Application of the modified Rayleigh model in the mathematical analysis, of Permalloy minor loops

• Published in: Materials today communications Vol. 35; p. 106043
• Main Authors: Paesano Jr, Andrea, Ferreira, Rafael F., Schafer, Deise, Alves, Tayla J.B., Barco, Reginaldo, Ivashita, Flávio F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-06-2023
• Subjects: Hill equation; hysteresis model; minor loops; Permalloy; Rayleigh model; Permalloy; hysteresis model; minor loops; Rayleigh model; Hill equation
• ISSN: 2352-4928; 2352-4928
• DOI: 10.1016/j.mtcomm.2023.106043

The descending and ascending branches of magnetic minor loops measured for a Permalloy sample were fitted with polynomials of varying degrees. The aim was to test whether the fitting method previously successfully applied to the minor loops of a soft and hard ferromagnetic material is applicable to a very soft magnet. The quality of the fits was very good, but the resulting polynomial coefficients revealed asymmetrical minor loops, independent of the polynomial degree considered in the numerical calculations. The asymmetry was attributed to a combination of factors: the magnetic softness and the different magnetic responses of the sample to the positive and negative directions of the applied field, the later possibly originating from defects in the specimen disk shape. Some fitted coefficients were directly identified with important magnetic parameters such as remanence and permeability, while the coercivity was calculated from a set of coefficients. All of them were shown to be more confident than those values usually obtained by direct interpolation on the experimental curves. The remanence, coercivity and maximum magnetization were traced as a function of the maximum magnetic field applied to the minor loops, and the resulting curves were fitted using the complementary function of the Hill equation. These fits were performed considering only points extracted from some initial minor loops, leading to saturation values, including the saturation magnetization for this sample. The same numerical treatment was applied to the hysteresis area and this fit was equally reliable, with the resulting Hill parameters showing a correlation with the magnetic softness of the Permalloy.
[Display omitted]
•Descendent and ascendent branches of minor loops were successfully fitted by polynomials.•This mathematical treatment represents a generalization of the Rayleigh law.•Minor loops are not symmetrical which was attributed to the magnetic softness of Permalloy.•Minor loops area varies with the maximum applied field according to the Hill equation.