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An equation describing the initial magnetisation curve and hysteresis loops of ferromagnetic materials has been derived theoretically based on a mean field approximation. The mutual interaction of the moments is expressed as a coupling coefficient and a restraining force on the motion of the domain walls, caused by the pinning of the walls at defect sites, is expressed as a pinning coefficient. The resulting equation of state for the model is a first order linear differential equation incorporating the two parameters and a scaling parameter λ which represents the ratio of the coupling to the two fields H and M.
Jiles et al. (Thu,) studied this question.