Ferromagnetic resonance frequency and spin wave mode of asymmetric strip nanomagnet

Chen Ya-Bo; Yang Xiao-Kuo; Wei Bo; Wu Tong; Liu Jia-Hao; Zhang Ming-Liang; Cui Huan-Qing; Dong Dan-Na; Cai Li

doi:10.7498/aps.69.20191622

Abstract

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.

Keywords:

Authors and contacts

1.
Department of Foundation, Air Force Engineering University, Xi’an 710051, China
2.
Department of Wired Communications, Air Force Communications NCO Academy, Dalian 116100, China

Corresponding author: Yang Xiao-Kuo, yangxk0123@163.com

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References

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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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 3 纳磁体的归一化的磁化分量m_z随外加磁场的激励时间的变化

Figure 3. Normalized magnetization components m_z of nanomagnets versus the excitation time of magnetic field applied.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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, H_m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

Figure 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. H_m 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.

DownLoad: Full-Size Img PowerPoint

map

[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 Google Scholar Yang X K, Zhang B, Cui H Q, Li W W, Wang S 2016 Acta Phys. Sin. 65 237502 Google Scholar
[6]	Dong D N, Cai L, Li C, Liu B J, Li C, Liu J H 2019 J. Phys. D: Appl. Phys. 52 295001 Google Scholar
[7]	Eklund A, Bonetti S, Sani S R,, Mohseni S M, Persson J, Chung S J, Banuazizi S A H, Iacocca E, Ostling M, Akerman J, Malm B G 2014 Appl. Phys. Lett. 104 092405 Google Scholar
[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
[9]	Liu M, Zhou Z Y, Nan T X, Howe B M, Brown G J, Sun N X 2013 Adv. Mater. 25 1435 Google Scholar
[10]	Zhou Z Y, Peng B, Zhu M M, Liu M 2016 J. Adv. Dielectr. 6 1630005 Google Scholar
[11]	Suto H, Kanao T, Nagasawa T, Kudo K, Mizushima K, Sato R 2017 Appl. Phys. Lett. 110 262403 Google Scholar
[12]	Yang X K, Zhang B, Liu J H, Zhang M L, Li W W, Cui H Q, Wei B 2018 Chin. Phys. Lett. 35 057501 Google Scholar
[13]	Okamoto S, Kikuchi N, Kato T, Kitakami O, Mitsuzuka K, Shimatsu T, Muraoka H, Aoi H, Lodder J C 2008 J. Magn. Magn. Mater. 320 2874 Google Scholar
[14]	Liu M, Howe B M, Grazulis L, Mahalingam K, Nan T X, Sun N X, Brown G J 2013 Adv. Mater. 25 4886 Google Scholar
[15]	Hu X K, Dey H, Liebing N, Csaba G, Orlov A, Bernstein G H, Porod W, Kryzysteczko P, Sievers S, Schumacher H W 2015 IEEE Trans. Magn. 51 3401004 Google Scholar
[16]	Wei B, Cai L, Yang X K, Li B J, Wang S, Feng C W, Cui H Q, Li C, Liu J H 2018 IEEE. Magn. Lett. 9 3706505
[17]	Imre A 2005 Disseration U of Notre Dame 8 803
[18]	Liu J H, Yang X K Zhang M L, Wei B, Li C, Dong D N, Li C 2018 IEEE Electron Device Lett. 40 220
[19]	顾文娟, 潘靖, 胡经国 2012 61 167501 Google Scholar Gu W J, Pan J, Hu J G 2012 Acta Phys. Sin. 61 167501 Google Scholar
[20]	Nembach H T, Shaw J M, Silva T J, Johnson W L, Kim S A, Mcmichael R D, Kabos P 2011 Phys. Rev. B 83 094427 Google Scholar
[21]	Mahato B K, Choudhury S, Mandal R, Barman S, Otani Y, Barman A 2015 J. Appl. Phys 117 213909 Google Scholar
[22]	Adhikari K, Barman S, Mandal R, Otani Y, Barman A 2018 Phys. Rev. Appl. 10 044010 Google Scholar
[23]	刘嘉豪, 杨晓阔, 危波, 张明亮, 李闯, 董丹娜 2019 68 017501 Google Scholar Liu J H, Yang X K, Wei B, Li C, Zhang M L, Li C, Dong D N 2019 Acta Phys. Sin. 68 017501 Google Scholar
[24]	Vacca M, Cairo F, Turvani G, Riente F, Zamboni M, Graziano M 2016 IEEE Trans. Nanotechnol. 15 962 Google Scholar
[25]	Abeed M A, Atulasimha J, Bandyopadhyay S 2018 J. Phys: Condens. Matter. 30 394001 Google Scholar
[26]	Melo L, Soares T, Neto O P V 2017 IEEE Trans. Magn. 53 1 Google Scholar
[27]	Niemier M T, Varga E, Bernstein G H, Porod W, Alam M T, Dingler A, Orlov A, Hu X S 2012 IEEE Trans. Nanotechnol. 11 220 Google Scholar
[28]	Zhang B, Yang X K, Wang Z C, Zhang M L 2014 Micro Nano Lett. 9 359 Google Scholar
[29]	Sivasubramani S, Mattela V, Pal C, Acharyya A 2019 Nanotechnology 30 37LT02 Google Scholar
[30]	Donahue M J, Porter D G 1999 OOMMF User’s Guide, Version 1.0 Interagency Report NISTIR 6376
[31]	Cui J Z, Hockel J L, Nordeen P K, Pisani D M, Liang C Y, Carman G P, Lynch C S 2013 Appl. Phys. Lett. 103 232905 Google Scholar
[32]	D’Souza N, Salehi Fashami M S, Bandyopadhyay S, Atulasimha J 2016 Nano Lett. 16 1069 Google Scholar
[33]	危波, 蔡理, 杨晓阔, 李成 2016 65 217501 Google Scholar Wei B, Cai L, Yang X K, Li C 2016 Acta Phys. Sin. 65 217501 Google Scholar
[34]	Fashami-Salehi M, D’Souza N 2017 J. Magn. Magn. Mater. 438 76 Google Scholar
[35]	Fashami M S, Roy K, Atulasimha J, Bandyopadhyay S 2011 Nanotechnology 22 155201 Google Scholar
[36]	Jin T L, Hao L, Cao J W, Liu M F, Dang H G, Wang Y, Wu D P, Bai J M, Wei F L 2014 Appl. Phys. Express 7 043002 Google Scholar
[37]	杨庆新, 李永建 2016 电工技术学报 31 1 Google Scholar Yang Q X, Li Y J 2016 Trans. Chin. Electrotechnical Society 31 1 Google Scholar
[38]	黄文美, 薛胤龙, 王莉, 翁玲, 王博文 2016 电工技术学报 31 173 Google Scholar Huang W M, Xue Y L, Wang L, Weng L, Wang B W 2016 Trans. Chin. Electrotechnical Society 31 173 Google Scholar
[39]	郜春艳, 黄文美, 刘卓锟, 曹晓宁 2018 传感技术学报 31 26 Gao C Y, Huang W M, Liu Z K, Cao X N 2018 Chin. J. Sens. Actuators 31 26
[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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