Mass and critical velocity of domain walls in thin magnetic films

Abstract

It is shown that the structure of domain walls moving at constant velocity ν can be obtained by maximizing a Lagrangian L= T− E, where the kinetic energy T is proportional to ν and E is the usual (potential) energy. For thin films having a uniaxial anisotropy axis in the plane of the film an approximate solution of the dynamic micromagnetic equations is obtained by maximizing L relative to a class of variational trial functions that describe one-dimensional domain walls (previously used for the static case by Dietze and Thomas). The dynamic solution obtained in this manner applies for wall velocities smaller than a certain critical velocity, at which the derivative of the wall energy with respect to velocity becomes infinite. For very thick and very thin films the critical velocity calculated using the Dietze-Thomas model approaches the known bulk value (approximately 8 × 104 cm/sec for permalloy) to within 1%. At intermediate film thicknesses, near the transition from Néel to Bloch walls, the critical velocity is much smaller (approximately 1/20 of the bulk value in the case of Permalloy). In this thickness range the predicted effective mass per unit area of the wall is larger than the bulk value by approximately 100 for Permalloy.