Enumeration and Representation Theory of Spin Space Groups

Chen, Xiaobing1,2; Ren, Jun1,2; Zhu, Yanzhou3,4; Yu, Yutong1,2; Zhang, Ao1,2; Liu, Pengfei1,2; Li, Jiayu1,2; Liu, Yuntian1,2; Li, Caiheng3,4; Liu, Qihang1,2,5,6

2024-08-28

10.1103/PhysRevX.14.031038

PHYSICAL REVIEW X   影响因子和分区

2160-3308

Fundamental physical properties, such as phase transitions, electronic structures, and spin excitations, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has come to light that a more comprehensive group, known as the spin space group (SSG), which combines separate spin and spatial operations, is necessary to fully characterize the geometry and underlying properties of magnetic ordered materials. However, the basic theory of SSG has seldom been developed. In this work, we present a systematic study of the enumeration and the representation theory of the SSG. Starting from the 230 crystallographic space groups and finite translation groups with a maximum order of eight, we establish an extensive collection of over 100 000 SSGs under a four-index nomenclature as well as international notation. We then identify inequivalent SSGs specifically applicable to collinear, coplanar, and noncoplanar magnetic configurations. To facilitate the identification of the SSG, we develop an online program that can determine the SSG symmetries of any magnetic ordered crystal. Moreover, we derive the irreducible corepresentations of the little group in momentum space within the SSG framework. Finally, we illustrate the SSG symmetries and physical effects beyond the framework of magnetic space groups through several representative material examples, including a candidate altermagnet RuO2, spiral spin polarization in the coplanar antiferromagnet CeAuAl3, and geometric Hall effect in the noncoplanar antiferromagnet CoNb3S6. Our work advances the field of group theory in describing magnetic ordered materials, opening up avenues for deeper comprehension and further exploration of emergent phenomena in magnetic materials.

Condensed Matter Physics Magnetism Materials Science

SCI

英语

第一 ; 通讯

National Key R&D Program of China[2020YFA0308900] ; National Natural Science Foundation of China[12274194] ; Guangdong Provincial Key Laboratory for Computational Science and Material Design[2019B030301001] ; Shenzhen Science and Technology Program["RCJC202210080 92722009","20231117091158001"] ; Science, Technology and Innovation Commission of Shenzhen Municipality[ZDSYS20190902092905285] ; Special Funds for the Cultivation of Guangdong College Students ' Scientific and Technological Innovation[pdjh2024c10202] ; China Postdoctoral Science Foundation[2023M741544]

Physics

Physics, Multidisciplinary

WOS:001302265700002

AMER PHYSICAL SOC

Web of Science

1.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China
6.Southern Univ Sci & Technol, Shenzhen Key Lab Adv Quantum Funct Mat & Devices, Shenzhen 518055, Peoples R China

Chen, Xiaobing,Ren, Jun,Zhu, Yanzhou,et al. Enumeration and Representation Theory of Spin Space Groups[J]. PHYSICAL REVIEW X,2024,14(3).

Chen, Xiaobing.,Ren, Jun.,Zhu, Yanzhou.,Yu, Yutong.,Zhang, Ao.,...&Liu, Qihang.(2024).Enumeration and Representation Theory of Spin Space Groups.PHYSICAL REVIEW X,14(3).

Chen, Xiaobing,et al."Enumeration and Representation Theory of Spin Space Groups".PHYSICAL REVIEW X 14.3(2024).