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We consider a thin ferromagnetic layer to which an external field or acurrent are applied along an in plane easy axis. The perpendicular hard axisanisotropy constant is large so that the out of plane magnetization componentis smaller than the in plane components. A perturbation approach is used toobtain the profile and velocity of the moving domain wall. The dynamics of thein plane components of the magnetization is governed by a reaction diffusionequation which determines the speed of the profile. We find a simple analyticexpression for the out of plane magnetization showing a symmetric distortiondue to the motion in addition to the asymmetric component due to theDzyaloshinskii--Moriya interaction. The results obtained complement previousstudies in which either the Dzyalozhinskii vector or the out of plane hard axisanisotropy were assumed small. In the regime studied the Walker breakdown isnot observed but the reaction diffusion dynamics predicts a slowing down of thedomain wall for sufficiently large magnetic field. The transition point dependson the applied field, saturation magnetization and easy axis anisotropy.

Domain wall dynamics for an in-plane magnetized thin film with large perpendicular hard axis anisotropy including Dzyaloshinskii-Moriya interaction