1 Key Laboratory of Optic-Electronic Information and Materials of Hebei Province, Research Center for Computational Physics, College of Physics Science and Technology, Hebei University, Baoding 071002, China; 2 College of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China; 3 Department of Materials Science and Engineering, Lanzhou University of Technology, Lanzhou 730050, China
Abstract Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current (AC) magnetic field, we investigate the spin-wave modes of skyrmion bags, which behave differently from the clockwise (CW) rotation mode and the counterclockwise (CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion-inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.
Received: 24 February 2023
Revised: 05 May 2023
Accepted manuscript online: 06 May 2023
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12104124 and 12274111), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2021201001 and A2021201008), the Central Guidance Fund on the Local Science and Technology Development of Hebei Province, China (Grant No. 236Z0601G), the Post-graduate’s Innovation Fund Project of Hebei Province, China (Grant No. CXZZSS2023007), the Advanced Talents Incubation Program of the Hebei University, China (Grant Nos. 521000981395, 521000981423, 521000981394, and 521000981390), the Research Foundation of Chongqing University of Science and technology, China (Grant No. ckrc2019017), and the High-Performance Computing Center of Hebei University, China.
Corresponding Authors:
Chen-Dong Jin
E-mail: jinchd@hbu.edu
Cite this article:
Shuang Li(李爽), Ke-Xin Li(李可欣), Zhao-Hua Liu(刘照华), Qi-Yuan Zhu(朱起源), Chen-Bo Zhao(赵晨博), Hu Zhang(张虎), Xing-Qiang Shi(石兴强), Jiang-Long Wang(王江龙), Rui-Ning Wang(王瑞宁), Ru-Qian Lian(连如乾), Peng-Lai Gong(巩朋来), and Chen-Dong Jin(金晨东) In-plane spin excitation of skyrmion bags 2023 Chin. Phys. B 32 117503
[1] Roessler U K, Bogdanov A and Pfleiderer C 2006 Nature442 797 [2] Seki S, Yu X Z, Ishiwata S and Tokura Y 2012 Science336 198 [3] Nagaosa N and Tokura Y 2013 Nat. Nanotechnol.8 899 [4] Kim J V, Garcia-Sanchez F, Sampaio J, Moreau-Luchaire C, Cros V and Fert A 2014 Phys. Rev. B90 064410 [5] Zhou Y and Ezawa M 2014 Nat. Commun.5 4652 [6] Jiang W J, Upadhyaya P, Zhang W, Yu G, Jungfleisch M B, Fradin F Y, Pearson J E, Tserkovnyak Y, Wang K L, Heinonen O, te Velthuis S G E and Hoffmann A 2015 Science349 283 [7] Du H F, Che R C, Kong L Y, Zhao X B, Jin C M, Wang C, Yang J Y, Ning W, Li R W, Jin C Q, Chen X H, Zang J D, Zhang Y H and Tian M L 2015 Nat. Commun.6 8504 [8] Boulle O, Vogel J, Yang H, Pizzini S, de Souza Chaves D, Locatelli A, Menteş T O, Sala A, Buda-Prejbeanu L D, Klein O, Belmeguenai M, Roussigné Y, Stashkevich A, Chérif S M, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M and Gaudin G 2016 Nat. Nanotechnol.11 449 [9] Jin C D, Song C K, Wang J S, Xia H Y, Wang J B and Liu Q F 2017 J. Appl. Phys.122 223901 [10] Yang Y C, Liu T, Bi L and Deng L J 2021 J. Alloys Compd.860 158235 [11] Wang X R, Hu X C and Wu H T 2021 Commun. Phys.4 142 [12] Wu H T, Hu X C, Jing K Y and Wang X R 2021 Commun. Phys.4 210 [13] Ye C, Li L L, Shu Y, Li Q R, Xia J, Hou Z P, Zhou Y, Liu X X, Yang Y Y and Zhao G P 2022 Rare Metals41 2200 [14] Du H F and Wang X R 2022 Chin. Phys. B31 087507 [15] Ma Y X, Wang J N, Zeng Z Z, Yuan Y Y, Yang J X, Liu H B, Zhang S F, Wei J W, Wang J B, Jin C D and Liu Q F 2022 J. Magn. Magn. Mater.564 170061 [16] Jing D Y, Wang H Y, Guo W X and Liu W M 2023 Chin. Phys. B32 017401 [17] Lin T, Wang C X, Qiu Z Y, Chen C, Xing T, Sun L, Liang J H, Wu Y Z, Shi Z and Lei N 2023 Chin. Phys. B32 027505 [18] Chui C P and Zhou Y 2015 AIP Adv.5 097126 [19] Jin C D, Song C K, Wang J B and Liu Q F 2016 Appl. Phys. Lett.109 182404 [20] Luo S J, Zhang Y, Shen M K, Ou-Yang J, Yan B Q, Yang X F, Chen S, Zhu B P and You L 2017 Appl. Phys. Lett.110 112402 [21] Jin C D, Wang J B, Wang W W, Song C K, Wang J S, Xia H Y and Liu Q F 2018 Phys. Rev. Appl.9 044007 [22] Hirohata A, Yamada