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通过建立微波激励下的非对称条形多铁纳磁体的微磁模型, 研究了倾斜角和缺陷角对该形纳磁体的铁磁共振谱和自旋波模式的影响. 通过对微磁仿真得到的动态磁化数据进行分析发现, 非对称条形纳磁体倾斜角度增加, 铁磁共振频率随之增加, 而这一现象与纳磁体的缺陷角度无关. 倾斜角不变, 非对称条形纳磁体的铁磁共振频率与缺陷角度呈单调递增关系, 并且不同缺陷角度纳磁体的自旋波模式显示出极大的差异. 非对称条形纳磁体与矩形纳磁体相比, 它的自旋波模式局部化, 具体为非对称条形纳磁体的自旋波模式不对称且高进动区域存在于边缘, 表现为非对称边缘模式. 倾斜角改变导致纳磁体内部退磁场变化, 引起纳磁体边缘模式的移动, 而中心模式对倾斜角的变化并不敏感. 最后, 对建立的模型在高频微波磁场激励下的磁损耗进行了分析, 验证了模型的可靠性. 这些结论说明缺陷角和倾斜角可用于纳磁体自旋波模式和铁磁共振频率的调谐, 所得结果为可调纳磁微波器件的设计提供了重要的理论依据和思路.Recently, the operating frequency of nanomagnetic logic device has reached the spin wave frequency of nanomagnets. Therefore, the dynamic magnetic properties of nanomagnets, which are excited by microwave magnetic field, have been explored by many researchers. In this paper, the micro-magnetic model of asymmetric strip nanomagnets under microwave excitation is established. By using the anisotropic stress field (along the x-axis direction) that is generated by a constant voltage and the SINC function microwave magnetic field (along the y-axis direction) to excite the nanomagnets at the same time, the effects of tilt angle and defect angle on the ferromagnetic resonance (FMR) spectrum and spin wave mode of the asymmetric strip nanomagnets are studied. Spectral analysis is performed on the micromagnetic simulation data. Simulation results show that as the tilt angle of the asymmetric strip nanomagnet increases, the ferromagnetic resonance frequency increases. What is more, this phenomenon is independent of the defect angle of the nanomagnet. When the tilt angle is constant, there exists a monotonically increasing relation between the ferromagnetic resonance frequency of the asymmetric strip nanomagnet and the defect angle. The spin wave modes of the nanomagnets differ a lot as defect angle changes. The asymmetric strip nanomagnet is compared with the rectangle nanomagnet, and the spin wave mode of the asymmetric strip nanomagnet is localized. Specifically, the spin wave mode of the asymmetric strip nanomagnets is asymmetric and the high precession region exists at the edge, which is termed asymmetric edge mode. The changes of the tilt angle lead to the changes in the demagnetizing field inside the nanomagnet, which gives rise to the movement of the edge mode. However, the center mode is not sensitive to the change of tilt angle. Finally, the magnetic loss of the model under the excitation of high frequency microwave magnetic field is analyzed and the reliability of the model is verified. These findings indicate that the defect angle and tilt angle can be used to tune the spin wave mode and the ferromagnetic resonance frequency of nanomagnets, and thus providing an important theoretical basis for designing the tunable microwave nanomagnetic devices.
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Keywords:
- asymmetric strip nanomagnet /
- ferromagnetic resonance (FMR) /
- spin wave mode /
- microwave devices
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图 1 (a) 微波磁场和应力各向异性场相互垂直激励纳磁体的结构示意图, 此图中纳磁体未倾斜; (b) 纳磁体的俯视图, θ是缺陷角度, φ是纳磁体长轴和y轴之间的倾斜角度
Fig. 1. (a) Schematic illustration of nanomagnet excited by perpendicular microwave magnetic field and bias magnetic field, the magnet in this figure is not tilted; (b) top view of nanomagnet, where θ is the defect angle and φ is the tilt angle between y-axis and the long axis of nanomagnets.
图 2 在室温下, 不同纳磁体(tanθ = 0, 1/6, 2/6, 3/6, 4/6, 5/6)在没有外加磁场激励下的静态自旋方向, 随着缺角的增大非对称条形纳磁体的磁化方向逐渐偏离y轴
Fig. 2. Static spin orientation without external excitation of different nanomagnets (tan θ = 0, 1/6, 2/6, 3/6, 4/6, 5/6) at room temperature. With the increasing of the defect angle, the magnetization direction of the asymmetric strip nanomagnets deviate from the y-axis gradually.
