The magnetic topological phases attract much interest, such as the axion insulator, higher-order topology, Weyl semimetals, and the quantum anomalous Hall effect (QAHE). Here, we predict that the axion insulator phase, magnetic Weyl points, and QAHE can be achieved in ${\mathrm{Eu}}_3{\mathrm{In}}_2{\mathrm{As}}_4$. Recently, single-crystal ${\mathrm{Eu}}_3{\mathrm{In}}_2{\mathrm{As}}_4$ was successfully synthesized, and it exhibits an antiferromagnetic (AFM) ground state. Our first-principles calculations show that it lies on the phase boundary between multiple magnetic topological phases, and the magnetic anisotropy is weak, with an energy difference less than 1 meV. In the AFM state, it can be tuned to an axion insulator by tensile strain. The quantized axion angle $\theta =\pi$ and the magnetic higher-order topology are characterized by the parity index $Z_4=2$. By applying an external magnetic field, the induced ferromagnetic (FM) state becomes an ideal magnetic topological semimetal with a single pair of Weyl points or a nodal ring. The QAHE can be achieved in FM multilayer films of ${\mathrm{Eu}}_3{\mathrm{In}}_2{\mathrm{As}}_4$ on a magnetic insulating substrate.

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• Electronic structure
• Quantum anomalous Hall effect
• Topological materials
• Weyl fermions
• Axions
• Density functional calculations