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亚铁磁畴壁在角动量补偿点附近具有非零净磁化强度, 同时具有超快动力学性质, 有望应用于未来的自旋电子学存储和逻辑器件中. 探寻低能耗和高效驱动畴壁的手段和机制可以为实验设计和器件开发提供重要参考. 本文使用理论分析和微磁学模拟研究了亚铁磁畴壁在正弦微波磁场驱动下的动力学行为, 表明了微波磁场在一定的频率范围内可有效驱动畴壁运动, 使得人们可通过调制不同频率的微波磁场来调控畴壁动力学. 本文详细分析和解释了正弦微波磁场驱动亚铁磁畴壁的物理机理, 探讨了双轴各向异性等参数对畴壁运动速度的影响, 表明了磁各向异性和外加微波磁场频率等参量对不同净自旋角动量亚铁磁畴壁的调控行为.Ferrimagnetic domain walls have received more and more attention because of their interesting physics and potential applications in future spintronic devices, particularly attributing their non-zero net magnetization and ultrafast dynamics. Exploring effective methods of driving domain walls with low energy consumption and high efficiency can provide important information for experimental design and device development. In this work, we study theoretically and numerically the dynamics of ferrimagnetic domain wall driven by the sinusoidal microwave magnetic field using the collective coordinate theory and Landau-Lifshitz-Gilbert simulations of atomistic spin model. It is revealed that the microwave field drives the propagation of the domain wall when the frequency falls into an appropriate range, which allows one to modulate the domain wall dynamics through tuning field frequency. Specifically, below the critical frequency, the domain wall velocity is proportional to the field frequency and the net angular momentum, while above the critical frequency, the domain wall velocity decreases rapidly to zero . The physical mechanisms of the results are discussed in detail, and the influences of the biaxial anisotropy and other parameters on the velocity of domain wall are studied. It is suggested that the wall dynamics can be effectively regulated by adjusting the basic magnetic structure and magnetic anisotropy, in addition to the external microwave field frequency. This work uncovers the interesting dynamics of ferrimagnetic domain wall driven by sinusoidal microwave magnetic field, which is helpful for designing domain wall-based spintronic device.
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图 1 磁矩排列示意图 (a)铁磁; (b)亚铁磁; (c)反铁磁
Fig. 1. Spin configurations: (a) Ferromagnetic; (b) ferrimagnetic; (c) antiferromagnetic states.
图 2 一维亚铁磁纳米线畴壁结构以及外加正弦微波磁场示意图
Fig. 2. Schematic depiction of a one-dimensional ferrimagnetic nanowire along the z direction with a domain wall under a sinusoidal microwave magnetic field.
图 3 h0 = 0.11J, 理论计算(实线)和模拟(实心点)不同δs下的畴壁速度v(ω)
Fig. 3. The calculated (solid lines) and simulated (solid points) v as a function of ω for various δs under h0 = 0.11J.
图 4 不同频率下, 畴壁面角ϕ振荡, 红线表示微波场的相位 (a) ω = 0.035, δs = –0.0218和0.0218; (b) ω = 0.21, δs = –0.0218; (c) ω = 0.24, δs = –0.0218
Fig. 4. The domain wall angle ϕ and phase position (red line) of microwave field as functions of time: (a) ω = 0.035, δs = –0.0218 and 0.0218; (b) ω = 0.21, δs = –0.0218; (c) ω = 0.24, δs = –0.0218.
图 5 (a) Kx = 0.004J时不同Kz, (b) Kz = 0.010J时不同Kx下模拟的v(ω)曲线
Fig. 5. The simulated v(ω) curves (a) for various Kz at Kx = 0.004J, and (b) for various Kx at Kz = 0.010J.
表 1 模拟选择的参数, 参数4为角动量补偿点TA, 净自旋密度δs = 0
Table 1. Parameters chosen for the simulations, the fourth parameter set corresponds to the angular momentum compensation point TA with the net spin density δs = 0.
