Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials

doi:10.1088/1674-1056/ad6425

Abstract Unconventional antiferromagnetism dubbed as altermagnetism was first discovered in rutile structured magnets, which is featured by spin splitting even without the spin-orbital coupling effect. This interesting phenomenon has been discovered in more altermagnetic materials. In this work, we explore two-dimensional altermagnetic materials by studying two series of two-dimensional magnets, including $M\mathrm{F_4}$ with $M$ covering all 3d and 4d transition metal elements, as well as $T\mathrm{S_2}$ with $T = {\rm V}$, Cr, Mn, Fe. Through the magnetic symmetry operation of RuF$_4$ and MnS$_2$, it is verified that breaking the time inversion is a necessary condition for spin splitting. Based on symmetry analysis and first-principles calculations, we find that the electronic bands and magnon dispersion experience alternating spin splitting along the same path. This work paves the way for exploring altermagnetism in two-dimensional materials.

Keywords: two-dimensional altermagnetic materials altermagnetism spin splitting first-principles calculations

Received: 27 June 2024
Revised: 16 July 2024
Accepted manuscript online: 17 July 2024

PACS:	75.50.Ee	(Antiferromagnetics)
	61.50.Ah	(Theory of crystal structure, crystal symmetry; calculations and modeling)
	11.55.Fv	(Dispersion relations)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12004439), Hunan Province Postgraduate Research and Innovation Project (Grant No. CX20230229), and the computational resources from the High Performance Computing Center of Central South University.

Corresponding Authors: Meng-Qiu Long, Yun-Peng Wang
E-mail: mqlong@csu.edu.cn;yunpengwang@csu.edu.cn

Cite this article:

Qian Wang(王乾), Da-Wei Wu(邬大为), Guang-Hua Guo(郭光华), Meng-Qiu Long(龙孟秋), and Yun-Peng Wang(王云鹏) Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials 2024 Chin. Phys. B 33 097507

