# Barkhausen effect and Hysteresis

## The Barkhausen effect

The Barkhausen effect was first observed in 1919 in the magnetization curve of ferromagnets. The magnetization as a function of the field is not smooth but increases in steps. This steps are noticeable in the form of of a noise with interesting properties. The Barkhausen effect is due to the disorder in the material wich is responsible for the jerky motion of domain walls. The amplitude of the noise is well described by a gamma distribution and it is possible to identify avalanches which are typically power law distributed. The exponents have been found to be universal in a large class of materials. We study the dynamics of domain walls in disordered ferromagnetic material by means of numerical simulation and analytical means. Based on energetic considerations, We derive an equation of motion for the domain wall and study the corresponding depinning transition. We compute the critical exponents and study the equation as a function of the driving rate and the demagnetization field. The result we obtain are in excellent agreement with the experiments. In addition, we show that the mean-field theory of our model is equivalent to a phenomenological model (ABBM) introduced previously. We investigated the scaling properties of the Barkhausen effect, recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents or or , for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff of the distributions to the demagnetizing factor which is in quantitative agreement with experiments. For more informations take a look at the original paper by Barkhausen, read our review article or jump to the homepage of Gianfranco Durin

## Demagnetization of disordered ferromagnets

The hysteresis properties of ferromagnetic materials at low field are described by the Rayleigh law. We analyze the problem in light of modern statistical mechanics models of hysteresis. In particular, we compute the demagnetization curve and derive the Rayleigh parameters a and b in the random-field Ising model (RFIM) and in a model of domain wall depinning. In the random-field Ising model the Rayleigh law is obeyed only in the disorder dominated phase, while in the low disorder phase it is not possible to demagnetize the sample. This approach allows us to link a and b to microstructural parameters, such as the domain wall energy, the internal disorder or the exchange interactions.

Using the RFIM as an example, we identify in the demagnetized state (DS) the correct non-equilibrium hysteretic counterpart of the T=0 ground state (GS), and present evidence of universality. Numerical simulations in d=3 indicate that exponents and scaling functions coincide, while the location of the critical point differs, as corroborated by exact results for the Bethe lattice. These results are of relevance for optimization, and for the generic question of universality in the presence of disorder.