Low-field hysteresis in disordered ferromagnets

We analyze low-field hysteresis close to the demagnetized state in disordered ferromagnets using the zero-temperature random-field Ising model. We solve the demagnetization process exactly in one dimension and derive the Rayleigh law of hysteresis. The initial susceptibility a and the hysteretic coefficient b display a peak as a function of the disorder width. This behavior is confirmed by numerical simulations $d=2,3$ showing that in the limit of weak disorder demagnetization is not possible and the Rayleigh law is not defined. These results are in agreement with experimental observations on nanocrystalline magnetic materials.