Magnetoelectric topology: The rope weaving in parameter space

doi:10.1088/1674-1056/ae2c6b

中国物理B ›› 2026, Vol. 35 ›› Issue (2): 27501-027501.doi: 10.1088/1674-1056/ae2c6b

• • 上一篇

Magnetoelectric topology: The rope weaving in parameter space

Ying Zhou(周颖), Ziwen Wang(王子文), Fan Wang(王凡), Haoshen Ye(叶浩燊), and Shuai Dong(董帅)†

Key Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University, Nanjing 211189, China

收稿日期:2025-10-13 修回日期:2025-11-27 接受日期:2025-12-15 发布日期:2026-01-21
通讯作者: Shuai Dong E-mail:sdong@seu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12325401, 12274069, and 123B2053). We thank Profs. Yisheng Chai, Chenliang Lu, and Junting Zhang for their contributions to the original works reviewed here.

Magnetoelectric topology: The rope weaving in parameter space

Ying Zhou(周颖), Ziwen Wang(王子文), Fan Wang(王凡), Haoshen Ye(叶浩燊), and Shuai Dong(董帅)†

Key Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University, Nanjing 211189, China

Received:2025-10-13 Revised:2025-11-27 Accepted:2025-12-15 Published:2026-01-21
Contact: Shuai Dong E-mail:sdong@seu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12325401, 12274069, and 123B2053). We thank Profs. Yisheng Chai, Chenliang Lu, and Junting Zhang for their contributions to the original works reviewed here.

摘要/Abstract

摘要： Topology, as a mathematical concept, has been introduced into condensed matter physics since the discovery of quantum Hall effect, which characterizes new physical scenario beyond the Landau theory. The topologically protected physical quantities, such as the dissipationless quantum transport of edge/surface states as well as magnetic/dipole quasi-particles like skyrmions/bimerons, have attracted great research enthusiasms in the past decades. In recent years, another kind of topology in condensed matter was revealed in the magnetoelectric parameter space of multiferroics, which deepens our understanding of magnetoelectric physics. This topical review summarizes recent advances in this area, involving three types of type-II multiferroics. With magnetism-induced ferroelectricity, topological behaviors can be manifested during the magnetoelectric switching processes driven by magnetic/electric fields, such as Roman-surface/Riemann-surface magnetoelectricity and magnetic crankshaft. These exotic topological magnetoelectric behaviors may be helpful to pursue energy-efficient and precise-control devices for spintronics and quantum computing.

关键词: magnetoelectricity, topology, winding number, multiferroicity

Abstract: Topology, as a mathematical concept, has been introduced into condensed matter physics since the discovery of quantum Hall effect, which characterizes new physical scenario beyond the Landau theory. The topologically protected physical quantities, such as the dissipationless quantum transport of edge/surface states as well as magnetic/dipole quasi-particles like skyrmions/bimerons, have attracted great research enthusiasms in the past decades. In recent years, another kind of topology in condensed matter was revealed in the magnetoelectric parameter space of multiferroics, which deepens our understanding of magnetoelectric physics. This topical review summarizes recent advances in this area, involving three types of type-II multiferroics. With magnetism-induced ferroelectricity, topological behaviors can be manifested during the magnetoelectric switching processes driven by magnetic/electric fields, such as Roman-surface/Riemann-surface magnetoelectricity and magnetic crankshaft. These exotic topological magnetoelectric behaviors may be helpful to pursue energy-efficient and precise-control devices for spintronics and quantum computing.

Key words: magnetoelectricity, topology, winding number, multiferroicity

中图分类号: (Magnetoelectric effects, multiferroics)

75.85.+t

77.80.-e (Ferroelectricity and antiferroelectricity) 75.50.-y (Studies of specific magnetic materials)

Ying Zhou(周颖), Ziwen Wang(王子文), Fan Wang(王凡), Haoshen Ye(叶浩燊), and Shuai Dong(董帅). Magnetoelectric topology: The rope weaving in parameter space[J]. 中国物理B, 2026, 35(2): 27501-027501.

Ying Zhou(周颖), Ziwen Wang(王子文), Fan Wang(王凡), Haoshen Ye(叶浩燊), and Shuai Dong(董帅). Magnetoelectric topology: The rope weaving in parameter space[J]. Chin. Phys. B, 2026, 35(2): 27501-027501.

