We summarize our experimental findings in the arrays of Ni80Fe20 circular nanodots with diameter 300 nm and thickness 20 nm ≤ L ≤ 100 nm, probed by broadband ferromagnetic resonance spectroscopy in the absence of external magnetic field. Spin excitation modes related to the vortex core gyrotropic dynamics were observed in the gigahertz frequency range. Micromagnetic simulations revealed that they are flexure oscillations of the vortex core string with n = 0, 1, 2 nodes along the dot thickness. It was found that for L > 70 nm the intensity of more complicated n = 1 vortex gyrotropic mode is unexpectedly higher than the one of the lowest n = 0 gyrotropic mode. This behavior was clarified on the basis of the inhomogeneous vortex mode phase profiles extracted from micromagnetic simulations and calculated analytically. Precise measurements of the dependence of resonance frequency of the vortex n = 0 mode on the dot thickness demonstrated a clear maximum around L = 70 nm, that was theoretically explained by introducing a vortex mass, which is a result of the vortex distortion due to interaction with spin waves having azimuthal indices m = ±1. Finally, several azimuthal spin-wave modes having curled structure at the dot top and bottom faces were found in the spectrum of the dots with thicknesses L ≥ 40 nm.

中文翻译：

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磁涡态纳米点中沿厚度方向的非均匀自旋激发

我们总结了在没有外部磁场的情况下通过宽带铁磁共振光谱探测的直径 300 nm 和厚度 20 nm ≤ L ≤ 100 nm 的 Ni80Fe20 圆形纳米点阵列的实验结果。在千兆赫频率范围内观察到与涡核回旋动力学相关的自旋激励模式。微磁模拟表明，它们是涡核弦的弯曲振荡，沿点厚度有 n = 0、1、2 个节点。发现对于 L > 70 nm，更复杂的 n = 1 涡旋回旋模式的强度出乎意料地高于最低的 n = 0 回旋模式之一。根据从微磁模拟中提取并通过分析计算的非均匀涡旋模式相位轮廓，这种行为得到了澄清。涡旋 n = 0 模式的共振频率对点厚度的依赖性的精确测量表明，在 L = 70 nm 附近有一个明显的最大值，这在理论上可以通过引入涡流质量来解释，这是由于相互作用引起的涡旋失真的结果具有方位角指数 m = ±1 的自旋波。最后，在厚度 L ≥ 40 nm 的点的光谱中发现了几种在点顶面和底面具有卷曲结构的方位角自旋波模式。