A 3-D hybrid Jiles-Atherton/Stoner-Wohlfarth magnetic hysteresis model for inductive sensors and actuators

The Jiles-Atherton (JA) theory of hysteresis is currently used in the majority of commercial CAD tools, mainly due to its implementation simplicity in fast and stable algorithms. The JA model provides precise results in the case of isotropic, polycrystalline, multidomain magnetic devices, where flux-reversal is governed by pinning mechanisms. Dynamic response of such devices, including Eddy-current loss and magnetic resonance, can also be accurately modeled. However, JA theory is not applied for three-dimensional (3-D) magnetization simulations and does not account for anisotropy that affects severely hysteresis curves of single-domain, thin-film devices, which are usually incorporated in miniature inductive sensors and actuators. In that case, the Stoner-Wohlfarth (SW) theory can be applied, which, however, does not account for dynamic response and incremental energy loss. In this work, we employ a virtual 3-D anisotropy-field vector calculated with SW theory that introduces magnetic feedback to the classical equation of Paramagnetism, in order to derive a proper 3-D "input" for the JA algorithm. This way, a hybrid 3-D JA/SW model is developed, which incorporates both models into one single formulation, capable of modeling simultaneously: 1) temperature effects, 2) pinning and Eddy-current loss, 3) magnetic resonance, and 4) uniaxial anisotropy, the orientation of which can be simulated to vary with time. The model that owns a solid physical basis has been implemented in a computation-efficient, stable algorithm capable of functioning with arbitrary excitation-field input. The algorithm has been successfully applied to model the behavior of a series of miniature Fluxgate magnetometers based on the Matteucci effect of thin glass-covered magnetic wires