The Preisach-Arrhenius model for aftereffect

Abstract

Summary form only given. In the presence of large energy barriers, the magnetization decays very slowly towards its ground state. In most permanent magnetic materials this decay is immeasurable in zero field. In order to estimate the useful lifetime of a magnetic material, this decay is accelerated by applying a reverse field, that we call the holding field, that is approximately equal to the remanent coercivity. Unfortunately, unless we know how much we have accelerated the decay rate, this does not tell us anything about how long it will be useful at other fields. It is necessary to have a model built on physical principles that can address this issue. The Preisach-Arrhenius (PA) model is just such a model. Some of the predictions of this model have been verified experimentally. In particular, the shift in log-time of the after effect curve by an applied field and the shape of the after effect curve in bimodal media. In this paper we discuss the experimental verification of the correct location of the peak in the decay coefficient, and the shape of the after effect curve for multilayer media. We also discuss how to compute the expected lifetime of a recording. The magnetization of the ground state is the same as the magnetization achieved after an anhysteretic magnetizing process. However, the anhysteretic magnetic state differs from the true ground state where the populations of energy levels obey Maxwell-Boltzmann statistics in the ground state. As the material relaxes to the true ground state its magnetization does not change since for a given time constant there are as many negative hysterons changing to a positive state as there are positive hysterons changing to the negative state. Thus, this difference in states is difficult to detect and may be only of academic interest. Had we started from positive saturation, then applied field equal to the negative coercivity and finally reduced the field to zero, then the after effect would have started from zero magnetization, risen to a positive magnetization and then finally returned to zero. Although in this case, the same number of hysterons would have to change from positive magnetization to negative as the other way around, this time they do so with different time constants. The time required for the magnetization to start decreasing to zero is so long that we have not been able to observe this. However, this effect has been observed in nonzero holding fields.