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