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亚铁磁材料在角动量补偿点附近具有类比于反铁磁的超快动力学, 且存在非零净自旋密度, 其磁结构可以被传统磁性手段探测和调控, 有望应用于新一代高性能自旋电子器件. 有效调控亚铁磁畴壁动力学是当前自旋电子学领域的重要课题. 本工作使用微磁学模拟研究了正弦波和方波振荡磁场驱动亚铁磁畴壁, 从理论上揭示不同的振荡磁场会诱导出不同方式的畴壁运动. 研究表明, 具有非零净自旋角动量的畴壁面随振荡磁场振荡, 正弦波磁场驱动亚铁磁畴壁的位移随时间单调增加, 而方波磁场驱动畴壁位移随时间曲折增大. 本工作系统探讨了亚铁磁畴壁速度与外部磁场和材料内部参数的关联, 表明了同强度下的正弦波磁场具有更高的驱动效率, 并揭示了相关物理机制, 可以为未来的实验和自旋器件设计提供参考.
Ferrimagnetic materials exhibit ultrafast dynamic behaviors similar to those of antiferromagnetic materials near the angular momentum compensation point, where a non-zero net spin density is maintained. This unique feature makes their magnetic structures detectable and manipulable by using traditional magnetic techniques, thus positioning ferrimagnetic materials as promising candidates for next-generation high-performance spintronic devices. However, effectively controlling the dynamics of ferrimagnetic domain walls remains a significant challenge in current spintronics research. In this work, based on the classic Heisenberg spin model, Landau-Lifshitz-Gilbert (LLG) simulation is used to investigate the dynamic behaviors of ferrimagnetic domain walls driven by sinusoidal wave periodic magnetic field and square wave periodic magnetic field, respectively. The results show that these two types of oscillating magnetic fields induce distinct domain wall motion modes. Specifically, the domain wall surface, which has non-zero net spin angular momentum, oscillates in response to the external magnetic field. It is found that the domain wall velocity decreases as the net spin angular momentum increases. Moreover, the displacement of the ferrimagnetic domain wall driven by a sinusoidal magnetic field increases monotonically with time, while the displacement driven by a square wave magnetic field follows a more tortuous trajectory over time. Under high-frequency field conditions, the domain wall displacement shows more pronounced linear growth, and the domain wall surface rotates linearly with time. In this work, how material parameters, such as net spin angular momentum, anisotropy, and the damping coefficient, influence domain wall dynamics is also explored. Specifically, increasing the anisotropy parameter (dz) or the damping coefficient (α) results in a reduction of domain wall velocity. Furthermore, the study demonstrates that, compared with the square wave magnetic fields, the sinusoidal magnetic fields drive the domain wall more efficiently, leading domain wall to move faster. By adjusting the frequency and waveform of the periodic magnetic field, the movement of ferrimagnetic domain walls can be precisely controlled, enabling fine-tuned regulation of both domain wall velocity and position. Our findings show that sinusoidal magnetic fields, even at the same intensity, offer higher driving efficiency. The underlying physical mechanisms are discussed in detail, providing valuable insights for guiding the design and experimental development of domain wall-based spintronic devices. -
Keywords:
- domain wall dynamics /
- spintronics /
- oscillating magnetic field /
- ferrimagnets
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图 1 亚铁磁畴壁纳米条模型示意图, 磁矩沿z轴方向排列, 在z轴方向分别施加周期为T的正弦波和方波动态磁场
Fig. 1. Schematic diagram of the ferrimagnetic domain wall model. The magnetic moments are arranged along the z-axis direction, and sine-wave and square-wave magnetic fields are applied along the z-axis direction.
图 2 不同净自旋角动量δs下, (a)正弦波磁场和(b)方波磁场驱动亚铁磁畴壁速度v与振荡磁场频率ω的关系图, 其中, z轴各向异性dz = 0.1J, 磁场振幅h0 = 0.005J, 阻尼系数α = 0.01
Fig. 2. Domain wall velocity v as functions of ω for various δs driven by the (a) sine-wave and (b) square-wave magnetic fields for dz = 0.1J, h0 = 0.005J, and the damping coefficient α = 0.01.
图 3 h0 = 0.005J, dz = 0.1J, α = 0.01, ω = 0.05γJ/μs时, 正弦波磁场和方波磁场驱动畴壁速度与净自旋角动量δs的关系
Fig. 3. Simulated domain wall velocity v as functions of the net angular momentum δs driven by the sine-wave and square-wave magnetic fields for h0 = 0.005J, dz = 0.1J, ω = 0.05γJ/μs, and α = 0.01.
