Simplification and inversion of the mean-field positive-feedback model: Application to constricted major and minor hysteresis loops in electrical steels

This paper describes new developments in the positive-feedback model (PFM) of ferromagnetism. An extreme simplification of the model requires only algorithms for the calculation of the major hysteresis loop, the firstorder reversal curve (FORC), and one more for nth-order reversal curves (NORCs) where the order can have any integer value n > 1. The way in which quantum-mechanical (QM) bistability, domain-scale, and macroscopic processes interact to produce the observed macroscopic behavior is explained in detail. The theory is presented in QM variable-spin form, making it possible to model weakly ferromagnetic and nanoparticle materials as well as the strongly ferromagnetic materials typically used in power engineering. In the latter case, the theoretical expressions are even further simplified. The PFM now incorporates a "built-in" inversion capability, so that it works equally well for either a defined input vector of reversal fields [H-r] or of reversal magnetizations [M-r] For practical utility, the model also introduces a simple way of incorporating magnetostriction effects, which are especially important in electrical steels.