Three-Dimensional Quantum Anomalous Hall Effect in Ferromagnetic Insulators

TL;DR

This paper predicts and demonstrates the existence of the quantum anomalous Hall effect in three-dimensional ferromagnetic insulators, expanding the understanding of topological states beyond two dimensions with potential spintronics applications.

Contribution

The work introduces the theoretical framework and first-principles calculations showing 3D QAHE in centrosymmetric ferromagnetic oxides, a novel extension of QAHE beyond 2D systems.

Findings

3D QAHE can occur in certain ferromagnetic insulators with inversion symmetry.

The Hall conductivity is quantized at -3e^2/h in identified compounds.

Chiral surface states are observed on surfaces parallel to the magnetic moment.

Abstract

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 (2D) system with time-reversal symmetry breaking. In this work, 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 3D QAHE based on the 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 non-layered compounds that share a centrosymmetric structure with space group $R\bar{3}m$ (No. 166). The Hall conductivity is quantized to be $-\frac{3e^2}{hc}$ with the lattice constant $c$ along $c$-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.