Hysteresis loops modeled from coercivity, anisotropy, and microstructure parameters

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Abstract
By modifying the microstructure (a/H) and magnetocrystalline anisotropy (b/H2) terms of the approach‐to‐saturation (ATS) law, the range of fields over which these terms remain finite is extended to low fields and a good approximation to the hysteresis loop may be constructed in its entirety. The model involves the introduction of the coercive field Hc, the anisotropy field HK, and a reverse domain nucleation field Hn as bias fields that are included in the denominators of the a and b terms. With these phenomenological refinements, the remanent magnetization becomes a function of a/(Hn+Hc), from which Hn may be obtained once a and Hc are determined. Initial results from several different magnetic materials, particularly garnets and spinel ferrites with square hysteresis loops, indicate good agreement with experiment. In cases where ATS analysis is not available because of inadequate sensitivity or inability to reach sufficiently high fields, curve fitting to a lower‐field portion of the hysteresis loop is an alternative method of estimating the a and b coefficients.