Domain walls in bubble films. II. Static properties of thick films

Abstract

The structure of static walls is analyzed assuming that the film thickness is much larger than the wall width. It is shown that several different types of wall structure can exist. For the normal wall type the twist angle (angle between the wall magnetization at the midplane of the film and at the film surface) is approximately π/2. For the first anomalous type this angle is approximately −3π/2, for the second type approximately 5π/2, etc. The width and energy of such walls are calculated using (i) a Bloch‐line approximation and (ii) a sinusoidal variational trial function (as in Paper I of this series). The ratio of the energy of a twisted wall (E) to the energy of an untwisted wall (E₀) can in all cases be represented as E/E₀=(1−βσ)^1/2, where σ=4πM₀/H_a [M₀ is the saturation magnetization, H_a is the anisotropy field]. According to the first method β=0.692 for the normal wall type and β=0.692− (π/c)(D/2πM)^1/2 for the first anomalous type. Here 2c is the film thickness, D=2A/M₀, and A is the exchange stiffness constant. According to the second method β=0.654 for the normal wall type, and β=0.319 for the first anomalous type.