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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
108/2007

Travelling waves with a singularity in magnetic nanowires

Katharina Kühn

Abstract

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.

Received:
Dec 13, 2007
Published:
Dec 13, 2007
MSC Codes:
82D40, 47J30

Related publications

inJournal
2009 Repository Open Access
Katharina Kühn

Travelling waves with a singularity in magnetic nanowires

In: Communications in partial differential equations, 34 (2009) 7, pp. 722-764