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

Abstract

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 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 dc = 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.

Avalanche statistics from data with low time resolution

“…In the limit of quasistatic driving, the maximum avalanche duration T a scales with distance to criticality k ≡ K/J as T a ∼ δtk −νz , where ν = 1 and z = 1 for mean-field depinning with long-ranged forces [2]. The other time scales pertaining to the avalanche durations also diverge as k → 0, but not necessarily with the same exponent.…”

“…Avalanches are observed in a variety of dynamical systems, including magnetic materials [1,2], charge density waves [3,4], vortices in superconductors [5], earthquakes [6,7], crystal plasticity [7][8][9][10][11], and amorphous plasticity [7,8,[12][13][14][15][16][17]. For these last two cases, deformation occurs through small jumps caused by slipping weak spots in the material.…”

Universality classes and crossover scaling of Barkhausen noise in thin films

“…The short length scale exponent is expected to be that of the LIM/qEW, τ LIM 1.11 [26] and 1/σ LIM = 3.0 [3].…”

“…The statistical properties of the Barkhausen noise are usually studied by measuring the size distribution P (s) of such jumps, or avalanches, which typically follows a power law P (s) ∼ s −τ , with the exponent τ characterizing the universality class of the avalanche dynamics. In three-dimensional bulk ferromagnetic materials, the scaling behavior of the Barkhausen effect is understood theoretically in terms of the depinning transition of domain walls [3] with two distinct universality classes for amorphous and polycrystalline materials [4]. A similar clear-cut classification does not exist in lower dimensions, despite Barkhausen avalanches having been studied experimentally for decades in several ferromagnetic thin films with in-plane [5][6][7][8][9][10] or out-of-plane anisotropy [11,12].…”

Random-Field Ising Models of Hysteresis

“…Zapperi et al (10) argue that the addition of dipoledipole interactions to the model lowers the upper critical dimension to three and produces meanfield exponents in three dimensions. Since large mean-field simulations are much easier than large simulations with dipole-dipole interactions, we will give results from mean-field simulations in this paper.…”