Theory of Hysteresis Loop in Ferromagnets
  We consider three mechanisms of hysteresis phenomena in alternating magnetic field: the domain wall motion in a random medium, the nucleation and the retardation of magnetization due to slow (critical) fluctuations. We construct quantitative theory for all these processes. The hysteresis is characterized by two dynamic threshold fields, by coercive field and by the so-called reversal field. Their ratios to the static threshold field is shown to be function of two dimensionless variables constituted from the frequency and amplitude of the ac field as well as from some characteristics of the magnet. The area and the shape of the hysteresis loop are found. We consider different limiting cases in which power dependencies are valid. Numerical simulations show the domain wall formation and propagation and confirm the main theoretical predictions. Theory is compared with available experimental data. 
Igor F.Lyuksyutov, Thomas Nattermann and Valery Pokrovsky