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(Φ˙) of the B flux rate Φ˙ should obey the equation P0(Φ˙)∝Φ˙^c~-1 exp(-c~Φ˙/〈Φ˙〉), with c~≫0. 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 D≪1. 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.