On the limiting velocity and forced motion of ferromagnetic domain walls in an external field perpendicular to the easy-magnetization axis

Abstract

A theory is constructed for the dynamics and braking of domain walls in ferromagnets when a magnetic field is applied perpendicular to the axis of easy magnetization (i.e., a transverse field H _⊥). The theory is valid for velocities v up to the limiting domain wall velocity v c. The Landau-Lifshitz equations in the dissipationless approximation are used to investigate the motion of domain walls and the change in the character of the wall motion as its velocity v approaches v _c. The force acting on a domain wall due to viscous friction is calculated within the framework of generalized relaxation theory, and the dependence of the domain wall velocity v on the forcing field H _z is investigated. Calculations of the braking force show that the contributions of various dissipation mechanisms to the friction force have different dependences on the domain wall velocity, which affects the form of the function v=v(H _z). The shapes of the curves v(H _z) differ very markedly from one another for different values of the field H _⊥. The theory developed here can be used to describe the experimental results, in particular the almost linear behavior of v=v(H _z) for small H _⊥ and its strongly nonlinear behavior when H _⊥∼H _a, whereas these data cannot be reconciled within the standard theory based on relaxation terms of Hilbert type.