Jiles-Atherton model

The Jiles–Atherton model of magnetic hysteresis was introduced in 1984 by David Jiles and D. L. Atherton. This is one of the most popular models of magnetic hysteresis. Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material. Jiles–Atherton model enables calculation of minor and major hysteresis loops. The original Jiles–Atherton model is suitable only for isotropic materials. However, an extension of this model presented by Ramesh et al. and corrected by Szewczyk enables the modeling of anisotropic magnetic materials. The Jiles–Atherton model of magnetic hysteresis was introduced in 1984 by David Jiles and D. L. Atherton. This is one of the most popular models of magnetic hysteresis. Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material. Jiles–Atherton model enables calculation of minor and major hysteresis loops. The original Jiles–Atherton model is suitable only for isotropic materials. However, an extension of this model presented by Ramesh et al. and corrected by Szewczyk enables the modeling of anisotropic magnetic materials. Magnetization M {displaystyle M} of the magnetic material sample in Jiles–Atherton model is calculated in the following steps for each value of the magnetizing field H {displaystyle H} : Original Jiles–Atherton model considers following parameters: Extension considering uniaxial anisotropy introduced by Ramesh et al. and corrected by Szewczyk requires additional parameters: Effective magnetic field H e {displaystyle H_{ ext{e}}} influencing on magnetic moments within the material may be calculated from following equation: This effective magnetic field is analogous to the Weiss mean field acting on magnetic moments within a magnetic domain. Anhysteretic magnetization can be observed experimentally, when magnetic material is demagnetized under the influence of constant magnetic field. However, measurements of anhysteretic magnetization are very sophisticated due to the fact, that the fluxmeter has to keep accuracy of integration during the demagnetization process. As a result, experimental verification of the model of anhysteretic magnetization is possible only for materials with negligible hysteresis loop.Anhysteretic magnetization of typical magnetic material can be calculated as a weighted sum of isotropic and anisotropic anhysteretic magnetization: Isotropic anhysteretic magnetization M an iso {displaystyle M_{ ext{an}}^{ ext{iso}}} is determined on the base of Boltzmann distribution. In the case of isotropic magnetic materials, Boltzmann distribution can be reduced to Langevin function connecting isotropic anhysteretic magnetization with effective magnetic field H e {displaystyle H_{ ext{e}}} : Anisotropic anhysteretic magnetization M an aniso {displaystyle M_{ ext{an}}^{ ext{aniso}}} is also determined on the base of Boltzmann distribution. However, in such a case, there is no antiderivative for Boltzmann distribution function. For this reason, integration has to be made numerically. In the original publication, anisotropic anhysteretic magnetization M an aniso {displaystyle M_{ ext{an}}^{ ext{aniso}}} is given as: