Theory of Domain-Wall Structure in Multiple Magnetic Films

This paper derives analytically a two-dimensional wall-structure applying to the case of two identical magnetic films separated by a non-magnetic film. It applies also to a variety of other multilayer problems. The calculation is based on the usual micro-magnetic principle of energy minimization and all approximations are justified. The wall-structure is found to consist of two “flank” regions, whose shape is governed by anisotropy and stray-field coupling between films, arranged symmetrically about a central “kernel” region whose shape is governed by anisotropy and exchange. In the widely applicable limit of negligible exchange the theory reduces to one given earlier [J. Appl. Phys. 37, 1268 (1966)]. Also included in the discussion are effects of quasi-walls and film-to-film exchange interactions. Existing experimental data on wall-shape confirm the shape of the kernel but are not of sufficient precision to test the shape of the flanks. Existing data for permalloy suggest that perpendicular anisotropy may play a significant role in reducing multiple-film wall energy and thickness.