Theory of Hysteresis Loop in Ferromagnet

TL;DR

This paper develops a theoretical model for the hysteresis loop in ferromagnets driven by domain wall motion, introducing key characteristics and predicting how the hysteresis loop area scales with frequency and field amplitude, supported by numerical simulations.

Contribution

It presents a new theory linking domain wall dynamics to hysteresis characteristics, including a scaling law for the hysteresis loop area with respect to frequency and field amplitude.

Findings

Hysteresis loop characteristics are governed by two dimensionless parameters.

The model predicts the hysteresis loop area scales as rac{1}{2} imes rac{1}{2} with frequency and amplitude.

Numerical simulations confirm the predicted scaling law.

Abstract

A theory of the hysteresis loop in ferromagnets controlled by the domain wall motion is presented. Domain walls are considered as plane or linear interfaces moving in a random medium under the action of the external ac magnetic field $H=H_0\sin\omega t$. We introduce important characteristics of the hysteresis loop, such as dynamic threshold fields, reversal field etc. together with well known characteristics as coercive field and hysteresis loop area (HLA) $\cal A$. We show that all these characteristics are regulated by two dimensionless combinations of the $H_0$ and $\omega$and intrinsic characteristics of the ferromagnet. The moving domain wall can create magnetic bubbles playing the role of pre-existing nuclei of the reversed magnetization. We discuss a simple model of this process. For magnetization reversal determined by domain inflation we predict that HLA scales as ${\cal A}\propto \omega^{\beta}H_0^{\alpha}$ with $\alpha =1/2$ and $\beta =1/2$. Numerical simulations confirmthis result.