Predicting Hysteresis With Preisach Models

Rock magnetists characterize magnetic systems using first order reversal curve (FORC) functions. These are functions of two fields derived from a particular set of magnetization curves called FORCs. FORC functions borrow the formalism of classical Preisach theory, which has also been used to predict hysteresis in nonlinear systems. The theory has two criteria that the hysteresis must satisfy for the model to work: "congruency" and "wiping out". If these criteria are satisfied then a function called the Preisach function can be derived from hysteresis measurements in the same way that the FORC function is derived. The Preisach function can be integrated to predict the hysteresis, or predictions can be made directly from the FORCs. It is shown that if the criteria for the classical Preisach model are not met, there are two FORC functions. One is derived from FORCs that start at positive saturation, another from FORCs that start at negative saturation. Predictions of classical Preisach theory for single-domain particles with uniaxial anisotropy are compared with direct predictions using Stoner-Wohlfarth theory. If FORC functions are used the predictions are entirely unlike the true hysteresis. Piecing together FORC curves works better, but the predictions accumulate errors as the field oscillates. As a result, remanence predictions are also incorrect. There are many varieties of Preisach theory besides classical Preisach theory. Nonlinear Preisach theory uses a function of three fields and is known to correctly predict hysteresis for Stoner-Wohlfarth systems. However, it is shown that nonlinear Preisach theory cannot predict the hysteresis of more complex magnetic particles. Preisach theories may still be able to predict hysteresis in multi-particle systems if certain statistical properties hold.