Modeling of micromagnetic Barkhausen activity using a stochastic process extension to the theory of hysteresis

Recent work by Bertotti [IEEE Trans. Magn. MAG-24, 621 (1988)] and others has shown that it is possible to model the micromagnetic Barkhausen discontinuities at the coercive point using a two-parameter stochastic model. However, the present formulation of the model is restricted to limited regions of the hysteresis curve over which dM/dH is approximately constant and when dH/dt is held at a constant rate. A natural extension of this model is to take the basic result, in which the level of Barkhausen activity in one time period is related to the activity in the previous time period, and increment it by a small amount which is dependent on the differential permeability. The extension of the model proposed here uses the theory of ferromagnetic hysteresis to determine the differential permeability at any point of the hysteresis loop. The Barkhausen activity is then assumed to vary in proportion to the differential permeability. The resulting model allows the Barkhausen sum of discontinuous changes in magnetization to be modelled around the entire hysteresis loop, leading to an important generalization of the basic model