Chapter 14
Topology in Magnetism
X. S. Wang and X. R. Wang
Abstract In this chapter, we review recent developments of two usages of topology
in magnetism. One is to classify spin structures with different topological numbers
(topology in real space). The other usage is to distinguish normal magnetic materials from those magnetic materials supporting topologically protected unidirectional
surface spin waves inside spin wave band gaps (topology in reciprocal space).
14.1 Introduction
Our knowledge about magnetic phenomena has a long history that can be traced
back to the 6th century B.C. when Thales of Miletus, one of the sages in ancient
Greece, told people that lodestones can attract iron. In the 4th century B.C., two
Chinese books, Master Lü’s Spring and Autumn Annual and Guiguzi reported the
same phenomenon [1]. Around 1000 A.D., Chinese people already knew how to
magnetize a normal iron needle with a lodestone and make magnetic compass (vol.
24 of Mengxi Bitan by Kuo Shen). After the industrial revolution, our understanding
of magnetism had greatly advanced. Based on the studies of Coulomb, Ampère,
Faraday, and many others, James Clerk Maxwell wrote down the famous Maxwell’s
equations in 1861 [2],
X. S. Wang
School of Physics and Electronics, Hunan University, Changsha 410082, China
X. R. Wang (B)
Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay,
Kowloon, Hong Kong
e-mail: phxwan@ust.hk
HKUST Shenzhen Research Institute, Shenzhen 518057, China
© Springer Nature Switzerland AG 2021
E. Kamenetskii (ed.), Chirality, Magnetism and Magnetoelectricity,
Topics in Applied Physics 138,
https://doi.org/10.1007/978-3-030-62844-4_14
357
Topology in Magnetism
X. S. Wang and X. R. Wang
Abstract In this chapter, we review recent developments of two usages of topology
in magnetism. One is to classify spin structures with different topological numbers
(topology in real space). The other usage is to distinguish normal magnetic materials from those magnetic materials supporting topologically protected unidirectional
surface spin waves inside spin wave band gaps (topology in reciprocal space).
14.1 Introduction
Our knowledge about magnetic phenomena has a long history that can be traced
back to the 6th century B.C. when Thales of Miletus, one of the sages in ancient
Greece, told people that lodestones can attract iron. In the 4th century B.C., two
Chinese books, Master Lü’s Spring and Autumn Annual and Guiguzi reported the
same phenomenon [1]. Around 1000 A.D., Chinese people already knew how to
magnetize a normal iron needle with a lodestone and make magnetic compass (vol.
24 of Mengxi Bitan by Kuo Shen). After the industrial revolution, our understanding
of magnetism had greatly advanced. Based on the studies of Coulomb, Ampère,
Faraday, and many others, James Clerk Maxwell wrote down the famous Maxwell’s
equations in 1861 [2],
X. S. Wang
School of Physics and Electronics, Hunan University, Changsha 410082, China
X. R. Wang (B)
Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay,
Kowloon, Hong Kong
e-mail: phxwan@ust.hk
HKUST Shenzhen Research Institute, Shenzhen 518057, China
© Springer Nature Switzerland AG 2021
E. Kamenetskii (ed.), Chirality, Magnetism and Magnetoelectricity,
Topics in Applied Physics 138,
https://doi.org/10.1007/978-3-030-62844-4_14
357