Fluctuation and elastic properties of domain walls in two-dimensional dipolar systems

We discuss the fluctuation of domain walls in two-dimensional systems interacting with short-range exchange, anisotropy, and long-range dipolar interactions. The elastic energy of different domain walls are calculated. Some of the domain-wall distortion modes are soft in the long-wavelength limit. The competition of the stabilizing long-range dipolar interaction and low-dimensional fluctuation suggests the possibility of a finite-temperature roughening of an array of one-dimensional walls in the film.