Eur. Phys. J. B 26, 191-198 (2002)
https://doi.org/10.1140/epjb/e20020080

On the steady motions of a flat domain wall in a ferromagnet

Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, Via di Tor Vergata, 110 - 00133 Roma, Italy

Corresponding author: ^a ppg@uniroma2.it

Received: 16 November 2001
Published online: 15 March 2002

Abstract

A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave motion of a flat domain wall at 180°. It is shown that a process during which the working of the applied magnetic field exactly compensates dissipation (the Walker condition) exists both under the constitutive circumstances considered in the standard Gilbert equation and when either the internal free-energy or the dissipation, or both, are generalized by the introduction of higher-gradient terms; but that such a process cannot solve the generalized Gilbert equation. It is also shown that, when dry-friction dissipation is considered and a suitable magnetic field is applied, the associated Gilbert equation has a Walker-type solution mimicking a flat wall, at 90° this time, which however does not satisfy the Walker condition. ynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) omain walls and domain structure