1302.0222 (Konstantin L. Metlov)
Konstantin L. Metlov
Collective-variable approach for study of non-linear dynamics of magnetic textures in planar nano-magnets is proposed. The variables are just arbitrary parameters (complex or real) in the specified analytical function of complex variable, describing the texture in motion. Starting with such a function, a formal procedure is outlined, allowing to obtain the (non-linear) system of differential equations of motion for the variables. The resulting equations are equivalent to Landau-Lifshitz-Gilbert dynamics as much as definition of collective variables allows it. Apart from collective-variable specification, the procedure does not involve any additional assumptions (such as translational invariance or steady-state motion). As an example, equations of weakly non-linear motion of magnetic vortex are derived and solved analytically. A simple formula for dependence of vortex precession frequency on its amplitude is derived. The results are verified against special cases from the literature and agree quantitatively with experiments and simulations.
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http://arxiv.org/abs/1302.0222
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