Three-dimensional quantum anomalous Hall effect in ferromagnetic insulators

The quantum anomalous Hall effect (QAHE) hosts the dissipationless chiral edge states associated with the nonzero Chern number, providing potentially significant applications in future spintronics. The QAHE usually occurs in a two-dimensional system with time-reversal symmetry breaking. In this Rapid Communication, we propose that the QAHE can exist in three-dimensional (3D) ferromagnetic insulators. By imposing inversion symmetry, we develop the topological constraints dictating the appearance of a 3D QAHE based on a parity analysis at the time-reversal invariant points in reciprocal space. Moreover, using first-principles calculations, we identify that 3D QAHE can be realized in a family of intrinsic ferromagnetic insulating oxides, including layered and nonlayered compounds that share a centrosymmetric structure with space group $R\overline{3}m$ (No. 166). The Hall conductivity is quantized to be $\ensuremath{-}\frac{3{e}^{2}}{hc}$ with the lattice constant $c$ along the $c$ axis. The chiral surface sheet states are clearly visible and uniquely distributed on the surfaces that are parallel to the magnetic moment. Our findings open a promising pathway to realize the QAHE in 3D ferromagnetic insulators.

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