On the modelling of the anhysteretic magnetization of homogeneous soft magnetic materials

The analysis and optimization of devices with soft magnetic cores, such as inductive sensors and electric machines, rely on a simple and precise modelling of their nonlinear anhysteretic magnetization. The Langevin-Weiss equation of state has the advantages of being physically-based and capable of accurately describing isotropic materials. In fact, it has even been adopted as the backbone of the popular Jiles-Atherton model to describe magnetic hysteresis. However, many studies show the difficulty of retrieving the modelling parameters given an experimental anhysteretic curve, for which stochastic optimization methods are generally used. In this work, we present a simple and deterministic method for finding the parameters of the Langevin-Weiss model: the saturation magnetization, the temperature dependent a parameter, and the molecular field constants. To this end, we optimize a problem with a nonlinear solver where the fitting variables are instrinsically bounded. We validated the approach by analyzing three widely used soft magnets; a grain-oriented silicon steel, a Mn-Zn soft ferrite, and a Fe-based nanocrystalline alloy with induced anisotropy. We demonstrate that, contrary to what has previously been assumed, the Langevin-Weiss function can provide a good description of the anhysteretic magnetization of any homogeneous material, even materials with strong transverse uniaxial anisotropy. The key, which seems to have been overlooked, is to allow the Weiss molecular field to be negative.

Automated summary

The analysis and optimization of devices with soft magnetic cores rely on a precise modelling of their nonlinear anhysteretic magnetization, which can be achieved through the physically-based Langevin-Weiss equation. Retrieving the modelling parameters given an experimental anhysteretic curve can be challenging, but a simple and deterministic method has been presented in this work. The key finding is that the Langevin-Weiss function can accurately describe the anhysteretic magnetization of any homogeneous material, even those with strong transverse uniaxial anisotropy, if the Weiss molecular field is allowed to be negative.