Dynamics of a ferromagnetic domain wall and the Barkhausen effect

TL;DR

This paper models the dynamics of ferromagnetic domain walls, deriving an equation of motion, analyzing the Barkhausen effect, and showing mean-field behavior in three-dimensional materials with results matching experimental data.

Contribution

It introduces a theoretical framework for domain wall dynamics including long-range interactions and depinning transition analysis, aligning with experimental observations.

Findings

Mean-field exponents describe the Barkhausen effect in 3D ferromagnets.

Scaling laws for Barkhausen jumps depend on field rate and demagnetizing field.

Quantitative agreement with experiments on various ferromagnetic alloys.

Abstract

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 $d_c=3$, 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.