Analysis of Aftereffect Phenomena and Noise Spectral Properties of Magnetic Hysteretic Systems Using Phenomenological Models of Hysteresis

A robust and computationally efficient Monte-Carlo based technique is developed to analyze the magnetic aftereffect and noise passage phenomena in magnetic hysteretic systems by using phenomenological models of hysteresis. The technique is universal and can be applied to model the aftereffect and noise passage phenomena in the framework of both scalar and vector models of hysteresis. Using this technique, we analyze a variety of magnetic viscosity phenomena. Numerical results related to the decay of the magnetization as a function of time as well as to the viscosity coefficient are presented. It is shown that a logt (logarithmic time) - type dependence of the average value of the magnetization can be predicted qualitatively in the framework of phenomenological models of hysteresis, such as the Preisach, Energetic, Jiles-Atherton, and Hodgdon models. The basic assumption of the techniques developed in this dissertation is that the total applied field is equal to the external applied field plus a random perturbation field. The total magnetic field is used as input in the scalar or vector models of hysteresis (vector models of hysteresis are defined in this dissertation as a superposition of scalar models of hysteresis distributed along all possible spatial directions). A statistical approach is developed to compute the average value and direction of the magnetization vector as a function of time. Whereas in the case of isotropic materials the magnetization vector usually moves on a straight line oriented towards the direction of the applied field, in the case of anisotropic materials the magnetization vector can switch from one easy axis to another and cross the direction of the applied field. It is shown that, depending on the initial hysteretic state, the trajectory of the magnetization vector can deviate substantially from the straight line, which is a pure vectorial relaxation effect. The vectorial properties of magnetic viscosity and data collapse phenomena are also investigated. The definition of the viscosity coefficient, which has been traditionally used to model aftereffect phenomena in scalar magnetic systems, is generalized in order to describe three dimensional systems, where both the direction and the magnitude of the magnetization vector can change in time. Using this generalization of the vector viscosity coefficient, we have analyzed data collapse phenomena in vectorial magnetization processes. It was found that the traditional bell-shaped curves of the scalar viscosity coefficient as a function of the applied field can have one or more maxima in the case of vectorial systems. The data collapse phenomena seem to apply to simple magnetization processes (such as first-order rotational reversal curves); however, it cannot be generalized to more complex magnetization processes because of the relatively complicated magnetization dynamics. In the final part of this dissertation we present a statistical technique based on Monte-Carlo simulations, which we developed to compute the spectral densities of the output variable in phenomenological models of hysteresis. The input signal is described by an Ornstein-Uhlenbeck process and the magnetization is computed by using various phenomenological models of hysteresis: the Energetic, Jiles-Atherton, and Preisach models. General qualitative features of these spectral densities are examined and their dependence on various parameters is discussed. For values of the diffusion coefficient near and smaller than the coercive field, the output spectra deviate significantly from the Lorentzian shape, characteristic to the input process. The intrinsic differences between the transcendental, differential, and integral modeling of hysteresis yield significantly different spectra at low frequency region, which reflect the long-time correlation behavior.