Magnetic topological insulators and quantum anomalous hall effect

When the magnetic order is introduced into topological insulators (TIs), the time-reversal symmetry (TRS) is broken, and the non-trivial topological surface is driven into a new massive Dirac fermions state. The study of such TRS-breaking systems is one of the most emerging frontiers in condensed-matter physics. In this review, we outline the methods to break the TRS of the topological surface states. With robust out-of-plane magnetic order formed, we describe the intrinsic magnetisms in the magnetically doped 3D TI materials and the approach to manipulate each contribution. Most importantly, we summarize the theoretical developments and experimental observations of the scale-invariant quantum anomalous Hall effect (QAHE) in both the 2D and 3D Cr-doped (BiSb)2Te3 systems; at the same time, we also discuss the correlations between QAHE and other quantum transport phenomena. Finally, we highlight the use of TI/Cr-doped TI heterostructures to both manipulate the surface-related ferromagnetism and realize electrical manipulation of magnetization through the giant spin-orbit torques.