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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

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Preprint
2006 Repository Open Access
Katharina Kühn

Scaling laws of domain walls in magnetic nanowires