图 4 ω = 0.05γJ/μs时, 正弦波磁场驱动下(a)畴壁位置和(b)畴壁面角随时间的演化, 以及方波磁场驱动下(c)畴壁位置和(d)畴壁面角随时间的演化. 在图(a)和(b)中, δs = –1.24×10–7 J·s·m–3, 在图(c)和(d)中, δs = 1.24×10–7 J·s·m–3. 场强度图用红色虚线标注
Fig. 4. Evolutions of the domain wall (DW) (a) position and (b) angle over time under the sine-wave magnetic field, and the DW (c) position and (d) angle evolutions under the square-wave magnetic field for ω = 0.05γJ/μs. In panels (a) and (b), δs = –1.24×10–7 J·s·m–3, while in panels (c) and (d), the opposite value is taken. The evolution of field magnitude is also depicted with red dashed lines.
图 5 ω = 0.25γJ/μs, δs = 1.24×10–7 J·s·m–3时, 正弦波磁场驱动下(a)畴壁位置和(b)畴壁面角随时间的演化, 以及方波磁场驱动下(c)畴壁位置和(d)畴壁面角随时间的演化
Fig. 5. The DW (a) position and (b) angle evolution over time under the triangular form magnetic field, and (c) position and (d) angle evolution under the square form magnetic field for ω = 0.25γJ/μs and δs = 1.24×10–7 J·s·m–3. The evolution of field magnitude is also depicted with red dashed lines.
图 6 h0 = 0.005J正弦波磁场作用下, δs = (a) 0, (b) 0.62 × 10–7 J·s·m–3时不同各向异性系数dz对应的v(ω)图(α = 0.01); 以及 δs = (c) 0, (d) –0.62 × 10–7 J·s·m–3时不同阻尼系数α对应的v(ω)图(dz = 0.1J )
Fig. 6. Simulated v(ω) curves driven by the sine-wave field for h0 = 0.005J for various dz for δs = (a) 0, (b) 0.62 × 10–7 J·s·m–3 and α = 0.01; and the curves for various α for δs = (c) 0, (d) –0.62×10–7 J·s·m–3 and dz = 0.1J.
表 1 模拟过程中采用的磁性过渡金属磁矩(MTM)、稀土磁矩(MRE)以及净自旋角动量(δs)
Table 1. Magnetic transition metal moments (MTM), rare earth moments (MRE), and net angular momentum (δs) used in the simulations.
参数 1 2 3 4 5 6 7 8 9 MTM/(kA·m–1) 1120 1115 1110 1105 1100 1095 1090 1085 1080 MRE/(kA·m–1) 1040 1030 1020 1010 1000 990 980 970 960 δs/(10–7 J·s·m–3) –1.24 –0.93 –0.62 –0.31 0 0.31 0.62 0.93 1.24 
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[1] Hirohata A, Yamada K, Nakatani Y, Prejbeanu I, Diény B, Pirro P, Hillebrands B 2020 J. Magn. Magn. Mater. 509 166711
Google Scholar
[2] Zhang Y, Feng X Q, Zheng Z Y, Zhang Z Z, Lin K L, Sun X H, Wang G D, Wang J K, Wei J Q, Vallobra P, He Y, Wang Z X, Chen L, Zhang K, Xu Y, Zhao W S 2023 Appl. Phys. Rev. 10 011301
Google Scholar
[3] 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
[4] 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
[5] Oh S H, Kim S K, Xiao J, Lee K J 2019 Phys. Rev. B 100 174403
Google Scholar
[6] 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
[7] 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
[8] Sun C, Yang H, Jalil M 2020 Phys. Rev. B 102 134420
Google Scholar
[9] 张玉洁, 李贵江, 刘恩克, 陈京兰, 王文洪, 吴光恒, 胡俊雄 2013 物理学报 62 037501
Google Scholar
Zhang Y J, Li G J, Liu E K, Chen J L, Wang W H, Wu G H, Hu J X 2013 Acta Phys. Sin. 62 037501
Google Scholar
[10] Chen Z Y, Qin M H, Liu J M, 2019 Phys. Rev. B 100 020402(R
Google Scholar
[11] Yu H, Xiao J, Schultheiss H 2021 Phys. Rep. 905 1
Google Scholar
[12] Jin M S, Hong I S, Kim D H, Lee K J, Kim S K 2021 Phys. Rev. B 104 184431
Google Scholar
[13] Jing K Y, Gong X, Wang X R 2022 Phys. Rev. B 106 174429
Google Scholar
[14] Haltz E, Krishnia S, Berges L, Mougin A, Sampaio J 2021 Phys. Rev. B 103 014444
