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

A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave motion of a fiat domain wall at 180degrees. 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, axe 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 90degrees this time, which however does not satisfy the Walker condition.