A Modified Frölich Magnetic Hysteresis Model for a ε-Fe2O3 Iron Ferrite

As bulk magnetic behaviors are different from those of nanomaterials, the well-known classical models are not appropriate to simulate the magnetization-induction curves. In this work, a novel formulation for modeling the hysteresis loop of an iron ferrite nanomaterial is presented. Three adapted models are tested, based on the Rayleigh, the Potter and the Frölich expressions. Results show a non-satisfying fitting curve. An improved model, based on the Frölich one, is then expressed. The added model coefficients facilitate an accurate non-linearity representation of nanomaterials magnetic response, thus resulting in a good agreement between simulated and measured hysteresis loop. To accomplish this goal, the appropriate values of these parameters have to be identified. Then, a constrained optimization approach is used. The generalized reduced gradient is adopted for the optimization process. The new model is verified. Thus, its numerical hysteresis loop shows a better fitting compared to the experimental curve. The root mean square error is reduced from 2.519 to 2.022. Furthermore, it demonstrates better magnetic response description of the ε-Fe2O3 nano-iron-ferrite material than the other models.