Statistical properties of barkhausen noise in thin Fe films

Resistive Avalanches in La1-xSrxCoO3-δ (x = 0, 0.3) Thin Films and Their Reversible Evolution by Tuning Lattice Oxygen Vacancies (δ)

Strong correlations are often manifested by exotic electronic phases and phase transitions. LaCoO3-δ (LCO) is a system that exhibits such strong electronic correlations with lattice-spin-charge-orbital degrees of freedom. Here, we show that mesoscopic oxygen-deficient LCO films show resistive avalanches of about 2 orders of magnitude due to the metal-insulator transition (MIT) of the film at about 372 K for the 25 W RF power-deposited LCO film on the Si/SiO2 substrate. In bulk, this transition is otherwise gradual and occurs over a very large temperature range. In thin films of LCO, the oxygen deficiency (0 < δ < 0.5) is more easily reversibly tuned, resulting in avalanches. The avalanches disappear after vacuum annealing, and the films behave like normal insulators (δ ∼0.5) with Co2+ in charge ordering alternatively with Co3+. This oxidation state change induces spin state crossovers that result in a spin blockade in the insulating phase, while the conductivity arises from hole hopping among the allowed cobalt Co4+ ion spin states at high temperature. The chemical pressure (strain) of 30% Sr2+ doping at the La3+ site results in reduction in the avalanche magnitude as well as their retention in subsequent heating cycles. The charge nonstoichiometry arising due to Sr2+ doping is found to contribute toward hole doping (i.e., Co3+ oxidation to Co4+) and thereby the retention of the hole percolation pathway. This is also manifested in energies of crossover from the 3D variable range hopping (VRH) type transport observed in the temperature range of 300-425 K, while small polaron hopping (SPH) is observed in the temperature range of 600-725 K for LCO. On the other hand, Sr-doped LCO does not show any crossover and only the VRH type of transport. The strain due to Sr2+ doping refrains the lattice from complete conversion of δ going to 0.5, retaining the avalanches.

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.

Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.

Barkhausen Noise as a Reliable Tool for Sustainable Automotive Production

This paper deals with the sustainable production of components in the automotive industry, with the focus on the nondestructive evaluation of components after plasma nitridation via the Barkhausen noise technique. This study investigates the influence of tool wear on surface state after turning, and the consecutive plasma nitriding process. Moreover, position in the nitriding chamber and the corresponding heterogeneity of components is investigated as well. The results of experiments indicate that an increasing mechanical and thermal load due to flank wear and the associated process dynamics negatively affects the heterogeneity of the surface state after turning, and consecutive nitriding in terms of Barkhausen noise emission. Moreover, it was found that the conditions in the chamber during the nitriding process vary and, especially near the venting system, the temperature is slightly lower, such that some components are found to be unacceptable as well. The study also unwraps the contribution of the diffusion and compound layers with respect to MBN and discusses the contribution of the MBN pulses of different frequencies. The pinning strength of nitrides is indicated with respect to their size and the related thickness of DWs. Finally, this study clearly demonstrates how the MBN technique can be employed for the monitoring nitrided components and the corresponding optimisation of manufacturing cycles.

Effect of a uniform random external magnetic field with spatiotemporal variation on compensation in Ising spin-1/2 trilayered square ferrimagnets

Trilayered spin-1/2 Ising ferrimagnets are interesting thin systems for compensation phenomenon. In this work, a Metropolis Monte Carlo study is performed on the magnetic and thermodynamic response of such a system on square Bravais lattice, driven by uniform random external magnetic field with spatiotemporal variations. In two distinct configurations, the surface layers are made up of A and the middle layer is made up of B atoms in an ABA-type stacking while in AAB-type stacking, the top layer and the middle layer is made up of A atoms while the bottom layer is made up of B atoms. The magnetic coupling between the like atoms (A-A and B-B) is ferromagnetic while between the unlike atoms (A-B), it is antiferromagnetic. For the time-dependent external uniform random field, the mean is always set to zero and the standard deviation is varied until spin-field energy is comparable to the dominant cooperative energy of the system. The findings show that the observed compensation and critical points shift and steady-state magnetic behaviors shift among N, L, P, and Q, etc., type of ferrimagnetic behaviors, depending on the strength of external uniform random field. The compensation phenomenon even vanishes after crossing a finite threshold of standard deviation of the magnetic field for particular choices of the other controlling parameters. Thus islands of ferrimagnetic phase without compensation appear within the phase area with compensation of field-free case, in the two-dimensional Hamiltonian parameter space. For both the configurations, the areas of such islands even grow with increasing standard deviation of the external field, σ, obeying a scaling relation of the form: f(σ,A(σ))=σ^{-b}A(σ) with b_{ABA}=1.958±0.122 and b_{AAB}=1.783±0.118.