K, Nakatani Y, Prejbeanu I L, Dieny B, Pirro P and Hillebrands B 2020 J. Magn. Magn. Mater.509 166711 [23] Shen L C, Xia J, Zhao G P, Zhang X C, Ezawa M, Tretiakov O A, Liu X X and Zhou Y 2018 Phys. Rev. B98 134448 [24] Shen L C, Xia J, Zhao G P, Zhang X C, Ezawa M, Tretiakov O A, Liu X X and Zhou Y 2019 Appl. Phys. Lett.114 042402 [25] Liang X, Xia J, Zhang X C, Ezawa M, Tretiakov O A, Liu X X, Qiu L, Zhao G P and Zhou Y 2021 Appl. Phys. Lett.119 062403 [26] Petrova O and Tchernyshyov O 2011 Phys. Rev. B84 214433 [27] Mochizuki M 2012 Phys. Rev. Lett.108 017601 [28] Iwasaki J, Beekman A J and Nagaosa N 2014 Phys. Rev. B89 064412 [29] Zhang X C, Ezawa M, Xiao D, Zhao G P, Liu Y W and Zhou Y 2015 Nanotechnology26 225701 [30] Liu Y Z, Yin G, Zang J D, Shi J and Lake R K 2015 Appl. Phys. Lett.107 152411 [31] Zhang X C, Muller J, Xia J, Garst M, Liu X X and Zhou Y 2017 New J. Phys.19 065001 [32] Yokouchi T, Hoshino S, Kanazawa N, Kikkawa A, Morikawa D, Shibata K, Arima T, Taguchi Y, Kagawa F, Nagaosa N and Tokura Y 2018 Sci. Adv.4 8 [33] Seki S, Garst M, Waizner J, Takagi R, Khanh N D, Okamura Y, Kondou K, Kagawa F, Otani Y and Tokura Y 2020 Nat. Commun.11 256 [34] Zhang X C, Xia J, Tretiakov O A, Diep H T, Zhao G P, Yang J B, Zhou Y, Ezawa M and Liu X X 2021 Phys. Rev. B104 L220406 [35] Chen J L, Yu H M and Gubbiotti G 2022 J. Phys. D55 123001 [36] Mruczkiewicz M, Krawczyk M and Guslienko K Y 2017 Phys. Rev. B95 094414 [37] Song C K, Ma Y X, Jin C D, Wang J S, Xia H Y, Wang J B and Liu Q F 2019 New J. Phys.21 083006 [38] Vigo-Cotrina H 2021 J. Magn. Magn. Mater.537 168166 [39] Bo L, Ji L Z, Hu C L, Zhao R Z, Li Y X, Zhang J and Zhang X F 2021 Appl. Phys. Lett.119 212408 [40] Zeng Z Z, Song C K, Wang J B and Liu Q F 2022 J. Phys. D55 185001 [41] Jin C D, Li S, Zhang H, Wang R N, Wang J L, Lian R Q, Gong P L and Shi X Q 2022 New J. Phys.24 043005 [42] Jin C D, Li S, Zhang H, Wang R N, Wang J L, Lian R Q, Gong P L and Shi X Q 2022 New J. Phys.24 073013 [43] Savchenko A S, Kuchkin V M, Rybakov F N, Blügel S and Kiselev N S 2022 APL Mater.10 071111 [44] Xing L D, Hua D Y and Wang W W 2018 J. Appl. Phys.124 123904 [45] Leonov A O and Pappas C 2019 Phys. Rev. B99 144410 [46] Foster D, Kind C, Ackerman P J, Tai J S B, Dennis M R and Smalyukh I I 2019 Nat. Phys.15 655 [47] Kuchkin V M, Barton-Singer B, Rybakov F N, Blugel S, Schroers B J and Kiselev N S 2020 Phys. Rev. B102 144422 [48] Zeng Z Z, Zhang C L, Jin C D, Wang J N, Song C K, Ma Y X, Liu Q F and Wang J B 2020 Appl. Phys. Lett.117 172404 [49] Finazzi M, Savoini M, Khorsand A R, Tsukamoto A, Itoh A, Duo L, Kirilyuk A, Rasing T and Ezawa M 2013 Phys. Rev. Lett.110 177205 [50] Zhang X C, Xia J, Zhou Y, Wang D W, Liu X X, Zhao W S and Ezawa M 2016 Phys. Rev. B94 094420 [51] Tang J, Wu Y D, Wang W W, Kong L Y, Lv B Y, Wei W S, Zang J D, Tian M L and Du H F 2021 Nat. Nanotechnol.16 1086 [52] Tang J, Wu Y D, Kong L Y, Wang W W, Chen Y T, Wang Y H, Soh Y, Xiong Y M, Tian M L and Du H F 2021 Natl. Sci. Rev.8 7 [53] Kind C, Friedemann S and Read D 2020 Appl. Phys. Lett.116 022413 [54] Kind C and Foster D 2021 Phys. Rev. B103 L100413 [55] Kuchkin V M, Chichay K, Barton-Singer B, Rybakov F N, Blügel S, Schroers B J and Kiselev N S 2021 Phys. Rev. B104 165116 [56] Göbel B, Schäffer A F, Berakdar J, Mertig I and Parkin S S P 2019 Sci. Rep.9 12119 [57] Donahue M J and Porter D G http://math.nist.gov/oommf[2023-02-24] [58] Sampaio J, Cros V, Rohart S, Thiaville A and Fert A 2013 Nat. Nanotechnol.8 839 [59] Xia J, Zhang X C, Ezawa M, Shao Q M, Liu X X and Zhou Y 2020 Appl. Phys. Lett.116 022407 [60] Moutafis C, Komineas S and Bland J A C 2009 Phys. Rev. B79 224429 [61] Li Z X, Chen Y F, Zhou Z W, Nie Y Z, Xia Q L, Wang D W and Guo G H 2017 J. Magn. Magn. Mater.433 216 [62] Ikka M, Takeuchi A and Mochizuki M 2018 Phys. Rev. B98 184428 [63] Okamura Y, Kagawa F, Mochizuki M, Kubota M, Seki S, Ishiwata S, Kawasaki M, Onose Y and Tokura Y 2013 Nat. Commun.4 2391
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