Calculation of the Error in the Zero-Crossing Method of Computing the Magnetic Thermal Fluctuation

The concept of the fluctuation field has been widely used to characterize thermal properties of magnetic materials; in particular, the characterization of aftereffect. The Preisach-Arrhenius method has been used successfully to determine the fluctuation field based on aftereffect curves from different holding fields. An approximate method used to determine the fluctuation field, the zero-crossing method, has led to erroneous and misleading results. In this paper, the accuracy of the zero-crossing method is tested, when applied to sets of preconditioned artificial data with a predetermined fluctuation field. The Preisach-Arrhenius method accurately calculates the correct fluctuation field for all various assumed parameters, while the zero-crossing method produces significant errors especially when the holding field approaches near the coercivity and fails when beyond the coercivity. The error of the zero-crossing method is a result of not properly accounting for the anhysteretic curve variation with holding field.