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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
58/2006

Scaling laws of domain walls in magnetic nanowires

Katharina Kühn

Abstract

This paper investigates magnetic 180 degree domain walls in thin wires. It establishes a crossover between two scaling regimes for the energy as a function of the radius $R$. For small radii the optimal scaling can be realized by a transverse wall for which the magnetization is constant on each cross section. For large radii a vortex wall yields the optimal scaling.

Moreover we show that for $R\to 0$ the energy minimization problem $\Gamma$-converges to a local, one dimensional problem where the energy is given by $\pi \|\partial_x m\|_{L^2(\mathbb{R})}^2+\frac{\pi}{2}\|m_y\|_{L^2(\mathbb{R})}^2$.

Received:
Jun 29, 2006
Published:
Jun 29, 2006
MSC Codes:
82D40, 47J30

Related publications

Preprint
2006 Repository Open Access
Katharina Kühn

Scaling laws of domain walls in magnetic nanowires