参数 1 2 3 4 5 6 7 M1 ( μs ) 1.13 1.12 1.11 1.10 1.09 1.08 1.07 M2 ( μs ) 1.06 1.04 1.02 1.0 0.98 0.96 0.94 δs ( μs/γ ) –0.03273 –0.0218 –0.0109 0 0.0109 0.0218 0.03273 
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[1] Žutić I, Fabian J, Sarma S Das 2004 Rev. Mod. Phys. 76 323
Google Scholar
[2] 赵巍胜, 张博宇, 彭守仲 2022 自旋电子科学与技术 (北京: 人民邮电出版社) 第6页
Zhao W S, Zhang B Y, Peng S Z 2022 Spintronic Science and Technology (Beijing: Posts and Telecommunications Press) p6
[3] 韩秀峰 2014 自旋电子学导论(上卷) (北京: 科学出版社) 第10页
Han X F 2014 Introduction to Spintronics (Vol. 1) (Beijing: Science Press) p10
[4] Chen X Z, Zarzuela R, Zhang J, Song C, Zhou X F, Shi G Y, Li F, Zhou H A, Jiang W J, Pan F, Tserkovnyak Y 2018 Phys. Rev. Lett. 120 207204
Google Scholar
[5] Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T, Tserkovnyak Y 2018 Rev. Mod. Phys. 90 015005
Google Scholar
[6] Yu W, Lan J, Xiao J 2018 Phys. Rev. B 98 144422
Google Scholar
[7] Wen D L, Chen Z Y, Li W H, Qin M H, Chen D Y, Fan Z, Zeng M, Lu X B, Gao X S, Liu J M 2020 Phys. Rev. Res. 2 013166
Google Scholar
[8] Jin Z, Liu T T, Li W H, Zhang X M, Hou Z P, Chen D Y, Fan Z, Zeng M, Lu X B, Gao X S, Qin M H, Liu J M 2020 Phys. Rev. B 102 054419
Google Scholar
[9] Chen Z Y, Qin M H, Liu J M 2019 Phys. Rev. B 100 020402(R
Google Scholar
[10] Zhang Y L, Chen Z Y, Yan Z R, Chen D Y, Fan Z, Qin M H 2018 Appl. Phys. Lett. 113 112403
Google Scholar
[11] Selzer S, Atxitia U, Ritzmann U, Hinzke D, Nowak U 2016 Phys. Rev. Lett. 117 107201
Google Scholar
[12] Tveten E G, Qaiumzadeh A, Brataas A 2014 Phys. Rev. Lett. 112 147204
Google Scholar
[13] Jin Z, Meng C Y, Liu T T, Chen D Y, Fan Z, Zeng M, Lu X B, Gao X S, Qin M H, Liu J M 2021 Phys. Rev. B 104 054419
Google Scholar
[14] Zvezdin A K, Gareeva Z V, Zvezdin K A 2020 J. Magn. Magn. Mater. 509 166876
Google Scholar
[15] Li W H, Jin Z, Wen D L, Zhang X M, Qin M H, Liu J M 2020 Phys. Rev. B 101 024414
Google Scholar
[16] Kim K J, Kim S K, Hirata Y, Oh S H, Tono T, Kim D H, Okuno T, Ham W S, Kim S, Go G, Tserkovnyak Y, Tsukamoto A, Moriyama T, Lee K J, Ono T 2017 Nat. Mater. 16 1187
Google Scholar
[17] Oh S H, Kim S K, Xiao J, Lee K J 2019 Phys. Rev. B 100 174403
Google Scholar
[18] Caretta L, Mann M, Büttner F, Ueda K, Pfau B, Günther C M, Hessing P, Churikova A, Klose C, Schneider M, Engel D, Marcus C, Bono D, Bagschik K, Eisebitt S, Beach G S D 2018 Nat. Nanotechnol. 13 1154
Google Scholar
[19] Caretta L, Oh S H, Fakhrul T, Lee D K, Lee B H, Kim S K, Ross C A, Lee K J, Beach G S D 2020 Science. 370 1438
Google Scholar
[20] Sun C, Yang H, Jalil M B A 2020 Phys. Rev. B 102 134420
Google Scholar
[21] Yuan H Y, Cao Y, Kamra A, Duine R A, Yan P 2022 Phys. Rep. 965 1
Google Scholar
[22] Yu H, Xiao J, Schultheiss H 2021 Phys. Rep. 905 1
Google Scholar
[23] Oh S H, Kim S K, Lee D K, Go G, Kim K J, Ono T, Tserkovnyak Y, Lee K J 2017 Phys. Rev. B 96 100407(R
Google Scholar
[24] Martínez E, Raposo V, Alejos Ó 2019 J. Magn. Magn. Mater. 491 165545
Google Scholar
[25] Wang X G, Guo G H, Nie Y Z, Wang D W, Zeng Z M, Li Z X, Tang W 2014 Phys. Rev. B 89 144418
Google Scholar
[26] Chen Z Y, Yan Z R, Zhang Y L, Qin M H, Fan Z, Lu X B, Gao X S, Liu J M 2018 New J. Phys. 20 063003
Google Scholar
[27] Jin M, Hong I S, Kim D H, Lee K J, Kim S K 2021 Phys. Rev. B 104 184431
Google Scholar
[28] Liu T T, Hu Y F, Liu Y, Jin Z J Y, Tang Z H, Qin M H 2022 Rare Met. 41 3815
Google Scholar
[29] Wadley P, Howells B, Železný J, Andrews C, Hills V, Campion R P, Novák V, Olejník K, Maccherozzi F, Dhesi S S, Martin S Y, Wagner T, Wunderlich J, Freimuth F, Mokrousov Y, Kuneš J, Chauhan J S, Grzybowski M J, Rushforth A W, Edmond K, Gallagher B L, Jungwirth T 2016 Science 351 587
Google Scholar
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