Energy of One-Dimensional Domain Walls in Ferromagnetic Films

Abstract

The energy of a one-dimensional 180° domain wall in a ferromagnetic film is minimized for all possible configurations of the magnetization distribution in the wall, using an approximate expression for the magnetostatic self-energy. It is shown analytically that there is no solution other than Néel or Bloch wall. There is, however, some degeneracy, which indicates a breakdown of the one-dimensional calculation, in the region of parameter values where cross-tie walls are observed experimentally. The Bloch wall energy for this approximation is shown to be rather close to the absolute minimum computed by Brown and LaBonte. Néel walls are found to have an infinitely long tail, the behavior being that of tanh. Using the functional form of this approximate minimization in the exact energy expressions, it is shown that the Néel wall energy is at most a few percent below previous estimations.