We review the present state of understanding of the Barkhausen effect in soft ferromagnetic materials. Barkhausen noise (BN) is generated by the discontinuous motion of magnetic domains as they interact with impurities and defects. BN is one of the many examples of crackling noise, arising in a variety of contexts with remarkably similar features, and occurring when a system responds in a jerky manner to a smooth external forcing. Among all crackling system, we focus on BN, where a complete and consistent picture emerges thanks to an exactly solvable model of avalanche dynamics, known as the ABBM model, which ultimately describes the system in terms of a Langevin equation for the velocity of the avalanche front. Despite its simplicity, the ABBM model is able to accurately reproduce the phenomenology observed in the experiments on a large class of magnetic materials, as long as universal properties are involved. To complete the picture and to understand the long-standing discrepancy between the ABBM theory and the experiments, which otherwise agree exceptionally well, consisting of the puzzling asymmetric shape of the noise pulses, microscopic details must be taken into account, namely the effects of eddy current retardation. These effects can be incorporated in the model, and result, to a first-order approximation, in a negative effective mass associated with the wall. The progress made in understanding BN is potentially relevant for other crackling systems: on the one hand, the ABBM model turns out to be a paradigmatic model for the universal behaviour of avalanche dynamics; on the other hand, the microscopic explanation of the asymmetry in the noise pulses suggests that inertial effects may also be at the origin of pulses asymmetry observed in other crackling systems.
Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
研究了在外加磁场作用下，无序介质中铁磁畴壁的动力学行为。钉扎结构之间的畴壁的雪崩式运动产生了称为巴克豪森效应的噪声。我们讨论了软铁磁材料的实验结果，参考畴结构和样品的几何形状，并报告巴克豪森噪声测量Fe $_{21}$ Co $_{64}$ B $_{15}$非晶合金。我们建立了一个柔性畴壁的运动方程，随着电场的增加，畴壁呈现出退钉扎的转变。长程偶极相互作用被示出设置上临界尺寸为$d_c=3$，这意味着平均场指数（可能的对数校正），预计描述巴克豪森效应。我们介绍了一个平均场的无限范围模型，并表明它是等效于以前介绍的单自由度模型，已知重现几个实验结果。我们在$d=3$中数值模拟了方程，证实了理论预测。我们计算的雪崩分布的磁场驱动率和退磁场的强度的函数。标度指数与驱动率成线性关系，而分布的截止点由退磁场决定，与实验结果非常吻合。
The role of stationarity in magnetic crackling noise
本文讨论了巴克沃森噪声信号的平稳性对雪崩统计量的影响。我们进行实验测量的Fe $_{85}$ B $_{15}$非晶带和比较周围的矫顽场，其中信号是固定的，通过整个磁滞回线采样的雪崩分布。在第一种情况下，我们恢复的标度指数通常观察到的其他非晶材料（$τ=1.3$，$α=1.5$）。而在第二种情况下，指数明显更大（$τ=1.7$，$α=2.2$）。我们提供了一个定量的解释实验结果，通过一个模型的铁磁畴壁的脱钉。本分析揭示了Spasojevic等人[Phys. Rev. E 54 2531（1996）]测量的巴克豪森噪声指数的异常高值。
Noise in disordered systems: The power spectrum and dynamic exponents in avalanche models
长期以来，人们已经知道巴克豪森噪声的功率谱在高频处具有幂律衰减。到目前为止，对这种衰变的理论预测是不正确的，或者只适用于一小部分模型。在本文中，我们描述了一个仔细的推导雪崩模型的功率谱指数，特别是在零温度随机场伊辛模型的变化。我们发现，天真的指数，（3-tau）/（σ nu z），这已经在其他几篇论文中推导出来，一般是不正确的小τ，当大雪崩是常见的。(tau是描述雪崩大小分布的指数，（σ nu z）是描述雪崩大小和雪崩持续时间之间关系的指数。我们发现，对于一个大类的雪崩模型，包括巴克豪森噪声的几个模型，正确的指数τ <2是1/（sigma nu z）。我们明确地推导出平均场指数2。在这个过程中，我们计算的平均雪崩形状的雪崩的固定持续时间和缩放形式的一些物理性质。
Antiferromagnetic Barkhausen noise induced by weak random-field disorder
Jožef Stefan Institute（约热·斯特凡研究所）；Complexity Science Hub（复杂科学中心）；Institute of Physics, Pregrevica 118, 11080 Belgrade, Serbia（塞尔维亚贝尔格莱德普雷格雷维察街118号物理研究所）
Istituto dei Sistemi Complessi - Consiglio Nazionale delle Ricerche（复杂系统研究所-意大利国家研究委员会）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；INFN, Sezione Roma2（意大利国家核物理研究所罗马第二分部）
Center for Complex Networks and Systems Research（复杂网络与系统研究所以）；Luddy School of Informatics, Computing, and Engineering（信息学、计算与工程学院）；Indiana University（印第安纳大学）；Bloomington, Indiana 47408, USA（印第安纳州布卢明顿市47408号）
