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

TLDR

The avalanchelike motion of domain walls between pinned configurations produces the Barkhausen noise. The study investigates the dynamics of a ferromagnetic domain wall driven by an external magnetic field through disorder and introduces a mean‑field infinite‑range model equivalent to a prior single‑degree‑of‑freedom model that reproduces experimental observations. The authors model the domain wall with an equation of motion exhibiting a depinning transition, compute avalanche distributions versus driving rate and demagnetizing field, simulate the model in three dimensions, and compare with experimental Barkhausen noise data from soft ferromagnetic materials such as Fe21Co64B15. The analysis shows that long‑range dipolar interactions set the upper critical dimension to d_c=3, so mean‑field exponents (with possible logarithmic corrections) describe the Barkhausen effect; numerical simulations in d=3 confirm these predictions, and the scaling exponents vary linearly with driving rate while the distribution cutoff is set by the demagnetizing field, matching experimental observations.

Abstract

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 ${\mathrm{Fe}}_{21}{\mathrm{Co}}_{64}{\mathrm{B}}_{15}$ 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 ${d}_{c}=3,$ 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.