We revise existing group-theoretical approaches for a treatment of nonrelativistic collinear magnetic systems with perfect translation invariance. We show that full symmetry groups of these systems, which contain elements with independent rotations in the spin and configuration spaces (spin groups), can be replaced by magnetic groups consisting of elements with rotations acting only on position vectors. This reduction follows from modified transformation properties of electron spin, which in the considered systems becomes effectively a pseudoscalar quantity remaining unchanged upon spatial operations but changing its sign due to an operation of antisymmetry. We introduce a unitary representation of the relevant magnetic point groups and use it for a classification of collinear magnets from the viewpoint of antiferromagnetism-induced spin splitting of electron bands near the center of Brillouin zone. We prove that the recently revealed different altermagnetic classes correspond in a unique way to all nontrivial magnetic Laue classes, i.e., to the Laue groups containing the operation of antisymmetry only in combination with a spatial rotation. Four of these Laue classes are found compatible with a nonzero spin conductivity. Subsequent inspection of a simple model allows us to address briefly the physical mechanisms responsible for the spin splitting in real systems.
Two-Dimensional Altermagnetism in Epitaxial CrSb Ultrathin Films
School of Physics Beihang University（北京航空航天大学物理学院）；Institute of High Energy Physics Chinese Academy of Sciences（中国科学院高能物理研究所）；Singapore University of Technology and Design（新加坡科技设计大学）
Atomic-scale visualization of d-wave altermagnetism
Tsinghua University（清华大学）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Beijing Institute of Technology（北京理工大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Southern University of Science and Technology（南方科技大学）；Hefei National Laboratory（合肥国家实验室）
Optical signatures of bulk g-wave altermagnetism in MnTe
RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道莱布尼茨技术大学）；Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Institute of Physics, Academy of Sciences of the Czech Republic（捷克科学院物理研究所）；Texas A&M University（德克萨斯农工大学）
Metallic d-wave altermagnetism in WFeB: a platform for electrically switchable perpendicular spin-splitter response
Iowa State University（爱荷华州立大学）；Ames National Laboratory, U.S. Department of Energy（美国能源部阿姆斯国家实验室）；University of Nebraska-Lincoln（内布拉斯加大学林肯分校）；Nebraska Center for Materials and Nanoscience（内布拉斯加材料纳米科学中心）；Oak Ridge National Laboratory（橡树岭国家实验室）；Middle Tennessee State University（中田纳西州立大学）；University of Tennessee Space Institute（田纳西大学太空研究所）
Observation of hidden altermagnetism in Cs$_{1-δ}$V$_2$Te$_2$O
Zhejiang University（浙江大学）；Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；Southern University of Science and Technology（南方科技大学）
Exploration of Altermagnetism in $\mathrm{RuO_{2}}$
China Three Gorges University（三峡大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Southern University of Science and Technology (SUSTech)（南方科技大学）；Hefei National Laboratory（合肥国家实验室）；University of Science and Technology of China（中国科学技术大学）
Suppression of p-Wave Altermagnetism by Localized 4f Electrons in CeNiAsO
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Condensed Matter Physics Data Center of Chinese Academy of Sciences（中国科学院凝聚态物理数据中心）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院）；Shanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院上海同步辐射光源）；National Key Laboratory of Materials for Integrated Circuits, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统信息技术研究所集成电路材料国家重点实验室）；Technical Institute of Physics and Chemistry, Chinese Academy of Sciences（中国科学院化学物理研究所）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Correlation-Driven Orbital Order Realizes 2D Metallic Altermagnetism
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Johannes Gutenberg Universität Mainz（美因茨约翰内斯·古腾堡大学）；National Institute of Science Education and Research（国家科学教育与研究所）
$d$-wave altermagnetism revealed by resonant inelastic X-ray scattering
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Department of Physics, Shanghai Normal University（上海师范大学物理系）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）；PSI Center for Neutron and Muon Sciences, Paul Scherrer Institute（保罗谢尔研究所中子与μ子科学中心）；Diamond Light Source, Harwell Campus（钻石光源哈韦尔园区）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Orbital altermagnetism on the kagome lattice and possible application to $A$V$_3$Sb$_5$
The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格雷恩格工程学院）；Anthony J. Leggett Institute for Condensed Matter Theory, The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格雷恩格工程学院安东尼·J·利盖特凝聚态理论研究所）；Department of Chemical Engineering and Materials Science, University of Minnesota（明尼苏达大学化学工程与材料科学系）
