Scaling laws of domain walls in magnetic nanowires
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Submission date: 29. Jun. 2006 (revised version: February 2007)
MSC-Numbers: 82D40, 47J30
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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 the energy minimization problem -converges to a local, one dimensional problem where the energy is given by .