Gianfranco Durin

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

We study the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium. The avalanchelike 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 Fe21Co64B15 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 dc53, 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 d53, 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.@S0163-1829~98!08833-X#

Scaling exponents for barkhausen avalanches in polycrystalline and amorphous ferromagnets

We investigate the scaling properties of the Barkhausen effect by 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+/-0.05 or tau = 1.27+/-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.

Universality beyond power laws and the average avalanche shape

Stefanos Papanikolaou, Felipe Bohn, 3 Rubem Luis Sommer, Gianfranco Durin, 5 Stefano Zapperi, 5 and James P. Sethna LASSP, Department of Physics, Clark Hall, Cornell University, Ithaca, NY 14853-2501 Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59072-970, Natal, RN, Brazil Centro Brasileiro de Pesquisas F́ısicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, RJ, Brazil INRIM, Strada delle Cacce 91, 10135 Torino, Italy ISI Foundation, Viale S. Severo 65, 10133 Torino, Italy CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy LASSP, Physics Department, Clark Hall, Cornell University, Ithaca, NY 14853-2501

Dynamics of a Ferromagnetic Domain Wall and the Barkhausen Effect

We derive an equation of motion for the the dynamics of a ferromagnetic domain wall driven by an external magnetic field through a disordered medium and we study the associated depinning transition. The long-range dipolar interactions set the upper critical dimension to be

The Barkhausen Effect

d_c=3

Random free energy model for the description of hysteresis

, so we suggest that mean-field exponents describe the Barkhausen effect for three-dimensional soft ferromagnetic materials. We analyze the scaling of the Barkhausen jumps as a function of the field driving rate and the intensity of the demagnetizing field, and find results in quantitative agreement with experiments on crystalline and amorphous soft ferromagnetic alloys.

FRACTALS, SCALING AND THE QUESTION OF SELF-ORGANIZED CRITICALITY IN MAGNETIZATION PROCESSES

There is such a large production and analysis of experimental data about the Barkhausen noise that there is a serious risk of confusion and misunderstanding. This chapter reviews this large production of data, ideas and takes into account the important results previously appearing in the literature, to propose a single framework to interpret the phenomenon. Data have been collected on nearly all possible soft magnetic materials, and considering many different properties, so that one can, in principle, assume them as sufficiently exhaustive and reliable. The absence of a coherent interpretation could then be ascribed to the lack of a proper theoretical model.. It is particularly important to deal with recent observations of the Barkhausen noise lacking a coherent interpretation–– such as, for measurements in thin films, hard materials, and low-dimensional systems.

Scaling aspects of domain wall dynamics and Barkhausen effect in ferromagnetic materials

The connection between hysteresis phenomena and free energy metastable states in magnetic systems is discussed. A random free energy model is introduced, which leads to a stochastic differential equation for the evolution of magnetization in time. We show that the solutions of this equation are equivalent to the Preisach model of hysteresis. The analytical form of the Preisach distribution is calculated.

Low-field hysteresis in disordered ferromagnets

The main physical aspects and the theoretical description of stochastic domain wall dynamics in soft magnetic materials are reviewed. The intrinsically random nature of domain wall motion results in the Barkhausen effect, which exibits scaling properties at low magnetization rates and 1/f power spectra. It is shown that the Barkhausen signal ν, as well as the size Δx and the duration Δu of jumps follow distributions of the form ν−α, Δx−β, Δu−γ, with α=1−c, β=3/2−c/2, γ=2–c, where c is a dimensionless parameter proportional to the applied field rate. These results are analytically calculated by means of a stochastic differential equation for the domain wall dynamics in a random perturbed medium with brownian properties and then compared to experiments. The Barkhausen signal is found to be related to a random Cantor dust with fractal dimension D=1−c, from which the scaling exponents are calculated using simple properties of fractal geometry. Fractal dimension Δ of the signal v is also studied using four different methods of calculation, giving Δ≈1.5, independent of the method used and of the parameter c. The stochastic model is analyzed in detail in order to clarify if the shown properties can be interpreted as manifestations of self-organized criticality in magnetic systems.

Stochastic model for magnetic hysteresis

It is shown through theoretical considerations on stochastic domain wall motion in a perturbed medium with quenched‐in disorder that the Barkhausen signal v, as well as the size Δx and duration Δu of Barkhausen jumps follow scaling distributions of the form v−α, Δx−β, Δu−γ, where α=1−c, β=3/2−c/2, γ=2−c, and c is proportional to the magnetization rate. In order to test these predictions, Barkhausen effect experiments were performed on polycrystalline SiFe alloys. Preliminary experiments to determine both the absolute value and the c dependence of the measured exponents are in agreement with the theoretical predictions.