General theory of the coercive force due to domain wall pinning

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Abstract
Due to the nonlinear nature of the relevant mathematical equations, previous solutions to the geometrically simple problem of pinning of a 180° ferromagnetic domain wall by a single planar defect in an infinite medium contain the approximation of small deviations in the nature of the defect material relative to the host matrix. We have enlarged the theory of such domain wall pinning to include all magnitudes of deviation of the magnetic anisotropy Ki , magnetization Mi , and/or magnetic exchange energy Ai , characterizing the defect for all defect widths. In particular, we have obtained graphs for the resultant reduced coercive force hc = HcM1/K1 , due to such domain wall pinning, as a function of the dimensionless constants F = A2M2/A1M1 and E = A2K2/A1K1 and of the defect width, as well as graphs for the maximum obtainable coercive force as a function of F and E. (Here i = 1 represents the host material and i = 2 the defect.) As an example, we discuss these results in terms of applications to the Sm2(Co,Cu,Zr,Fe)17 hard magnetic materials.