Vol. 08  No. 02 ( 2019 ), Article ID: 30415 , 11 pages
10.12677/CMP.2019.82006

Spin Wave Modes and Dynamics of Three-Dimensional Magnetic Nanodisks under Perpendicular Resonant Magnetic Field

Jinming Xu1, Ruifang Wang1,2

1Department of Physics, Xiamen University, Xiamen Fujian

2Collaborative Innovation Centre for Optoelectronic Semiconductors and Efficient Devices, Xiamen University, Xiamen Fujian

Received: May 6th, 2019; accepted: May 20th, 2019; published: May 27th, 2019

ABSTRACT

We studied the spin wave modes in permalloy nanodisks with different thicknesses under the excitation of a perpendicular ac magnetic field, using micromagnetic simulations. When the thickness of permalloy nanodisks is comparable to its radius, the magnetic moments are nonuniform along the disk thickness, forming a football-like vortex core in which middle part is larger than the ends, due to competition between demagnetization energy and exchange energy. And we observe not only the excitation of radial spin wave modes, but also hybridization of standing wave along the disk thickness with radial spin wave modes. The eigenfrequencies of such hybrid modes are much larger than the low-order radial spin wave modes. When the thickness of the disk is large enough, we observe hybridization of the high-order standing wave with radial spin wave modes, but near absence of pure common radial spin wave mode. By applying a perpendicular phase-matched resonant magnetic field, the vortex polarity can be easily switched.

Keywords:Magnetic Vortex, Spin Wave Modes, Magnetic Simulation

1厦门大学物理学系，福建 厦门

2厦门大学半导体光电材料及其高效转换器件协同创新中心，福建 厦门

1. 引言

2. 模型及初始态分析

Figure 1. Magnetization distribution of initial vortex states in permalloy nanodisks with diameter of 300 nm and thickness of 20 nm (a) and 80 nm (b), respective. For simplicity, only one half of the nanodisk is displayed. The color bar shows the z-component of magnetization. (c) Variation of vortex core diameter and the biggest diameter difference, in the bottom, middle and top layer, with respect to the sample thickness

Figure 2. Spatial distribution of the total, exchange and demagnetization energy in a cross section along a diameter in nanodisks with thicknesses of 20 (a), 50 (b), and 80 nm (c), respectively. The color bar denotes the relative magnitude of energies

3. 自旋激发频谱分析

Figure 3. (a) The FFT amplitude spectrum of a nanodisk with diameter of 300 nm and thickness of 20 nm, after excitation of a pulse square field applied along z direction. The inset shows spatial distribution of FFT amplitude of radial spin wave modes in the bottom layer of the nanodisk. (b) Spatial distribution of FFT amplitude and phase of mixed spin wave modes in the bottom layer of the nanodisk

Figure 4. Spatial distribution of FFT amplitude and phase of radial spin wave modes (a), and mixed spin wave modes (b),in a cross section along a diameter of the nanodisk with diameter of 300 nm and thickness of 20 nm. The color bars on the lower left and lower right represent the FFT amplitude and phase, respectively. Use the color bars in all amplitude and phase profiles

Figure 5. (a) FFT amplitude spectrum of a nanodisk with diameter of 300 nm and thickness of 30 nm. The inset shows spatial distribution of FFT amplitude of radial spin wave modes in the bottom layer of the nanodisk. (b) Spatial distribution of FFT amplitude and phase of radial spin wave modes in a cross section along a diameter of the nanodisk

Figure 6. Spatial distribution of FFT amplitude and phase of mixed spin wave modes of a 30 nm thick nanodisk. The number of nodes along the thickness is TS = 1. The numbers of nodes along the radial direction are n = 1, 2, 3, and 4 for (a), (b), (c) and (d) respectively.The FFT amplitude and phase images are displayed underneath the cross sections images

Figure 7. The spatial distributions of FFT amplitude and phase of hybridization of the high-order standing wave with high-order radial spin wave modes in thick nanodisks

4. 混合模式下的动力学

Figure 8. Snap shots of the magnetization dynamics of the top (a), middle (b) and bottom (c) layers of a 20 nm thick magnetic vortex, under the excitation of a phase-matched resonant field

5. 总结

Spin Wave Modes and Dynamics of Three-Dimensional Magnetic Nanodisks under Perpendicular Resonant Magnetic Field[J]. 凝聚态物理学进展, 2019, 08(02): 41-51. https://doi.org/10.12677/CMP.2019.82006

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