Scaling exponents for Barkhausen avalanches in polycrystals and
  amorphous ferromagnets

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Abstract

We investigate the scaling properties of the Barkhausen effect, recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents \tau = 1.50 \pm 0.05 or \tau = 1.27 \pm 0.03, for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff of the distributions to the demagnetizing factor which is in quantitative agreement with experiments.

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Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect

Pierre Cizeau, H. Stanley, Stefano Zapperi … (1998)

We study the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium. The avalanche-like motion of the domain walls between pinned configurations produces a noise known as the Barkhausen effect. We discuss experimental results on soft ferromagnetic materials, with reference to the domain structure and the sample geometry, and report Barkhausen noise measurements on Fe\(_{21}\)Co\(_{64}\)B\(_{15}\) amorphous alloy. We construct an equation of motion for a flexible domain wall, which displays a depinning transition as the field is increased. The long-range dipolar interactions are shown to set the upper critical dimension to \(d_c=3\), which implies that mean-field exponents (with possible logarithmic correction) are expected to describe the Barkhausen effect. We introduce a mean-field infinite-range model and show that it is equivalent to a previously introduced single-degree-of-freedom model, known to reproduce several experimental results. We numerically simulate the equation in \(d=3\), confirming the theoretical predictions. We compute the avalanche distributions as a function of the field driving rate and the intensity of the demagnetizing field. The scaling exponents change linearly with the driving rate, while the cutoff of the distribution is determined by the demagnetizing field, in remarkable agreement with experiments.

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Barkhausen noise: Elementary signals, power laws, and scaling relations

Djordje Spasojević, Srdjan Bukvić, Sava Milosevic … (1996)

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Avalanches, Barkhausen Noise, and Plain Old Criticality

James Sethna, Karin A. Dahmen, Olga Perkovic (1995)

We explain Barkhausen noise in magnetic systems in terms of avalanches near a plain old critical point in the hysteretic zero-temperature random-field Ising model. The avalanche size distribution has a universal scaling function, making non-trivial predictions of the shape of the distribution up to 50\% above the critical point, where two decades of scaling are still observed. We simulate systems with up to \(1000^3\) domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2d and \(6-\epsilon\) predictions, and compare to a variety of experimental Barkhausen measurements.