Dynamics of a domain wall in soft-magnetic materials: barkhausen effect and relation with sandpile models

The CZDE model [P. Cizeau, S Zapperi, G. Durin, and H. E. Stanley, Phys. Rev. Lett. 79, 4669 (1997)] for the dynamics of a domain wall in soft-magnetic materials is investigated. The equation of motion for the domain wall is reduced to a dimensionless form where the control parameters are clearly identified. In this way we show that in soft-magnetic materials with low anisotropies the noise can be approximated by a columnar disorder, and perturbation theory gives a good estimate of the avalanche exponents. Moreover, the resulting exponents are found to be identical to those obtained for directed Abelian sandpile models. The analogies and differences with these models and the question of self-organized criticality in the Barkhausen effect are discussed.