Statistical properties of Barkhausen noise in amorphous ferromagnetic films

Barkhausen noise in disordered striplike ferromagnets: Experiment versus simulations

In this work, we present a systematic comparison of the results obtained from the low-frequency Barkhausen noise recordings in nanocrystalline samples with those from the numerical simulations of the random-field Ising model systems. We performed measurements at room temperature on a field-driven metallic glass stripe made of VITROPERM 800 R, a nanocrystalline iron-based material with an excellent combination of soft and magnetic properties, making it a cutting-edge material for a wide range of applications. Given that the Barkhausen noise emissions emerging along a hysteresis curve are stochastic and depend in general on a variety of factors (such as distribution of disorder due to impurities or defects, varied size of crystal grains, type of domain structure, driving rate of the external magnetic field, sample shape and temperature, etc.), adequate theoretical modeling is essential for their interpretation and prediction. Here the Random field Ising model, specifically its athermal nonequilibrium version with the finite driving rate, stands out as an appropriate choice due to the material's nanocrystalline structure and high Curie temperature. We performed a systematic analysis of the signal properties and magnetization avalanches comparing the outcomes of the numerical model and experiments carried out in a two-decade-wide range of the external magnetic field driving rates. Our results reveal that with a suitable choice of parameters, a considerable match with the experimental results is achieved, indicating that this model can accurately describe the Barkhausen noise features in nanocrystalline samples.

Denouement of the Energy-Amplitude and Size-Amplitude Enigma for Acoustic-Emission Investigations of Materials

There are many systems producing crackling noise (avalanches) in materials. Temporal shapes of avalanches, U(t) (U is the detected voltage signal, t is the time), have self-similar behaviour and the normalized U(t) function (e.g., dividing both the values of U and t by S^1/2, where S is the avalanche area), averaged for fixed S, should be the same, independently of the type of materials or avalanche mechanisms. However, there are experimental evidences that the temporal shapes of avalanches do not scale completely in a universal way. The self-similarity also leads to universal power-law-scaling relations, e.g., between the energy, E, and the peak amplitude, A_m, or between S and A_m. There are well-known enigmas, where the above exponents in acoustic emission measurements are rather close to 2 and 1, respectively, instead of E~Am3 and S~Am2, obtained from the mean field theory, MFT. We show, using a theoretically predicted averaged function for the fixed avalanche area, U(t)=atexp(−bt2) (where a and b are non-universal, material-dependent constants), that the scaling exponents can be different from the MFT values. Normalizing U by A_m and t by t_m (the time belonging to the A_m: rise time), we obtain tm~Am1−φ (the MFT values can be obtained only if φ would be zero). Here, φ is expected to be material-independent and to be the same for the same mechanism. Using experimental results on martensitic transformations in two different shape-memory single-crystals, φ = 0.8 ± 0.1 was obtained (φ is the same for both alloys). Thus, dividing U by A_m as well as t by Am1−φ (~t_m) leads to the same common, normalized temporal shape for different, fixed values of S. This normalization can also be used in general for other experimental results (not only for acoustic emission), which provide information about jerky noises in materials.

Waiting-time statistics in magnetic systems

Many complex systems, from earthquakes and financial markets to Barkhausen effect in ferromagnetic materials, respond with a noise consisting of discrete avalanche-like events with broad range of sizes and durations, separated by waiting times. Here we focus on the waiting-time statistics in magnetic systems. By investigating the Barkhausen noise in amorphous and polycrystalline ferromagnetic films having different thicknesses, we uncover the form of the waiting-time distribution in time series recorded from the irregular and irreversible motion of magnetic domain walls. Further, we address the question of if the waiting-time distribution evolves with the threshold level, as well as with the film thickness and structural character of the materials. Our results, besides informing on the temporal avalanche correlations, disclose the waiting-time statistics in magnetic systems also bring fingerprints of the universality classes of Barkhausen avalanches and a dimensional crossover in the domain wall dynamics.

Playing with universality classes of Barkhausen avalanches

Many systems crackle, from earthquakes and financial markets to Barkhausen effect in ferromagnetic materials. Despite the diversity in essence, the noise emitted in these dynamical systems consists of avalanche-like events with broad range of sizes and durations, characterized by power-law avalanche distributions and typical average avalanche shape that are fingerprints describing the universality class of the underlying avalanche dynamics. Here we focus on the crackling noise in ferromagnets and scrutinize the traditional statistics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films having different thicknesses. We show how scaling exponents and average shape of the avalanches evolve with the structural character of the materials and film thickness. We find quantitative agreement between experiment and theoretical predictions of models for the magnetic domain wall dynamics, and then elucidate the universality classes of Barkhausen avalanches in ferromagnetic films. Thereby, we observe for the first time the dimensional crossover in the domain wall dynamics and the outcomes of the interplay between system dimensionality and range of interactions governing the domain wall dynamics on Barkhausen avalanches.

Broadband spectroscopy of thermodynamic magnetization fluctuations through a ferromagnetic spin-reorientation transition

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar⁺ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, S(ν), exhibits a remarkably robust ν ^-3/2 power law over frequencies ν from 1 kHz to 1 MHz. As the SRT region is traversed, however, S(ν) spectra develop a steadily-increasing critical frequency, ν ₀, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.

Universal temporal characteristics and vanishing of multifractality in Barkhausen avalanches

Barkhausen effect in ferromagnetic materials provides an excellent area for investigating scaling phenomena found in disordered systems exhibiting crackling noise. The critical dynamics is characterized by random pulses or avalanches with scale-invariant properties, power-law distributions, and universal features. However, the traditional Barkhausen avalanches statistics may not be sufficient to fully characterize the complex temporal correlation of the magnetic domain walls dynamics. Here we focus on the multifractal scenario to quantify the temporal scaling characteristics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films with thicknesses from 50 to 1000 nm. We show that the multifractal properties are dependent on film thickness, although they seem to be insensitive to the structural character of the materials. Moreover, we observe for the first time the vanishing of the multifractality in the domain walls dynamics. As the thickness is reduced, the multifractal behavior gives place to a monofractal one over the entire range of time scales. This reorganization in the temporal scaling characteristics of Barkhausen avalanches is understood as a universal restructuring associated to the dimensional crossover, from three- to two-dimensional magnetization dynamics.

Critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model on a triangular lattice

We present a numerical study of the critical behavior of the nonequilibrium zero-temperature random field Ising model in two dimensions on a triangular lattice. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations of systems with linear sizes up to L=65536, show that the model is in a different universality class than the same model on a quadratic lattice, which is relevant for a better understanding of model universality and the analysis of experimental data.

Quantitative Scaling of Magnetic Avalanches

We provide the first quantitative comparison between Barkhausen noise experiments and recent predictions from the theory of avalanches for pinned interfaces, both in and beyond mean field. We study different classes of soft magnetic materials, including polycrystals and amorphous samples-which are characterized by long-range and short-range elasticity, respectively-both for thick and thin samples, i.e., with and without eddy currents. The temporal avalanche shape at fixed size as well as observables related to the joint distribution of sizes and durations are analyzed in detail. Both long-range and short-range samples with no eddy currents are fitted extremely well by the theoretical predictions. In particular, the short-range samples provide the first reliable test of the theory beyond mean field. The thick samples show systematic deviations from the scaling theory, providing unambiguous signatures for the presence of eddy currents.