In this article, we propose a new concept of bilayer stacking A-type altermagnet (BSAA), in which two identical ferromagnetic monolayers are stacked with antiferromagnetic coupling to form a two-dimensional A-type altermagnet. By solving the stacking model, we derive all BSAAs for all layer groups and draw three key conclusions: (1) Only 17 layer groups can realize intrinsic A-type altermagnetism. All 2D A-type altermagnets must belong to these 17 layer groups, which will be helpful to search for 2D A-type altermagnet. (2) It is impossible to connect the two sublattices of BSAA using $S_{3z}$ or $S_{6z}$, a constraint that is also applicable to all 2D altermagnets. (3) $C_{2α}$ is a general stacking operation to generate BSAA for an arbitrary monolayer. Our theory not only can explain the previously reported twisted-bilayer altermagnets, but also can provide more possibilities to generate A-type altermagnets. Our research has significantly broadened the range of candidate materials for 2D altermagnets. Based on conclusion (1), the bilayer NiZrCl$_6$ is predicted to exhibit intrinsic A-type altermagnetism. Additionally, we use twisted-bilayer NiCl$_2$, previously reported in the literature, as the second example of BSAA. Furthermore, utilizing symmetry analysis and first-principles calculation, we scrutinize their spin-momentum locking characteristic to substantiate their altermagnetic properties.
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）
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）
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）
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）
Stacking-Engineered Switchable Altermagnetism in Topological FeSe bilayer systems
Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）；School of Materials Science and Engineering, Xiangtan University（湘潭大学材料科学与工程学院）；Department of Physics and Astronomy, University of California, Irvine（加州大学尔湾分校物理与天文学系）
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）
Ferroelectricity-driven altermagnetism in two-dimensional van der Waals multiferroics
Technical University of Darmstadt（达姆施塔特工业大学）；Institute for Quantum Science and Technology, State Key Laboratory of Advanced Refractories, Materials Genome Institute, Physics Department, Shanghai University（上海大学量子科学与技术研究所、先进耐火材料国家重点实验室、材料基因组研究所、物理系）
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）
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）
Linear magneto-birefringence as a probe of altermagnetism
Institute of Science and Technology Austria（奥地利科学技术研究所）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Stacking-Controlled Altermagnetism and Topological Magnons in Bilayer CrI$_3$
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Institute of Neutron Science and Technology, School of Physics, Sun Yat-Sen University（中山大学物理学院中子科学与技术研究所光电材料与技术国家重点实验室磁电物理与器件广东省重点实验室）
Vacancy-driven inverse Lieb geometry: A general route to $d$-wave altermagnetism in two dimensions
Vellore Institute of Technology（维罗尔理工大学）；Kwansei Gakuin University（关西学院大学）；National Institute for Materials Science (NIMS)（国立材料研究所）；Osaka University（大阪大学）
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）
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）
Ultrafast Magneto-optical Fingerprints of Altermagnetism in MnTe
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；Department of Physics, The Hong Kong University of Science and Technology（香港科技大学物理系）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Robust and tunable Floquet altermagnets in sliding A-type antiferromagnetic bilayers
Beijing National Laboratory for Condensed Matter Physics, and 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）；Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (Ministry of Education), School of Physics, Beijing Institute of Technology（北京理工大学物理学院，先进光电子量子架构与测量教育部重点实验室，量子物理中心）；University of Chinese Academy of Sciences（中国科学院大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）