Local Probe Comparison of Ferroelectric Switching Event Statistics in the Creep and Depinning Regimes in Pb(Zr_{0.2}Ti_{0.8})O_{3} Thin Films

Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two Pb(Zr_{0.2}Ti_{0.8})O_{3} thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent τ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98-2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered-the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.

Critical disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems

In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.

Scaling of domain cascades in stripe and skyrmion phases

The origin of deterministic macroscopic properties often lies in microscopic stochastic motion. Magnetic fluctuations that manifest as domain avalanches and chaotic magnetization jumps exemplify such stochastic motion and have been studied in great detail. Here we report Fourier space studies of avalanches in a system exhibiting competing magnetic stripe and skyrmion phase using a soft X-ray speckle metrology technique. We demonstrate the existence of phase boundaries and underlying critical points in the stripe and skyrmion phases. We found that distinct scaling and universality classes are associated with these domain topologies. The magnitude and frequency of abrupt magnetic domain jumps observed in the stripe phase are dramatically reduced in the skyrmion phase. Our results provide an incisive way to probe and understand phase stability in systems exhibiting complex spin topologies.

Switching of magnetic materials often occurs through discrete random avalanches. Singh et al. observe sharply reduced avalanches in the topologically protected skyrmion phase of a Fe/Gd heterostructure and obtain different critical behaviour in the stripe and skyrmion phases, suggesting distinct universality classes.

The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary

The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the time-scale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the two-dimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.

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.

Statistical properties of Barkhausen noise in amorphous ferromagnetic films

We investigate the statistical properties of the Barkhausen noise in amorphous ferromagnetic films with thicknesses in the range between 100 and 1000 nm. From Barkhausen noise time series measured with the traditional inductive technique, we perform a wide statistical analysis and establish the scaling exponents τ,α,1/σνz, and ϑ. We also focus on the average shape of the avalanches, which gives further indications on the domain-wall dynamics. Based on experimental results, we group the amorphous films in a single universality class, characterized by scaling exponents τ=1.28±0.02,α=1.52±0.3, and 1/σνz=ϑ=1.83±0.03, values compatible with that obtained for several bulk amorphous magnetic materials. Besides, we verify that the avalanche shape depends on the universality class. By considering the theoretical models for the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium found in literature, we interpret the results and identify an experimental evidence that these amorphous films, within this thickness range, present a typical three-dimensional magnetic behavior with predominant short-range elastic interactions governing the domain-wall dynamics. Moreover, we provide experimental support for the validity of a general scaling form for the average avalanche shape for non-mean-field systems.

Statistical and Multifractal Properties of Barkhausen Jumps in Exchange-Coupled Antiferromagnetic/Ferromagnetic Bilayers

Statistical and multifractal properties of Barkhausen jumps in exchange-coupled ferromagnet/antiferromagnet bilayers are studied on Co/IrMn and NiFe/NiO heterostructures using a magneto-optical indicator film technique. The statistical analysis proves a nonstochastic character of magnetization jumps. In particular, power-law behavior is observed for Co/IrMn samples. Furthermore, the statistics depends on the ferromagnet layer thickness and antiferromagnet layer material structure. The average jump size displays an asymmetry between the forward and backward branches of the hysteresis loop, particularly pronounced for the structure with a thin Co layer. In spite of the observation of such an asymmetry in the activity of the domain nucleation and pinning centers, the statistical distributions of jumps do not show any significant differences for two branches of the hysteresis loop. The conclusion on a nonrandom character of the magnetization process is supported by the multifractal analysis which reveals the presence of correlations in the time arrangement of the Barkhausen jumps.

Universal properties of magnetization dynamics in polycrystalline ferromagnetic films

We investigate the scaling behavior in the statistical properties of Barkhausen noise in ferromagnetic films. We apply the statistical treatment usually employed for bulk materials in experimental Barkhausen noise time series measured with the traditional inductive technique in polycrystalline ferromagnetic films having different thickness from 100 to 1000 nm and determine the scaling exponents. Based on this procedure, we group the samples in a single universality class, since the scaling behavior of Barkhausen avalanches is characterized by exponents τ∼1.5, α∼2.0, and 1/σνz∼ϑ∼2.0 for all the films. We interpret these results in terms of theoretical models and provide experimental evidence that a well-known mean-field model for the dynamics of a ferromagnetic domain wall in three-dimensional ferromagnets can be extended for films. We identify that the films present an universal three-dimensional magnetization dynamics, governed by long-range dipolar interactions, even at the smallest thicknesses, indicating that the two-dimensional magnetic behavior commonly verified for films cannot be generalized for all thickness ranges.

