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The scaling hypothesis was first postulated by Widom based on phenomenological grounds. It provides data collapse and a relation between critical exponents, which allows one to reduce the number of independent parameters characterizing the critical behavior [1, 2]. Scaling and data collapse are usually used to analyze critical phenomena and phase transitions. However, they can also be applied to analyze phenomena far from the critical point, e.g. related to magnetization phenomena as hysteresis loop [3–8] or magnetic viscosity [9, 10]. The Widom scaling has been successfully applied in analysis of power losses for various types of soft magnetic materials [11–15]. The Widom procedure was also used in scaling of magnetic coercivity [16]. However, the results of the coercivity scaling were not satisfactory. The modified procedure for the coercivity scaling using the hyperbolic tangent transformation was proposed in [17]. Although this procedure improved the coercivity scaling, it also introduced a large number of new parameters to be estimated. In the paper, a new approach to the scaling of magnetic coercivity, based on a fractional procedure, is presented. The proposed coercivity scaling is examined for electrical steels with different internal structures as non-oriented, grain-oriented and microcrystalline ones.

Fractional Scaling of Magnetic Coercivity in Electrical Steels