Measurement and exponential model of ferromagnetic hysteresis

Abstract

The cooperative anisotropic hysteresis model of ferromagnetic susceptibility has been recast in exponential form. After field reversals, susceptibility increases cooperatively with magnetization change and then decreases toward saturation until it becomes reversible again. The proposed exponential decrease in susceptibility agrees with measurements and with the Jiles-Atherton Langevin anhysteretic model; our model also accurately represents virgin, minor and first order reversals to saturation. The model is validated experimentally using a thin steel ring and pipe and a thin disk in a vibrating sample magnetometer, all isolated from stress and thermal effects by applying half cycles of sinusoidal magnetic field or using quasistatic field steps to remove eddy currents and stabilize viscosity. Precisely calibrated field and magnetization changes M(H) are controlled and measured with a National Instrument data acquisition system and custom LabView software, and differential susceptibilities X(M) are computed. The proposed model is a function of measurable physical constants including initial susceptibility, Xi, anhysteretic field, Hanh, saturation magnetization, Ms, and normalized symmetric crystalline and domain coupling anisotropy functions, Xr and Xc.