图 3 纳磁体的归一化的磁化分量mz随外加磁场的激励时间的变化
Fig. 3. Normalized magnetization components mz of nanomagnets versus the excitation time of magnetic field applied.
图 4 不同纳磁体的FMR频率谱和最高吸收峰对应的自旋波模式(tan θ = 0, 1/6, 2/6, 3/6, 4/6, 5/6), 图中的自旋波模式为边缘模式, 红色区域为磁矩的高进动幅值的位置, 蓝色区域为磁矩的低进动幅值的位置
Fig. 4. FMR spectra and spin wave modes of different nanomagnets (tan θ = 0, 1/6, 2/6, 3/6, 4/6, 5/6). The spin wave mode in this figure is the edge mode, the red region is the position of the high precession amplitude of the magnetic moment, and the blue region is the position of the low precession amplitude of the magnetic moment.
图 5 四种纳磁体(矩形, tanθ = 2/6, 4/6, 5/6的三种非对称条形纳磁体)在不同倾斜角度φ下的铁磁共振频率谱, 绿色箭头标记了最高吸收峰
Fig. 5. FMR spectra of nanomagnets(tan θ = 0, 2/6, 4/6, 5/6) for different tilt angle φ. The green arrow marks the highest absorption peak.
图 6 矩形和非对称条形纳磁体(tanθ = 4/6)在不同倾斜角度φ下的自旋波模式. 图的右侧为自旋波模式的进动幅度的色标, 红色区域为磁矩的高进动幅值的位置, 蓝色区域为磁矩的低进动幅值的位置
Fig. 6. Spin wave mode of rectangular and asymmetric strip nanomagnets (tanθ = 4/6) at different tilt angle. The color scale for the precession intensity of the spin modes is shown at the right side of the figure, the red region is the position of the high precession amplitude of the magnetic moment, and the blue region is the position of the low precession amplitude of the magnetic moment.
图 7 纳磁体在高频(15 GHz)交变磁场激励下, 外加磁场在内部作用的效果与纳磁体深度的关系, Hm是外加交变磁场作用在材料内部的磁场幅值, H0为交变磁场的幅值
Fig. 7. Under the excitation of high frequency (15 GHz) alternating magnetic field, the relation between the effect of external magnetic field acting on the inside and the depth of the nanomagnet. Hm is the amplitude of the external alternating magnetic field acting on the inside of the material, and H0 is the amplitude of the alternating magnetic field.
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[1] Zhang S L, Zhang J Y, Baker A A, Wang S G, Yu G H, Hesjedal A T 2014 Sci. Rep. 4 6109
Google Scholar
[2] Liu J H, Yang X K, Cui H Q, Wei B, Li C, Chen Y B, Zhang M L, Li C, Dong D N 2019 J. Magn. Magn. Mater. 491 165607
Google Scholar
[3] Kudo K, Suto H, Nagasawa T, Mizushima K, Sato R 2015 Appl. Phys. Express 8 103001
Google Scholar
[4] Lavrijsen R, Lee J H, Fernández-Pacheco A, Petit D C M C, Mansell R, Cowburn R P 2013 Nature 493 647
Google Scholar
[5] 杨晓阔, 张斌, 崔焕卿, 李伟伟, 王森 2016 65 237502
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Yang X K, Zhang B, Cui H Q, Li W W, Wang S 2016 Acta Phys. Sin. 65 237502
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[8] 张光富, 张学军, 蒋练军 2016 材料导报: 研究篇 30 148
Zhang G F, Zhang X J, Jiang L J 2016 Mater. Rep B: Res. 30 148
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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[40] 李劲松, 杨庆新, 李永建, 张长庚 2016 高电压技术 42 994
Li J S, Yang Q X, Li Y J, Zhang C G 2016 High Voltage Engineering 42 994
[41] 钟文定 2017 铁磁学 (北京: 科学出版社) 第366页
Zhong W D 2017 Ferromagnetism (Beijing: Science Press) p366 (in Chinese)
[42] Butterill H J 1948 Nature 161 554
[43] 严密, 彭晓领 2006 磁学基础与磁性材料 (杭州: 浙江大学出版社) 第111页
Yan M, Peng X L 2006 Fundamentals of Magnetism and Magnetic Materials (Hangzhou: Zhejiang University Press) p111 (in Chinese)
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