Magnetoelectric topology: The rope weaving in parameter space

doi:10.1088/1674-1056/ae2c6b

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.

Keywords: magnetoelectricity topology winding number multiferroicity

Received: 13 October 2025
Revised: 27 November 2025
Accepted manuscript online: 15 December 2025

PACS:	75.85.+t	(Magnetoelectric effects, multiferroics)
	77.80.-e	(Ferroelectricity and antiferroelectricity)
	75.50.-y	(Studies of specific magnetic materials)

Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos. 12325401, 12274069, and 123B2053).

Corresponding Authors: Shuai Dong
E-mail: sdong@seu.edu.cn

Cite this article:

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 2026 Chin. Phys. B 35 027501

[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

[1]	Superconductivity and band topology of double-layer honeycomb structure M₂N₂ (M = Nb, Ta) Jin-Han Tan(谭锦函), Na Jiao(焦娜), Meng-Meng Zheng(郑萌萌), Ping Zhang(张平), and Hong-Yan Lu(路洪艳). Chin. Phys. B, 2025, 34(9): 097402.
[2]	Doping-induced magnetic and topological transitions in Mn₂X₂Te₅ (X = Bi, Sb) bilayers Wei Chen(陈威), Chuhan Tang(唐楚涵), Chao-Fei Liu(刘超飞), and Mingxing Chen(陈明星). Chin. Phys. B, 2025, 34(9): 097304.
[3]	Broadband polarization-independent terahertz multifunctional liquid crystal coding metasurface based on topological optimization Yu Chen(陈羽), Wu-Hao Cao(曹吴昊), Jia-Qi Li(李嘉琦), Ming-Zhe Zhang(张明哲), Xin-Yi Du(杜欣怡), Ding-Shan Gao(郜定山), and Pei-Li Li(李培丽). Chin. Phys. B, 2025, 34(4): 044205.
[4]	Angle-resolved photoemission spectroscopy study on transition-metal kagome materials Jiangang Yang(杨鉴刚), Jianwei Huang(黄建伟), Lin Zhao(赵林), and X. J. Zhou(周兴江). Chin. Phys. B, 2025, 34(4): 047101.
[5]	Higher-order topology in twisted multilayer systems: A review Chunbo Hua(花春波) and Dong-Hui Xu(许东辉). Chin. Phys. B, 2025, 34(3): 037301.
[6]	SNSAlib: A python library for analyzing signed network Ai-Wen Li(李艾纹), Jun-Lin Lu(陆俊霖), Ying Fan(樊瑛), and Xiao-Ke Xu(许小可). Chin. Phys. B, 2025, 34(3): 038902.
[7]	Exceptional rings and non-Abelian topology in non-Hermitian high-spin systems Peng-Zhen Sun(孙鹏震), Zhou-Tao Lei(雷周涛), and Yuan-Gang Deng(邓元刚). Chin. Phys. B, 2025, 34(11): 110303.
[8]	Photoinduced Floquet higher-order Weyl semimetal in C₆ symmetric Dirac semimetals Xin-Xin Xu(许欣欣), Zi-Ming Wang(王梓名), Dong-Hui Xu(许东辉), and Chui-Zhen Chen(陈垂针). Chin. Phys. B, 2024, 33(6): 067801.
[9]	Interplay between topology and localization on superconducting circuits Xin Guan(关欣), Bingyan Huo(霍炳燕), and Gang Chen(陈刚). Chin. Phys. B, 2024, 33(6): 060311.
[10]	Manipulation of internal blockage in triangular triple quantum dot Yue Qi(齐月) and Jian-Hua Wei(魏建华). Chin. Phys. B, 2024, 33(5): 057301.
[11]	A Weibo local network growth model constructed from the perspective of following-followed Fu-Zhong Nian(年福忠) and Ran-Qing Yao(姚然庆). Chin. Phys. B, 2024, 33(12): 128702.
[12]	Ultra-broadband and wide-angle reflective terahertz polarization conversion metasurface based on topological optimization Ya-Jie Zhang(张亚杰), Chao-Long Li(李潮龙), Jia-Qi Luan(栾迦淇), Ming Zhao(赵茗), Ding-Shan Gao(郜定山), and Pei-Li Li(李培丽). Chin. Phys. B, 2024, 33(10): 104210.
[13]	Optimization of communication topology for persistent formation in case of communication faults Guo-Qiang Wang(王国强), He Luo(罗贺), Xiao-Xuan Hu(胡笑旋), and Jian-Wei Tai(台建玮). Chin. Phys. B, 2023, 32(7): 078901.
[14]	Topological properties of tetratomic Su-Schrieffer-Heeger chains with hierarchical long-range hopping Guan-Qiang Li(李冠强), Bo-Han Wang(王博涵), Jing-Yu Tang(唐劲羽), Ping Peng(彭娉), and Liang-Wei Dong(董亮伟). Chin. Phys. B, 2023, 32(7): 077102.
[15]	Fault-tolerant finite-time dynamical consensus of double-integrator multi-agent systems with partial agents subject to synchronous self-sensing function failure Zhi-Hai Wu(吴治海) and Lin-Bo Xie(谢林柏). Chin. Phys. B, 2022, 31(12): 128902.

