Theory of Hysteresis Loop in Ferromagnet

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.