Domain-wall dynamics and Barkhausen effect in metallic ferromagnetic materials. I. Theory

The Barkhausen effect (BE) in metallic ferromagnetic systems is theoretically investigated by a Langevin description of the stochastic motion of a domain wall in a randomly perturbed medium. BE statistical properties are calculated from approximate analytical solutions of the Fokker–Planck equation associated with the Langevin model, and from computer simulations of domain-wall motion. It is predicted that the amplitude probability distribution P0(Φ̇) of the B flux rate Φ̇ should obey the equation P0(Φ̇)∝Φ̇c̃−1 exp(−c̃Φ̇/〈Φ̇〉), with c̃0. This result implies scaling properties in the intermittent behavior of BE at low magnetization rates, which are described in terms of a fractal structure of fractal dimension D1. Analytical expressions for the B power spectrum are also derived. Finally, the extension of the theory to the case where many domain walls participate in the magnetization process is discussed.