Microscopic foundations of the Rayleigh law of hysteresis

The hysteresis properties of ferromagnetic materials at low field are described by the Rayleigh law. We analyze the problem in the 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 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. Finally, our results are compared with experiments.