Stability Conditions for Saw-Tooth Walls Between Head-On Domains

Abstract

The boundary between head‐on magnetized domains in a continuous ferromagnetic film takes the form of a saw‐tooth wall, along which a distribution of magnetic poles is localized. The purpose of this paper is to derive theoretically the significant parameters of the sawtooth (angle and wavelength) from the properties of the material and the film thickness. This has been accomplished by minimization of the total energy per unit length, given by exchange, anisotropy, dipoles and poles; the last term is divergent, but it has been properly renormalized. With no applied field, for each wavelength the energy exhibits a minimum at one tip angle, but it is always a decreasing function of the wavelength. If, however, we take into account the fact that a wall can be displaced only if the effective field acting on it exceeds coercivity, we can find out a condition of frozen equilibrium which determines the stable wavelength also in zero field.