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# Magnetic topological insulators

## Abstract

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.

## Key points

• The chemical doping of topological insulators with transition metal elements induces a spontaneous magnetization that interacts with the topological surface state to open a mass gap at the Dirac point.

• The precise tuning of the Fermi level at the mass gap enables the observation of the quantum anomalous Hall effect — a zero-magnetic-field quantum Hall effect arising in the presence of a spontaneous magnetization — which is further stabilized by heterostructure engineering.

• Chiral edge conduction associated with the quantum anomalous Hall effect is manipulated by magnetic domain walls, and the edge modes can be turned into chiral Majorana edge modes via proximity coupling with a superconductor.

• Heterostructure engineering and terahertz measurements enable the observation of the quantized topological magnetoelectric effect.

• The spin–momentum-locked conduction electrons in the surface state lead to versatile spintronic functionalities, such as an efficient generation of spin transfer torque, as a result of charge-to-spin conversion.

• The further development of materials design and engineering will realize the quantum anomalous Hall effect at higher temperatures, the control of this state with external fields and exotic topological states of matter.

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## Acknowledgements

The authors thank R. Yoshimi, M. Mogi, M. Kawamura, N. Nagaosa, M. Kawasaki and T. Dietl for enlightening discussions on magnetic topological insulators. This research was supported in part by the Japan Society for the Promotion of Science (JSPS; no. 16J03476), the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan (no. JP15H05853), and Core Research for Evolutional Science and Technology (CREST), Japanese Science and Technology (JST; no. JPMJCR16F1).

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Tokura, Y., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat Rev Phys 1, 126–143 (2019). https://doi.org/10.1038/s42254-018-0011-5

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