Dynamic behavior of domain walls in thin magnetic films

The structure of moving domain walls is obtained by maximizing a Lagrange function, assuming that the film has a uniaxial anisotropy axis in the plane of the film. The variational calculation is based on a class of trial functions previously used for the static case of Dietze and Thomas. The solution applies for wall velocities smaller than a certain critical velocity. At the critical velocity the derivative of the wall energy with respect to velocity becomes infinite and the energy remains finite. For very thick and very thin films the critical velocity calculated with the chosen trial function approaches the critical velocity for bulk material to within one percent. At intermediate film thicknesses, near the transition from a Bloch to a Néel wall, the critical velocity is much smaller (approximately 1/20 of the bulk value in the case of Permalloy). The effective mass per unit area of the wall increases with increasing film thickness for Néel walls and decreases for Bloch walls. This dependence is qualitatively similar to that of the inverse (static) wall width on film thickness, but considerably stronger. Néel walls and Bloch walls in thick films contract with increasing velocity. At intermediate film thicknesses a region exists in which Bloch walls expand slightly with increasing velocity.