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The interplay of magnetism and topology is a key research subject incondensed matter physics and material science, which offers great opportunitiesto explore emerging new physics, like the quantum anomalous Hall (QAH) effect,axion electrodynamics and Majorana fermions. However, these exotic physicaleffects have rarely been realized in experiment, due to the lacking of suitableworking materials. Here we predict that van der Waals layeredMnBi$_2$Te$_4$-family materials show two-dimensional (2D) ferromagnetism in thesingle layer and three-dimensional (3D) $A$-type antiferromagnetism in thebulk, which could serve as a next-generation material platform for thestate-of-art research. Remarkably, we predict extremely rich topologicalquantum effects with outstanding features in an experimentally availablematerial MnBi$_2$Te$_4$, including a 3D antiferromagnetic topological insulatorwith the long-sought topological axion states, the type-II magnetic Weylsemimetal (WSM) with simply one pair of Weyl points, and the high-temperatureintrinsic QAH effect. These striking predictions, if proved experimentally,could profoundly transform future research and technology of topologicalquantum physics.

Intrinsic magnetic topological insulators in van der Waals layered MnBi$_2$Te$_4$-family materials