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Vortex mechanics in planar nanomagnets

机译：平面纳米磁体中的涡旋力学

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A collective-variable approach for the study of nonlinear dynamics of magnetic textures in planar nanomagnets is proposed. The variables are just arbitrary parameters (complex or real) in the specified analytical function of a complex variable describing the texture in motion. Starting with such a function, a formal procedure is outlined, allowing a (nonlinear) system of differential equations of motion to be obtained for the variables. The resulting equations are equivalent to Landau-Lifshitz-Gilbert dynamics as far as the definition of collective variables allows it. Apart from the collective-variable specification, the procedure does not involve any additional assumptions (such as translational invariance or steady-state motion). As an example, the equations of weakly nonlinear motion of a magnetic vortex are derived and solved analytically. A simple formula for the dependence of the 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.
机译：提出了一种集体变量方法，用于研究平面纳米磁体中磁织构的非线性动力学。变量只是描述运动纹理的复杂变量的指定分析函数中的任意参数（复杂或实数）。从这样的函数开始，概述了一个正式的过程，允许为变量获得一个（非线性的）运动微分方程系统。只要集体变量的定义允许，所得方程就等同于Landau-Lifshitz-Gilbert动力学。除了集合变量规范外，该过程不涉及任何其他假设（例如平移不变性或稳态运动）。例如，推导并解析地求解了磁涡旋的弱非线性运动方程。得出了旋涡进动频率与其振幅的关系的简单公式。结果针对文献中的特殊情况进行了验证，并与实验和模拟定量地吻合。

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