Google Scholar
[15] Tono T, Taniguchi T, Kim K J, Moriyama T, Tsukamoto A, Ono T 2015 Appl. Phys. Express 8 073001
Google Scholar
[16] Luo C, Chen K, Ukleev V, Wintz S, Weigand M, Abrudan R M, Prokeš K, Radu F 2023 Comm. Phys. 6 218
Google Scholar
[17] Nishimura T, Kim D H, Hirata Y, Okuno T, Futakawa Y, Yoshikawa H, Tsukamoto A, Shiota Y, Moriyama T, Ono T 2018 Appl. Phys. Lett. 112 172403
Google Scholar
[18] Chen J, Dong S 2021 Phys. Rev. Lett. 126 117603
Google Scholar
[19] 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
[20] Ghosh S, Komori T, Hallal A, Garcia J P, Gushi T, Hirose T, Mitarai H, Okuno H, Vogel J, Chshiev M, Attané J P, Vila L, Suemasu T, Pizzini S 2021 Nano Lett. 21 2580
Google Scholar
[21] Caretta L, Avc C O 2024 APL Mater. 12 011106
Google Scholar
[22] Gushi T, Klug M J, Garcia J P, Ghosh S, Attané J P, Okuno H, Fruchart O, Vogel J, Suemasu T, Pizzini S, Vila L 2019 Nano Lett. 19 8716
Google Scholar
[23] Vélez S, Ruiz-Gómez S, Schaab J, Gradauskaite E, Wörnle M S, Welter P, Jacot B J, Degen C L, Trassin M, Fiebig M, Gambardella P 2022 Nat. Nanotechnol. 17 834
Google Scholar
[24] Haltz E, Sampaio J, Krishnia S, Berges L, Weil R, Mougin A 2020 Sci. Rep. 10 16292
Google Scholar
[25] Kim D H, Kim D H, Kim K J, Moon K W, Yang S M, Lee K J, Kim S K 2020 J. Magn. Magn. Mater. 514 167237
Google Scholar
[26] Sala G, Gambardella P 2022 Adv. Mater. Interfaces 9 2201622
Google Scholar
[27] Li Z L, Su J, Lin S Z, Liu D, Gao Y, Wang S G, Wei H X, Zhao T Y, Zhang Y, Cai J W, Shen B G 2021 Nat. Commun. 12 5604
Google Scholar
[28] Donges A, Grimm N, Jakobs F, Selzer S, Ritzmann U, Atxitia U, Nowak U 2020 Phys. Rev. Res. 2 013293
Google Scholar
[29] Yan Z R, Chen Z Y, Qin M H, Lu X B, Gao X S, Liu J M, 2018 Phys. Rev. B 97 054308
Google Scholar
[30] Yurlov V V, Zvezdin K A, Skirdkov P N, Zvezdin A K 2021 Phys. Rev. B 103 134442
Google Scholar
[31] Lepadatu S, Saarikoski H, Beacham R, Benitez M J, Moore T A, Burnell G, Sugimoto S, Yesudas, Wheeler M C, Miguel J, Dhesi S S, McGrouther D, McVitie S, Tatara G, Marrows C H 2017 Sci. Rep. 7 1640
Google Scholar
[32] Balan C, Garcia J P, Fassatoui A, Vogel J, Chaves D D S, Bonfim M, Rueff J P, Ranno L, Pizzini S 2022 Phys. Rev. Appl. 18 034065
Google Scholar
[33] 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
[34] Liu T T, Liu Y, Liu, Y H, Tian G, Qin M H 2024 J. Phys. D Appl. Phys. 57 335002
Google Scholar
[35] Liu T T, Hu Y F, Liu Y, Jin Z J Y, Tang Z H, Qin M H 2022 Rare Metals 41 3815
Google Scholar
[36] 赵晨蕊, 魏云昕, 刘婷婷, 秦明辉 2023 物理学报 72 208502
Google Scholar
Zhao C R, Wei Y X, Liu T T, Qin M H 2023 Acta Phys. Sin. 72 208502
Google Scholar
[37] 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
[38] Bassirian P, Hesjedal T, Parkin S S P, Litzius K 2022 APL Mater. 10 101107
Google Scholar
[39] Zhang X C, Xia J, Tretiakov O A, Zhao G P, Zhou Y, Mochizuki M, Liu X X, Ezawa M 2023 Phys. Rev. B 108 064410
Google Scholar
[40] Consolo G, Lopez-Diaz L, Torres L, Azzerboni B 2007 IEEE T. Magn. 43 2974
Google Scholar
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