[1] Chumak A V, Vasyuchka V I, Serga A A and Hillebrands B 2015 Nat. Phys. 11 453
[2] Wang Y P and Long M Q 2020 Phys. Rev. B 101 024411
[3] Baltz V, Manchon A, Tsoi M, Moriyama T, Ono T and Tserkovnyak Y 2018 Rev. Mod. Phys. 90 015005
[4] Cheng R, Xiao D and Zhu J G 2018 Phys. Rev. Lett. 121 207202
[5] Zhou W, Zheng G, Li A, Zhang D and Ouyang F 2023 Phys. Rev. B 107 035139
[6] Qi B T, Guo J J, Miao Y Q, Zhong M Z, Li B, Luo Z Y, Wang X G, Nie Y Z, Xia Q L and Guo G H 2022 Frontiers in Physics 10 851838
[7] Šmejkal L, Sinova J and Jungwirth T 2022 Phys. Rev. X 12 031042
[8] Šmejkal L, Sinova J and Jungwirth T 2022 Phys. Rev. X 12 040501
[9] Yuan L D, Wang Z, Luo J W, Rashba E I and Zunger A 2020 Phys. Rev. B 102 014422
[10] Yuan L D and Zunger A 2023 Adv. Mater. 35 2211966
[11] Egorov S A, Litvin D B and Evarestov R A 2021 J. Phys. Chem. C 125 16147
[12] Turek I 2022 Phys. Rev. B 106 094432
[13] Fernandes R M, de Carvalho V S, Birol T and Pereira R G 2024 Phys. Rev. B 109 024404
[14] Raghottam M S, Giuseppe C and Carmine A 2021 Nanoscale 15 16998
[15] Li J, Shi Z, Ortiz V H, Aldosary M, Chen C, Aji V, Wei P and Shi J 2019 Phys. Rev. Lett. 122 217204
[16] Wu S M, Zhang W, KC A, Borisov P, Pearson J E, Jiang J S, Lederman D, Hoffmann A and Bhattacharya A 2016 Phys. Rev. Lett. 116 097204
[17] Uchida K, Xiao J, Adachi H, Ohe J, Takahashi S, Ieda J, Ota T, Kajiwara Y, Umezawa H, Kawai H, Bauer G E W, Maekawa S and Saitoh E 2010 Nat. Mater. 9 894
[18] Shi Z, Xi Q, Li J, Li Y, Aldosary M, Xu Y, Zhou J, Zhou S M and Shi J 2021 Phys. Rev. Lett. 127 277203
[19] Bai H, Zhang Y C, Zhou Y J, Chen P, Wan C H, Han L, Zhu W X, Liang S X, Su Y C, Han X F, Pan F and Song C 2023 Phys. Rev. Lett. 130 216701
[20] Cheng R, Okamoto S and Xiao D 2016 Phys. Rev. Lett. 117 217202
[21] Zyuzin V A and Kovalev A A 2016 Phys. Rev. Lett. 117 217203
[22] Šmejkal L, Marmodoro A, Ahn K H, González-Hernández R, Turek I, Mankovsky S, Ebert H, D’Souza S W, Šipr O, Sinova J, et al. 2023 Phys. Rev. Lett. 131 256703
[23] Cui Q, Zeng B, Cui P, Yu T and Yang H 2023 Phys. Rev. B 108 L180401
[24] Krempaský J, Šmejkal L, D’Souza S W, Hajlaoui M, Springholz G, Uhlírová K, Alarab F, Constantinou P C, Strocov V, Usanov D, Pudelko W R, Gonzalez-Hernández R, Hellenes A B, Jansa Z, Reichlová H, Šobán Z, Betancourt R D G, Wadley P, Sinova J, Kriegner D, Min ár J, Dil J H and Jungwirth T 2024 Nature 626 517
[25] Zhu Y P, Chen X, Liu X R, Liu Y, Liu P, Zha H, Qu G, Hong C, Li J, Jiang Z, Ma X M, Hao Y J, Zhu M Y, Liu W, Zeng M, Jayaram S, Lenger M, Ding J, Mo S, Tanaka K, Arita M, Liu Z, Ye M, Shen D, Wrachtrup J, Huang Y, He R H, Qiao S, Liu Q and Liu C 2024 Nature 626 523
[26] He R, Wang D, Luo N, Zeng J, Chen K Q and Tang L M 2023 Phys. Rev. Lett. 130 046401
[27] Kresse G and Hafner J 1993 Phys. Rev. B 47 558
[28] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[29] Ozaki T 2003 Phys. Rev. B 67 155108
[30] Ozaki T and Kino H 2005 Phys. Rev. B 72 045121
[31] Wang H, Qi J and Qian X 2020 Appl. Phys. Lett. 117 083102
[32] Liechtenstein A I, Anisimov V I and Zaanen J Phys. Rev. B 52 R5467
[33] Xiang H J, Kan E J, Wei S H, Whangbo M H and Gong X G 2011 Phys. Rev. B 84 224429
[34] He X, Helbig N, Verstraete M J and Bousquet E 2021 Computer Physics Communications 264 107938
[35] Xiang H, Lee C, Koo H J, Gong X and Whangbo M H 2013 Dalton Trans. 42 823
[36] M-H, Whangbo, Koo H J and Dai D 2003 J. Solid State Chem. 176 417
[37] Steenbock T and Herrmann C 2018 Journal of Computational Chemistry 39 81
[38] Wang N, Chen J, Ding N, Zhang H, Dong S and Wang S S 2022 Phys. Rev. B 106 064435
[39] Casteel W J J, Wilkinson A P, Borrmann H, Serfass R E and Bartlett N 1992 Inorganic Chemistry 31 3124
[40] Lifshitz R 2004 arXiv preprint cond-mat/0406675
[41] Sodequist J and Olsen T 2024 Appl. Phys. Lett. 124 182409

