Langevin approach to hysteresis and Barkhausen jump modeling in steel

To represent the multiplicity of metastable states in a bulk ferromagnetic material with domain-wall pinning effects, fluctuations in the domain-wall energies are described in terms of an ensemble of stochastic Langevin functions. The model parameters used are a correlation length, a rms value for the amplitude of the fluctuations in the domain-wall energy gradient, and a ‘‘demagnetizing factor.’’ The model generates both hysteresis loops and Barkhausen effect (BE) jump size distributions. Jump size distributions were determined experimentally for low-carbon rolled sheet steel with the field applied both parallel and perpendicular to the rolling direction. Both the model and the experimental BE jump size distributions show a power-law behavior for small jumps and a rapid cutoff at large jump sizes.