We derive a low-energy Hamiltonian for the elastic energy of a Néel domain wall in a thin film with in-plane magnetization, where we consider the contribution of the long-range dipolar interaction beyond the quadratic approximation. We show that such a Hamiltonian is analogous to the Hamiltonian of a one-dimensional polaron in an external random potential. We use a replica variational method to compute the roughening exponent of the domain wall for the case of two-dimensional dipolar interactions.

• Received 10 October 2001

DOI:https://doi.org/10.1103/PhysRevE.65.031608