We derive an equation of motion for 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 dc0ex0ex=0ex0ex3, 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.
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Cizeau et al. (1997) studied this question.
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