模拟方位角梯度磁振子景观中径向自旋波的河马曲线
Hippopede curves for modelling radial spin waves in an azimuthal graded magnonic landscape
摘要：
我们提出了一个数学模型来描述径向传播的自旋波发射的核心区域中的磁补丁与n个顶点的磁涡旋状态。表面自旋波（SSW）的方位角各向异性传播到域中，以及域壁中的受限自旋波（或Winter's Magnons，WM）增加了磁振子景观的复杂性。为了理解这些系统中的自旋波传播，我们首先使用一种基于几何曲线的方法，称为“双足”，但它没有提供对底层物理的洞察。分析模型依赖于从SSW的色散关系与磁化M和波数k之间的任意角度的广义表达式。导出的方位角色散的代数表达式被发现是等价的“蜈蚣”曲线。从模型的拟合曲线产生的自旋波波长为任何给定的方位角方向，补丁顶点的数量和激发频率，显示与交换为主的表面自旋波的基本物理的连接。分析结果表明，与微磁模拟良好的协议，可以很容易地外推到任何n-角补丁的几何形状。
英文摘要：
We propose a mathematical model for describing radially propagating spin waves emitted from the core region in a magnetic patch with n vertices in a magnetic vortex state. The azimuthal anisotropic propagation of surface spin waves (SSW) into the domain, and confined spin waves (or Winter's Magnons, WM) in domain walls increases the complexity of the magnonic landscape. In order to understand the spin wave propagation in these systems, we first use an approach based on geometrical curves called 'hippopedes', however it provides no insight into the underlying physics. Analytical models rely on generalized expressions from the dispersion relation of SSW with an arbitrary angle between magnetization M and wavenumber k. The derived algebraic expression for the azimuthal dispersion is found to be equivalent to that of the 'hippopede' curves. The fitting curves from the model yield a spin wave wavelength for any given azimuthal direction, number of patch vertices and excitation frequency, showing a connection with fundamental physics of exchange dominated surface spin waves. Analytical results show good agreement with micromagnetic simulations and can be easily extrapolated to any n-corner patch geometry.
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