[1]	ZHENG JIAN-GUO (郑建国), LI QI (李齐), FENG DUAN (冯端). DISLOCATION DISSOCIATION ON CLIMB PLANE IN TEXTURED YBa₂Cu₃O_7-$\delta$ SUPERCONDUCTOR[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(1): 35 -41 .
[2]	SI JIN-HAI (司金海), ZHAO JIANG (赵江), WANG YOU-GUI (王友贵), YE PEI-XIAN (叶佩弦). THEORETICAL STUDIES ON LASER-INDUCED GRATINGS IN ORGANIC PHOTOISOMERS[J]. Acta Physica Sinica (Overseas Edition), 1996, 5(7): 511 -519 .
[3]	Wei Hong-Xiang (魏红祥), Lu Qing-Feng (路庆凤), Zhao Su-Fen (赵素芬), Zhang Xie-Qun (张谢群), Feng Jia-Feng (丰家峰), Han Xiu-Feng (韩秀峰). Vortex domain structures and dc current dependence of magneto-resistances in magnetic tunnel junctions[J]. Chinese Physics, 2004, 13(9): 1553 -1559 .
[4]	Zhang Li-Ping(张丽萍) and Xue Ju-Kui(薛具奎). Continuous feedback control of KdV Burgers system[J]. Chinese Physics, 2007, 16(8): 2264 -2271 .
[5]	Wang Can-Jun(王参军) and Mei Dong-Cheng(梅冬成). Transitions in a genotype selection model driven by coloured noises[J]. Chin. Phys. B, 2008, 17(2): 479 -485 .
[6]	Dong Ya-Bin(董雅宾), Gao Jiang-Rui(郜江瑞), and Dong You-Er(董有尔). Quantum coherent effects in multi-Zeeman-sublevel atomic systems[J]. Chin. Phys. B, 2008, 17(9): 3306 -3312 .
[7]	Yun Jiang-Ni(贠江妮) and Zhang Zhi-Yong(张志勇). Electronic structure and optical properties of Nb-doped Sr₂TiO₄ by density function theory calculation[J]. Chin. Phys. B, 2009, 18(7): 2945 -2952 .
[8]	Liu Fei(刘飞), Mo Fu-Yao(莫富尧), Li Li(李力), Su Zan-Jia(苏赞加), Huang Ze-Qiang(黄泽强), Deng Shao-Zhi(邓少芝), Chen Jun(陈军), and Xu Ning-Sheng(许宁生). No-catalyst growth of vertically-aligned AlN nanocone field electron emitter arrays with high emission performance at low temperature[J]. Chin. Phys. B, 2010, 19(10): 107205 .
[9]	Liu Bo(刘波), Gu Mu(顾牡), Liu Xiao-Lin(刘小林), Huang Shi-Ming(黄世明), Ni Chen(倪晨), Li Ze-Ren(李泽仁), and Wang Rong-Bo(王荣波). First-principles study of lattice dynamics and thermodynamics ofosmium under pressure[J]. Chin. Phys. B, 2010, 19(2): 26301 -026301 .
[10]	Liu Qi(刘琪), Tang Chao(汤超), and Ouyang Qi(欧阳颀). *Fluctuation theorem for the mutation process in in vitro* evolution**[J]. Chin. Phys. B, 2010, 19(4): 40202 .

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Magnetoelectric topology: The rope weaving in parameter space

Cite this article:

Online attention