We formulate a Landau theory for altermagnets, a class of colinear compensated magnets with spin-split bands. Starting from the non-relativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters and the effect of non-zero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO$_2$, MnTe and CuF$_2$ that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity and magneto-elastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems deriving from the zero spin-orbit coupled limit.
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）
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）
Catalog of Altermagnetism in Magnetic Wallpaper/Space Groups and Nonsymmorphic Altermagnets
Hefei National Laboratory（合肥国家实验室）；School of Emerging Technology, University of Science and Technology of China（中国科学技术大学先进技术学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Department of Physics and Center for Theoretical Physics, National Taiwan University（国立台湾大学物理系暨理论物理中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）
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）
Unlocking Doping Effects on Altermagnetism in MnTe: Emergence of Quasi-altermagnetism
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Indian Institute of Science, Bangalore（印度科学研究所班加罗尔分校）；Scuola Internazionale Superiore di Studi Avanzati (SISSA)（国际高等研究院）
Engineering Altermagnetism via Layer Shifts and Spin Order in Bilayer MnPS$_3$
Universidad de Antofagasta（安托法加斯塔大学）；Technische Universität Dresden（德累斯顿工业大学）；Universidad Técnica Federico Santa María（费德里科·圣塔玛丽亚技术大学）；Universidad de Chile（智利大学）；Dresden University of Technology, Institute for Solid State and Materials Physics（德累斯顿工业大学固体与材料物理研究所）
Emergent altermagnetism at surfaces of antiferromagnets: full symmetry classification and material identification
Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学）；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）；Texas A&M University（德克萨斯农工大学）；University of Münster（明斯特大学）
Projectively implemented altermagnetism in an exactly solvable quantum spin liquid
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of Cologne（科隆大学）；Imperial College London（帝国理工学院）
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）
School of Physics, Peking University（北京大学物理学院）；Department of Materials Science and Engineering, University of Utah（犹他大学材料科学与工程系）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
$d$-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）
