Magnetic topological insulators

The importance of global band topology is unequivocally recognized in condensed matter physics, and new states of matter, such as topological insulators, have been discovered. Owing to their bulk band topology, 3D topological insulators possess a massless Dirac dispersion with spin–momentum locking at the surface. Although 3D topological insulators were originally proposed in time-reversal invariant systems, the onset of a spontaneous magnetization or, equivalently, a broken time-reversal symmetry leads to the formation of an exchange gap in the Dirac band dispersion. In such magnetic topological insulators, tuning of the Fermi level in the exchange gap results in the emergence of a quantum Hall effect at zero magnetic field, that is, of a quantum anomalous Hall effect. Here, we review the basic concepts of magnetic topological insulators and their experimental realization, together with the discovery and verification of their emergent properties. In particular, we discuss how the development of tailored materials through heterostructure engineering has made it possible to access the quantum anomalous Hall effect, the topological magnetoelectric effect, the physics related to the chiral edge states that appear in these materials and various spintronic phenomena. Further theoretical and experimental research on magnetic topological insulators will provide fertile ground for the development of new concepts for next-generation electronic devices for applications such as spintronics with low energy consumption, dissipationless topological electronics and topological quantum computation. Magnetic topological insulators enable the investigation of the interplay between magnetism and topological electronic states. This Review summarizes the basic notions of magnetic topological insulators and the progress in the experimental realization of exotic topological phenomena.