Dynamics of ferrimagnetic domain wall driven by oscillating magnetic field

ZHAO Chenrui; YANG Qianqian; JIAO Ju; TANG Zhenghua; QIN Minghui

doi:10.7498/aps.74.20241033

Abstract

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 (d_z) 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:

Authors and contacts

1.
Microelectronics and Optoelectronics Technology Key Laboratory of Hunan Higher Education, School of Physics and Electronic Electrical Engineering, Xiangnan University, Chenzhou 423000, China
2.
Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Institute of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China

Corresponding author: TANG Zhenghua, tangzh@xnu.edu.cn ; QIN Minghui, qinmh@scnu.edu.cn

Funds: Project supported by the Natural Science Foundation of China (Grant Nos. U22A20117, 52371243), the Basic and Applied Basic Research Foundation of Guangdong Province, China (Grant Nos. 2022A1515011727, 2024A1515012665), and the 2021 College Student Innovation Project of Xiangnan University, China.

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References

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[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
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Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 2 不同净自旋角动量δ_s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d_z = 0.1J, 磁场振幅h₀ = 0.005J, 阻尼系数α = 0.01

Figure 2. Domain wall velocity v as functions of ω for various δ_s driven by the (a) sine-wave and (b) square-wave magnetic fields for d_z = 0.1J, h₀ = 0.005J, and the damping coefficient α = 0.01.

DownLoad: Full-Size Img PowerPoint

图 3 h₀ = 0.005J, d_z = 0.1J, α = 0.01, ω = 0.05γJ/μ_s时, 正弦波磁场和方波磁场驱动畴壁速度与净自旋角动量δ_s的关系

Figure 3. Simulated domain wall velocity v as functions of the net angular momentum δ_sdriven by the sine-wave and square-wave magnetic fields for h₀ = 0.005J, d_z = 0.1J, ω = 0.05γJ/μ_s, and α = 0.01.

DownLoad: Full-Size Img PowerPoint

图 4 ω = 0.05γJ/μ_s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, δ_s = –1.24×10^–7 J·s·m^–3, 在图(c)和(d)中, δ_s = 1.24×10^–7 J·s·m^–3. 场强度图用红色虚线标注

Figure 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/μ_s. In panels (a) and (b), δ_s = –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.

DownLoad: Full-Size Img PowerPoint

图 5 ω = 0.25γJ/μ_s,δ_s = 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

Figure 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/μ_s and δ_s = 1.24×10^–7 J·s·m^–3. The evolution of field magnitude is also depicted with red dashed lines.

DownLoad: Full-Size Img PowerPoint

图 6 h₀= 0.005J正弦波磁场作用下, δ_s = (a) 0, (b) 0.62 × 10^–7 J·s·m^–3时不同各向异性系数d_z对应的v(ω)图(α = 0.01); 以及 δ_s= (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(d_z = 0.1J )

Figure 6. Simulated v(ω) curves driven by the sine-wave field for h₀= 0.005J for various d_z for δ_s = (a) 0, (b) 0.62 × 10^–7 J·s·m^–3 and α = 0.01; and the curves for various α for δ_s= (c) 0, (d) –0.62×10^–7 J·s·m^–3 and d_z = 0.1J.

DownLoad: Full-Size Img PowerPoint

表 1 模拟过程中采用的磁性过渡金属磁矩(M_TM)、稀土磁矩(M_RE)以及净自旋角动量(δ_s)

Table 1. Magnetic transition metal moments (M_TM), rare earth moments (M_RE), and net angular momentum (δ_s) used in the simulations.

参数	1	2	3	4	5	6	7	8	9
M_TM/(kA·m^–1)	1120	1115	1110	1105	1100	1095	1090	1085	1080
M_RE/(kA·m^–1)	1040	1030	1020	1010	1000	990	980	970	960
δ_s/(10^–7 J·s·m^–3)	–1.24	–0.93	–0.62	–0.31	0	0.31	0.62	0.93	1.24

DownLoad: CSV

[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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Vol. 74, Issue 3 - 2025-02-05

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