This paper presents a study on intrinsic magnetic topological insulators in van der Waals (vdW) layered MnBi₂Te₄-family materials. The authors predict that these materials exhibit two-dimensional (2D) ferromagnetism in single layers and three-dimensional (3D) A-type antiferromagnetism in the bulk. These properties make them promising candidates for next-generation materials in topological quantum physics research. The study highlights the potential of MnBi₂Te₄ to host a variety of exotic topological quantum states, including a 3D antiferromagnetic topological insulator with long-sought topological axion states, a type-II magnetic Weyl semimetal with a single pair of Weyl points, and a high-temperature intrinsic quantum anomalous Hall (QAH) effect. The research explores the interplay between magnetism and topology in materials, which is crucial for understanding and developing new quantum phenomena. The study emphasizes the importance of developing topological quantum materials (TQMs) that combine topology with other quantum phases, such as magnetism, ferroelectricity, and superconductivity. The authors argue that intrinsic TQMs, which do not require doping or heterostructures, are more promising for practical applications. The MnBi₂Te₄-family materials are shown to have a layered structure with tunable properties, making them suitable for studying various quantum phases in different spatial dimensions. The study uses first-principles calculations to predict the existence of multiple intrinsic magnetic topological states in MnBi₂Te₄, including a 3D antiferromagnetic topological insulator, a type-II magnetic Weyl semimetal, and a high-temperature QAH insulator. These predictions are supported by detailed calculations of band structures, surface states, and symmetry properties. The research also discusses the potential of MnBi₂Te₄ for probing topological axion states and for developing dissipationless electronic devices. The study highlights the unique properties of vdW layered materials, which allow for tunable quantum size effects and the integration of magnetic and topological states in the same material. The findings suggest that MnBi₂Te₄ is a promising candidate for future research in topological quantum physics and materials science.This paper presents a study on intrinsic magnetic topological insulators in van der Waals (vdW) layered MnBi₂Te₄-family materials. The authors predict that these materials exhibit two-dimensional (2D) ferromagnetism in single layers and three-dimensional (3D) A-type antiferromagnetism in the bulk. These properties make them promising candidates for next-generation materials in topological quantum physics research. The study highlights the potential of MnBi₂Te₄ to host a variety of exotic topological quantum states, including a 3D antiferromagnetic topological insulator with long-sought topological axion states, a type-II magnetic Weyl semimetal with a single pair of Weyl points, and a high-temperature intrinsic quantum anomalous Hall (QAH) effect. The research explores the interplay between magnetism and topology in materials, which is crucial for understanding and developing new quantum phenomena. The study emphasizes the importance of developing topological quantum materials (TQMs) that combine topology with other quantum phases, such as magnetism, ferroelectricity, and superconductivity. The authors argue that intrinsic TQMs, which do not require doping or heterostructures, are more promising for practical applications. The MnBi₂Te₄-family materials are shown to have a layered structure with tunable properties, making them suitable for studying various quantum phases in different spatial dimensions. The study uses first-principles calculations to predict the existence of multiple intrinsic magnetic topological states in MnBi₂Te₄, including a 3D antiferromagnetic topological insulator, a type-II magnetic Weyl semimetal, and a high-temperature QAH insulator. These predictions are supported by detailed calculations of band structures, surface states, and symmetry properties. The research also discusses the potential of MnBi₂Te₄ for probing topological axion states and for developing dissipationless electronic devices. The study highlights the unique properties of vdW layered materials, which allow for tunable quantum size effects and the integration of magnetic and topological states in the same material. The findings suggest that MnBi₂Te₄ is a promising candidate for future research in topological quantum physics and materials science.