参考文献

[1] Armstrong M A 1983 Basic Topology (New York: Springer) pp. 1–26
[2] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[3] Nakahara M 2003 Geometry, Topology and Physics, 2nd Edn. (Boca Raton: Taylor & Francis) pp. 168–225
[4] Thouless D J, Kohmoto M, NightingaleMP and DennijsM1982 Phys. Rev. Lett. 49 405
[5] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[6] Ali M N, Xiong J, Flynn S, Tao J, Gibson Q D, Schoop L M, Liang T, Haldolaarachchige N, Hirschberger M, Ong N P and Cava R J 2014 Nature 514 205
[7] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[8] Wan X G, Dong J M and Savrasov S Y 2011 Phys. Rev. B 83 205101
[9] Wang K F, Graf D, Lei H C, Tozer SWand Petrovic C 2011 Phys. Rev. B 84 220401
[10] Sau J, Simon S, Vishveshwara S andWilliams J R 2020 Nat. Rev. Phys. 2 667
[11] Tschernig K, Jimenez-Galán A, Christodoulides D N, Ivanov M, Busch K, Bandres M A and Perez-Leija A 2021 Nat. Commun. 12 1974
[12] Tang S J, Zhang C F, Wong D, Pedramrazi Z, Tsai H Z, Jia C J, Moritz B, Claassen M, Ryu H, Kahn S, Jiang J, Yan H, Hashimoto M, Lu D H, Moore R G, Hwang C C, Hwang C, Hussain Z, Chen Y L, Ugeda M M, Liu Z, Xie X M, Devereaux T P, Crommie M F, Mo S K and Shen Z X 2017 Nat. Phys. 13 683
[13] Kou X F, Guo S T, Fan Y B, Pan L, Lang M R, Jiang Y, Shao Q M, Nie T X, Murata K, Tang J S, Wang Y, He L, Lee T K, Lee W L and Wang K L 2014 Phys. Rev. Lett. 113 137201
[14] Nagaosa N and Tokura Y 2013 Nat. Nanotechnol. 8 899
[15] Fert A, Reyren N and Cros V 2017 Nat. Rev. Mater. 2 17031
[16] Chauleau J Y, Chirac T, Fusil S, Garcia V, Akhtar W, Tranchida J, Thibaudeau P, Gross I, Blouzon C, Finco A, Bibes M, Dkhil B, Khalyavin D D, Manuel P, Jacques V, Jaouen N and Viret M 2020 Nat. Mater. 19 576
[17] Guo M F, Guo C Q, Han J, Chen S L, He S, Tang T X, Li Q, Strzalka J, Ma J, Yi S, Wang K, Xu B, Gao P, Huang H B, Chen L Q, Zhang S J, Lin Y H, Nan C W and Shen Y 2021 Science 371 1050
[18] Choi T, Horibe Y, Yi H T, Choi Y J, Wu W D and Cheong S W 2010 Nat. Mater. 9 253
[19] Seki S, Yu X Z, Ishiwata S and Tokura Y 2012 Science 336 198
[20] Huang F T and Cheong S W 2017 Nat. Rev. Mater. 2 17004
[21] Tokura Y and Nagaosa N 2018 Nat. Commun. 9 3740
[22] Du K, Gao B, Wang Y Z, Xu X H, Kim J, Hu R W, Huang F T and Cheong S W 2018 Npj Quantum Mater. 3 33
[23] Liu G X, Pi M C, Zhou L, Liu Z H, Shen X D, Ye X B, Qin S J, Mi X R, Chen X, Zhao L, Zhou B W, Guo J, Yu X H, Chai Y S, Weng H M and Long Y W 2022 Nat. Commun. 13 2373
[24] Wang Z W, Chai Y S and Dong S 2023 Phys. Rev. B 108 L060407
[25] Ponet L, Artyukhin S, Kain T, Wettstein J, Pimenov A, Shuvaev A, Wang X, Cheong S W, Mostovoy M and Pimenov A 2022 Nature 607 81
[26] Zhou Y, Ye H S, Zhang J T and Dong S 2024 Phys. Rev. B 110 054424
[27] Wang H W, Wang F, Yang M, Chang Y T, Shi M Y, Li L, Liu J M, Wang J F, Dong S and Lu C L 2025 Phys. Rev. Lett. 134 016708
[28] Zhang J J, Lin L F, Zhang Y, Wu M H, Yakobson B I and Dong S 2018 J. Am. Chem. Soc. 140 9768
[29] Xiang H J, Kan E J,Wei S H, WhangboMH and Gong X G 2011 Phys. Rev. B 84 224429
