Nucleation and Growth of Reverse Domains

Abstract

The nucleation and growth of ``spike'' domains of reverse magnetization at grain boundaries are analyzed in detail to show how these domain may account for hysteresis‐loop rectangularity in polycrystalline soft magnetic materials. In a development based on the usual idealizations and approximations, the minimum‐energy‐condition equations are solved numerically for material values representative of the Mg–Mn ferrites. Results are presented to show (1) the variation of the size and shape of reverse domains with applied field, and (2) the critical fields for nucleation (nucleation field) and for unlimited growth (threshold field) of such domains as a function of grain‐to‐grain misalignment of magnetization vectors. The coercive force (equal to minimum threshold field) is shown to be H_c=4.9 σ_w/M_sD and a condition for hysteresis‐loop rectangularity to be 〈ω*²〉≪12.9 σ_w/D, both in fair approximation. Here σ_w is the domain‐wall energy density, M_s is the saturation magnetization, D is the grain size, 〈ω*²〉 is the average of ω*², where ω*=n·(M₁−M₂) is the pole density at the grain boundary. These results are in satisfactory agreement with earlier qualitative ideas.