[1]	Two-dimensional Cr₂Cl₃S₃ Janus magnetic semiconductor with large magnetic exchange interaction and high-T_C Lei Fu(伏磊), Shasha Li(李沙沙), Xiangyan Bo(薄祥䶮), Sai Ma(马赛), Feng Li(李峰), and Yong Pu(普勇). Chin. Phys. B, 2024, 33(9): 096301.
[2]	Strain-tuned electronic and valley-related properties in Janus monolayers of SWSiX₂ (X = N, P, As) Yunxi Qi(戚云西), Jun Zhao(赵俊), and Hui Zeng(曾晖). Chin. Phys. B, 2024, 33(9): 096302.
[3]	Electronic transport evolution across the successive structural transitions in Ni_50-xFe_xTi₅₀ shape memory alloys Ping He(何萍), Jinying Yang(杨金颖), Qiusa Ren(任秋飒), Binbin Wang(王彬彬), Guangheng Wu(吴光恒), and Enke Liu(刘恩克). Chin. Phys. B, 2024, 33(7): 077201.
[4]	Regulating the dopant clustering in LiZnAs-based diluted magnetic semiconductor Zihang Jia(贾子航), Bo Zhou(周波), Zhenyi Jiang(姜振益), and Xiaodong Zhang(张小东). Chin. Phys. B, 2024, 33(5): 058101.
[5]	Spin direction dependent quantum anomalous Hall effect in two-dimensional ferromagnetic materials Yu-Xian Yang(杨宇贤) and Chang-Wen Zhang(张昌文). Chin. Phys. B, 2024, 33(4): 047101.
[6]	Optical spectrum of ferrovalley materials: A case study of Janus H-VSSe Chao-Bo Luo(罗朝波), Wen-Chao Liu(刘文超), and Xiang-Yang Peng(彭向阳). Chin. Phys. B, 2024, 33(1): 016303.
[7]	Design of sign-reversible Berry phase effect in 2D magneto-valley material Yue-Tong Han(韩曰通), Yu-Xian Yang(杨宇贤), Ping Li(李萍), and Chang-Wen Zhang(张昌文). Chin. Phys. B, 2023, 32(9): 097101.
[8]	Quantum tunneling in the surface diffusion of single hydrogen atoms on Cu(001) Xiaofan Yu(于小凡), Yangwu Tong(童洋武), and Yong Yang(杨勇). Chin. Phys. B, 2023, 32(8): 086801.
[9]	Modulation of CO adsorption on 4,12,2-graphyne by Fe atom doping and applied electric field Yu Dong(董煜), Zhi-Gang Shao(邵志刚), Cang-Long Wang(王苍龙), and Lei Yang(杨磊). Chin. Phys. B, 2023, 32(8): 087101.
[10]	Structural, electronic, and Li-ion mobility properties of garnet-type Li₇La₃Zr₂O₁₂ surface: An insight from first-principles calculations Jing-Xuan Wang(王靖轩), Bao-Zhen Sun(孙宝珍), Mei Li(李梅), Mu-Sheng Wu(吴木生), and Bo Xu(徐波). Chin. Phys. B, 2023, 32(6): 068201.
[11]	Prediction of LiCrTe₂ monolayer as a half-metallic ferromagnet with a high Curie temperature Li-Man Xiao(肖丽蔓), Huan-Cheng Yang(杨焕成), and Zhong-Yi Lu(卢仲毅). Chin. Phys. B, 2023, 32(5): 057505.
[12]	Evaluating thermal expansion in fluorides and oxides: Machine learning predictions with connectivity descriptors Yilin Zhang(张轶霖), Huimin Mu(穆慧敏), Yuxin Cai(蔡雨欣), Xiaoyu Wang(王啸宇), Kun Zhou(周琨), Fuyu Tian(田伏钰), Yuhao Fu(付钰豪), and Lijun Zhang(张立军). Chin. Phys. B, 2023, 32(5): 056302.
[13]	Room temperature quantum anomalous Hall insulator in honeycomb lattice, RuCS₃, with large magnetic anisotropy energy Yong-Chun Zhao(赵永春), Ming-Xin Zhu(朱铭鑫), Sheng-Shi Li(李胜世), and Ping Li(李萍). Chin. Phys. B, 2023, 32(5): 057301.
[14]	Rational design of Fe/Co-based diatomic catalysts for Li-S batteries by first-principles calculations Xiaoya Zhang(张晓雅), Yingjie Cheng(程莹洁), Chunyu Zhao(赵春宇), Jingwan Gao(高敬莞), Dongxiao Kan(阚东晓), Yizhan Wang(王义展), Duo Qi(齐舵), and Yingjin Wei(魏英进). Chin. Phys. B, 2023, 32(3): 036803.
[15]	Coexistence of giant Rashba spin splitting and quantum spin Hall effect in H-Pb-F Wenming Xue(薛文明), Jin Li(李金), Chaoyu He(何朝宇), Tao Ouyang(欧阳滔), Xiongying Dai(戴雄英), and Jianxin Zhong(钟建新). Chin. Phys. B, 2023, 32(3): 037101.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials

Cite this article:

Online attention