Chapter 5 - Elementary domain structures and hysteresis

Summary

Introduction

Landau and Lifschitz (1935) predicted the existence of ferromagnetic domains as a means of reducing magnetostatic energy. As they put it, ‘Elementary regions of nearly saturation magnetization in a ferromagnetic crystal result from the demagnetizing effect of the surface of the body’. Their predicted domain configurations (Fig. 5.1a) agree quite closely with the patterns observed on a polished {110} surface of magnetite (e.g., Figs. 1.2, 5.8b). Landau and Lifschitz proposed a layered structure: lamellar body domains, with alternating directions of magnetization M_s1, M_s2, in the interior of the crystal; wedge-shaped surface closure domains, with M_sc parallel or nearly parallel to the surface, providing flux closure paths between adjacent domains; and narrow domain walls in which M_s rotates through 90° or 180° between neighbouring domains. In magnetite, M_s rotates through 70.5° or 109.5° (the angles between adjacent 〈111〉 easy directions) rather than 90° across walls between closure and body domains (Fig. 5.1b).

The Landau–Lifschitz (LL) structure is remarkably effective in reducing demagnetizing energy. M_s is uniform within body and closure domains, and so there are no volume poles. M_s is parallel to 180° walls, and so for these walls. The 90° (or 70.5° and 109.5°) walls bisect the angle between M_s vectors in neighbouring body and closure domains. Thus σ_m due to the body domain exactly cancels σ_m due to the closure domain, and no surface poles appear on any interior boundaries.