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Travelling waves with a singularity in magnetic nanowires
We model the evolution of the magnetisation in an infinite cylinder by harmonic map heat flow with an additional external field. Using variational methods, we prove the existence of corotationally symmetric travelling wave solutions with a moving vortex. We moreover show that for weak and strong fields the travelling waves connect the original state anti-parallel to the external magnetic field with the totally reversed state in direction of the external field.
Our results match numeric simulations. For thicker wires several groups have observed a reversal mode where a domain wall with a corotational symmetry and a vortex is propagating through the wire.