the domain-wall motion and pinning by weak disorder or geometrical constraints in mag- netic nanowires [10]. A direct observation of the domain-wall motion in different experimental settings [11–14] revealed their stochastic kinetics, exhibiting certain universal features and dependence on the type and density of pinning centers. Consequently, a deeper understanding of the stochastic pro- cesses on the hysteresis loop becomes a topic of increased in- terest for these systems. Robust scale invariance of the magnetisation reversal avalanches in disordered ferromagnets has been observed both in experiments and numerical simulations [15–19]. The scal- ing behaviour of Barkhausen avalanches resembles familiar critical phenomena [18], while the dynamics of domain walls and spin flips can be related with criticality in sandpile au- tomata [20] or bootstrap percolation [21]. Moreover, it shares some general features with the collective dynamical phenom- ena observed at fixed points by the renormalization-group analysis of model disordered systems [22]. The scale invari- ance of the reversal avalanches depends on the system’s di- mensionality, range of interactions and the spin symmetry. In addition, these dynamical phenomena on the hysteresis were shown to depend on the magnetic anisotropy and strength of disorder [19, 23], topology of the substrate [24], as well as the driving mode [25, 26]. The occurrence of a variety of the exponents (a summary of the exponents can be found in Refs. [19, 27]) and universality classes in the scaling of avalanches is believed to strictly reflect differences in the underlying dy- namical mechanisms [28]. Specifically, for the weak disorder the system spanning avalanches can occur, whose fronts rep- resent moving individual domain walls. On the other hand, the occurrence of many domains at strong disorder makes the mu- tually constrained motion of many domain walls that results in small (subcritical) avalanches. The transition between these regimes has been considered as a disorder-induced critical point [18, 29]. While the scaling of the spanning avalanches has been studied numerically with an astonishing precision [30–33], there is little knowledge about the fine-scale struc- ture of the collective fluctuations, which are encoded in the accompanying Barkhausen noise. Here, we study the multifractal properties of Barkhausen noise signals across a broad range of pinning and driving con- ditions. We simulate the processes of magnetisation reversal