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Spin space groups (SSGs) impose fundamentally different constraints on magnetic configurations in real and reciprocal spaces. As a consequence, the correspondence between real-space and momentum-space spin arrangements is far richer than…

Materials Science · Physics 2025-12-16 Ziyin Song , Ziyue Qi , Chen Fang , Zhong Fang , Hongming Weng

Those fundamental physical properties, such as phase transitions, Weyl fermions, and spin excitation, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has come…

Materials Science · Physics 2024-09-04 Xiaobing Chen , Jun Ren , Yanzhou Zhu , Yutong Yu , Ao Zhang , Pengfei Liu , Jiayu Li , Yuntian Liu , Caiheng Li , Qihang Liu

Symmetries of three-dimensional periodic scalar fields are described by 230 space groups (SGs). Symmetries of three-dimensional periodic (pseudo-) vector fields, however, are described by the spin-space groups (SSGs), which were initially…

Materials Science · Physics 2024-09-02 Yi Jiang , Ziyin Song , Tiannian Zhu , Zhong Fang , Hongming Weng , Zheng-Xin Liu , Jian Yang , Chen Fang

Unconventional magnets that combine antiferromagnetic structures with ferromagnetic-like responses are essential for the development of next-generation spintronics. Their emergent properties are fundamentally dictated by the interplay…

Materials Science · Physics 2026-04-24 Yutong Yu , Xiaobing Chen , Yanzhou Zhu , Yuhui Li , Renzheng Xiong , Jiayu Li , Yuntian Liu , Qihang Liu

Unconventional magnetism has typically been classified into two fundamental classes: even-parity magnets (EPMs) and odd-parity magnets (OPMs). These two classes exhibit identical and opposite spin splittings, respectively, under momentum…

Strongly Correlated Electrons · Physics 2026-03-10 Xun-Jiang Luo , Jin-Xin Hu , Mengli Hu , K. T. Law

Given the scarcity of experimentally confirmed magnetic structures, the reliable prediction of magnetic ground states is crucial; however, it remains a long-sought challenge because of the complex magnetic potential energy landscape. Here,…

Materials Science · Physics 2025-12-29 Yuhui Li , Sike Zeng , Xiaobing Chen , Renzheng Xiong , Yutong Yu , Yu-Jun Zhao , Qihang Liu

In a collinear magnet, the predominant magnetic moments are collectively aligned along a specific spatial orientation, and this alignment may yield intriguing phenomena such as spin orientation driven polarization. It is well known that…

Materials Science · Physics 2025-12-12 Yixun Zhang , Longju Yu , Yizhou Tong , Ying Sun , Xu Li , Hong Jian Zhao , Yanming Ma

In this work, we exhaust all the spin-space symmetries, which fully characterize collinear, non-collinear, commensurate, and incommensurate spiral magnetism, and investigate enriched features of electronic bands that respect these…

Mesoscale and Nanoscale Physics · Physics 2024-08-30 Zhenyu Xiao , Jianzhou Zhao , Yanqi Li , Ryuichi Shindou , Zhi-Da Song

A crystal symmetry search is crucial for computational crystallography and materials science. Although algorithms and implementations for the crystal symmetry search have been developed, their extension to magnetic space groups (MSGs)…

Materials Science · Physics 2023-06-08 Kohei Shinohara , Atsushi Togo , Isao Tanaka

We propose a framework for generating magnetic structures, inspired by the concept of oriented spin space groups (SSGs): magnetic structures are first generated as totally symmetric representations of an SSG and are then rotated such that…

Materials Science · Physics 2026-01-23 Takuya Nomoto , Kohei Shinohara , Hikaru Watanabe , Ryotaro Arita

Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles to condensed matter systems. Here, by combining symmetry analysis and tight-binding model calculations, we elucidate…

Materials Science · Physics 2022-11-04 Pengfei Liu , Jiayu Li , Jingzhi Han , Xiangang Wan , Qihang Liu

Unconventional magnetism represents a paradigm shift in condensed matter physics, effectively bridging the fast, high-density advantages of antiferromagnets with the facile read-write capability of ferromagnets. Recent developments in spin…

Materials Science · Physics 2026-03-31 Xiaobing Chen , Weizhao Chen , Qihang Liu

Nanoscale detection and control of the magnetic order underpins a broad spectrum of fundamental research and practical device applications. The key principle involved is the breaking of time-reversal ($\cal{T}$) symmetry, which in…

Altermagnetism has recently emerged as a new class of spin compensated magnetic materials that exhibit momentum dependent spin splitting despite having zero net magnetization. The origin of these electronic signatures lies in symmetry…

Materials Science · Physics 2026-03-06 Diego López-Alcalá , Andrei Shumilin , José J. Baldoví

We introduce the concept of \emph{orbital altermagnetism}, a symmetry-protected magnetic order of pure orbital degrees of freedom. It is characterized with ordered anti-parallel orbital magnetic moments in real space but momentum-dependent…

Materials Science · Physics 2026-05-22 Mingxiang Pan , Feng Liu , Huaqing Huang

Large spin systems can exhibit unconventional types of magnetic ordering different from the ferromagnetic or N\'eel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break…

Control and detection of spin order in ferromagnets is the main principle allowing storing and reading of magnetic information in nowadays technology. The large class of antiferromagnets, on the other hand, is less utilized, despite its…

Materials Science · Physics 2019-09-23 P. Nemec , M. Fiebig , T. Kampfrath , A. V. Kimel

Unconventional magnetism has emerged as a transformative frontier in condensed matter physics. Such phases are characterized by substantial non-relativistic spin splitting (NSS) in symmetry-compensated magnets. They have been classified by…

Materials Science · Physics 2026-05-21 Xun-Jiang Luo , Dan Li , Rui-Chun Xiao , Ding-Fu Shao , Lei Li , Mingliang Tian , Yugui Yao

Magnetic materials have been applied in a large variety of technologies, from data storage to quantum devices. The development of 2D materials has opened new arenas for magnetic compounds, even when classical theories discourage their…

Materials Science · Physics 2022-02-11 Carlos Mera Acosta , Elton Ogoshi , Jose Antonio Souza , Gustavo M. Dalpian

The recent discovery of altermagnetism has sparked growing interest in compensated magnetic systems as promising platforms for highly scalable spintronics. Altermagnetism is a distinct magnetic order where opposite spin sublattices are…

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