[30] Xiang H J, Kan E J, Zhang Y, WhangboMH and Gong X G 2011 Phys. Rev. Lett. 107 157202
[31] Johnson R D, Chapon L C, Khalyavin D D, Manuel P, Radaelli P G and Martin C 2012 Phys. Rev. Lett. 108 067201
[32] Zhang G Q, Dong S, Yan Z B, Guo Y Y, Zhang Q F, Yunoki S, Dagotto E and Liu J M 2011 Phys. Rev. B 84 174413
[33] Lu X Z, Whangbo M H, Dong S, Gong X G and Xiang H J 2012 Phys. Rev. Lett. 108 187204
[34] Wang X, Chai Y S, Zhou L, Cao H B, Cruz C D, Yang J Y, Dai J H, Yin Y Y, Yuan Z, Zhang S J, Yu R Z, Azuma M, Shimakawa Y, Zhang H M, Dong S, Sun Y, Jin C Q and Long Y W2015 Phys. Rev. Lett. 115 087601
[35] Long Y W and Shimakawa Y 2010 New J. Phys. 12 063029
[36] Long Y W 2016 Chin. Phys. B 25 078108
[37] Shimakawa Y 2008 Inorg. Chem. 47 8562
[38] Long YW, Hayashi N, Saito T, Azuma M, Muranaka S and Shimakawa Y 2009 Nature 458 60
[39] Feng J S and Xiang H J 2016 Phys. Rev. B 93 174416
[40] Chai Y S, Chun S H, Cong J Z and Kim K H 2018 Phys. Rev. B 98 104416
[41] Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N and Tokura Y 2010 Nature 465 901
[42] Das S, Tang Y L, Hong Z, Gonçalves M A P, McCarter M R, Klewe C, Nguyen K X, Gómez-Ortiz F, Shafer P, Arenholz E, Stoica V A, Hsu S L, Wang B, Ophus C, Liu J F, Nelson C T, Saremi S, Prasad B, Mei A B, Schlom D G, Iñiguez J, García-Fernández P, Muller D A, Chen L Q, Junquera J, Martin L W and Ramesh R 2019 Nature 568 368
[43] Wang B, Zhang X W, Zhang Y H, Yuan S J, Guo Y, Dong S and Wang J L 2020 Mater. Horiz 7 1623
[44] Xiao D, Liu G B, Feng W X, Xu X D and Yao W 2012 Phys. Rev. Lett. 108 196802
[45] Zhou Y, Ye H S, Zhang J T and Dong S 2024 Phys. Rev. Mater. 8 104403
[46] Hur N, Park S, Sharma P A, Guha S and Cheong S W 2004 Phys. Rev. Lett. 93 107207
[47] Higashiyama D, Miyasaka S, Kida N, Arima T and Tokura Y 2004 Phys. Rev. B 70 174405
[48] Abrahams S C and Bernstein J L 1967 J. Chem. Phys. 46 3776
[49] Hur N, Park S, Sharma P A, Ahn J S, Guha S and Cheong S W 2004 Nature 429 392
[50] Kim J W, Haam S Y, Oh Y S, Park S, Cheong S W, Sharma P A, Jaime M, Harrison N, Han J H, Jeon G S, Coleman P and Kim K H 2009 Proc. Natl. Acad. Sci. USA 106 15573
[51] Chapon L C, Radaelli P G, Blake G R, Park S and Cheong S W 2006 Phys. Rev. Lett. 96 097601
[52] Chapon L C, Blake G R, Gutmann M J, Park S, Hur N, Radaelli P G and Cheong S W 2004 Phys. Rev. Lett. 93 177402
[53] Giovannetti G and van den Brink J 2008 Phys. Rev. Lett. 100 227603
[54] Lee N, Vecchini C, Choi Y J, Chapon L C, Bombardi A, Radaelli P G and Cheong S W 2013 Phys. Rev. Lett. 110 137203
[55] Kim J H, van der Vegte M A, Scaramucci A, Artyukhin S, Chung J H, Park S, Cheong S W, Mostovoy M and Lee S H 2011 Phys. Rev. Lett. 107 097401
[56] Wang F, Zhou Y, Shen X F, Dong S and Zhang J T 2023 Phys. Rev. Appl. 20 064011
[57] Geng Y N, Das H, Wysocki A L, Wang X Y, Cheong S W, Mostovoy M, Fennie C J and Wu W D 2014 Nat. Mater. 13 163

Magnetoelectric topology: The rope weaving in parameter space

Magnetoelectric topology: The rope weaving in parameter space

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