Abstract
The stability of the well-known Walker propagating domain wall (DW) solution of the Landau-Lifshitz-Gilbert equation is analytically investigated. Surprisingly, a propagating DW is always dressed with spin waves so that the Walker rigid-body propagating DW mode does not occur in reality. In the low field region only stern spin waves are emitted while both stern and bow waves are generated under high fields. In a high enough field, but below the Walker breakdown field, the Walker solution could be convective or absolute unstable if the transverse magnetic anisotropy is larger than a critical value, corresponding to a significant modification of the DW profile and DW propagating speed.
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