Vortex Motion for the Landau-Lifshitz-Gilbert Equation with Applied Magnetic Field

Matthias Kurzke (), Christof Melcher () and Roger Moser ()
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Matthias Kurzke: Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Angewandte Mathematik
Christof Melcher: RWTH Aachen University, Department of Mathematics I & JARA – Fundamentals of Future Information Technology
Roger Moser: University of Bath, Department of Mathematical Sciences

A chapter in Singular Phenomena and Scaling in Mathematical Models, 2014, pp 113-132 from Springer

Abstract: Abstract In micromagnetics, the fundamental evolution law for the magnetization m in a solid is given by the Landau-Lifshitz-Gilbert equation 1 $$\displaystyle{ \frac{\partial \mathbf{m}} {\partial t} = \mathbf{m} \times \left (\alpha \frac{\partial \mathbf{m}} {\partial t} -\gamma \,\boldsymbol{ h}_{\mathrm{eff}}\right ), }$$ which is used to describe the dynamics of a great variety of magnetic microstructures, in particularly the motion of domain walls and vortices in thin films, see e.g. [3]. Here $$\boldsymbol{h}_{\mathrm{eff}}$$ is the effective field, essentially the L 2 gradient of the micromagnetic energy.

Keywords: Effective Field; Unique Minimizer; Vortex Trajectory; Magnetic Microstructure; Standard Volume Form (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-00786-1_6

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