Avalanche spatial structure and multivariable scaling functions: sizes, heights, widths, and views through windows

We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven quenched Kardar-Parisi-Zhang (qKPZ) equation. We fully characterize the spatial structure of these avalanches--we report universal scaling functions for size, height, and width distributions, and also local front heights. Furthermore, we resolve a problem that arises in many imaging experiments of crackling noise and avalanche dynamics, where the observed distributions are strongly distorted by a limited field of view. Through artificially windowed data, we show these distributions and their multivariable scaling functions may be written in terms of two control parameters: the window size and the characteristic length scale of the dynamics. For the entire system and the windowed distributions we develop accurate parametrizations for the universal scaling functions, including corrections to scaling and systematic error bars, facilitated by a novel software environment SloppyScaling.

Universal hysteresis scaling for incommensurate magnetic order in dysprosium

We study the scaling properties of magnetic minor hysteresis loops in a polycrystalline dysprosium metal, varying temperature and magnetic-field amplitudes. We observe irreversibility-related hysteresis loss in the helical antiferromagnetic phase, which is related with remanent flux density as a power law with the same scaling exponent of 1.25±0.05 as that in ferromagnetic materials. In contrast to hysteresis scalings in ferromagnets associated with 180° Bloch walls, the observed law is governed by spiral walls which separate helical domains with oppositely rotating spins.

Multiple avalanches across the metal-insulator transition of vanadium oxide nanoscaled junctions

The metal-insulator transition of nanoscaled VO2 devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in magnitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump sizes, demonstrating an inherent property of the VO2 films. We report a surprising relation between jump magnitude and device size. A percolation model captures the general transport behavior, but cannot account for the statistical behavior.

Search for universal roughness distributions in a critical interface model

We study the probability distributions of interface roughness, sampled among successive equilibrium configurations of a single-interface model used for the description of Barkhausen noise in disordered magnets, in space dimensionalities d = 2 and 3. The influence of a self-regulating (demagnetization) mechanism is investigated, and evidence is given to show that it is irrelevant, which implies that the model belongs to the Edwards-Wilkinson universality class. We attempt to fit our data to the class of roughness distributions associated to 1/falpha noise. Periodic, free, "window," and mixed boundary conditions are examined, with rather distinct results as regards quality of fits to 1/falpha distributions.

Driving rate effects in avalanche-mediated first-order phase transitions

We study the driving-rate and temperature dependence of the power-law exponents that characterize the avalanche distribution in first-order phase transitions. Measurements of acoustic emission in structural transitions in Cu-Zn-Al and Cu-Al-Ni are presented. We show how the observed behavior emerges within a general framework of competing time scales of avalanche relaxation, driving rate, and thermal fluctuations. We confirm our findings by numerical simulations of a prototype model.

Dimensional crossover and universal roughness distributions in Barkhausen noise

We investigate the dimensional crossover of scaling properties of avalanches (domain-wall jumps) in a single-interface model, used for the description of Barkhausen noise in disordered magnets. By varying the transverse aspect ratio A=L(y)/L(x) of simulated samples, the system dimensionality changes from two to three. We find that perturbing away from d=2 is a relevant field. The exponent tau characterizing the power-law scaling of avalanche distributions varies between 1.06(1) for d=2 and 1.275(15) for d=3, according to a crossover function f(x), x identical with (L-1x)(phi)/A, with phi=0.95(3). We discuss the possible relevance of our results to the interpretation of thin-film measurements of Barkhausen noise. We also study the probability distributions of interface roughness, sampled among successive equilibrium configurations in the Barkhausen noise regime. Attempts to fit our data to the class of universality distributions associated to 1/f(alpha) noise give alpha approximately 1-1.1 for d=2 and 3 (provided that suitable boundary conditions are used in the latter case).

Direct observation of Barkhausen avalanche in Co thin films

We report direct full-field magneto-optical observations of Barkhausen avalanches in Co polycrystalline thin films at criticality. We provide experimental evidence for the validity of a phenomenological model of the Barkhausen avalanche originally proposed by Cizeau, Zapperi, Durin, and Stanley [Phys. Rev. Lett. 79, 4669 (1997)]], where the model describes a 180 degrees -type flexible domain wall deformed by a localized defect with consideration of long-range dipolar interaction. The Barkhausen jump areas show a power-law scaling distribution with critical exponent tau approximately 1.33 for all the samples having different thickness from 5 to 50 nm, which is in accord with the two-dimensional prediction of the model.

Hysteresis in the random-field Ising model and bootstrap percolation

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging L small star, filled increases as exp[exp(J/Delta)] in 2D, and as exp(exp[exp(J/Delta)]) in 3D, for disorder strength Delta much less than the exchange coupling J. For system size 1<<L<L small star, filled, the coercive field h(coer) varies as 2J-DeltalnlnL for the square lattice, and as 2J-DeltalnlnlnL on the cubic lattice. Its limiting value is 0 for L-->infinity for both square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and h(coer) tends to J.