### BIT Makes Significant Advances in Topological Magneto-optical Effects and Their Quantization

** Beijing Institute of Technology, Jan 13 ^{th}, 2020:** Recently, professor Yao Yugui, associate professor Feng Wanxiang of School of Physics of Beijing Institute of Technology (BIT) and their team members have made significant advances in topological magneto-optical effects and their quantization. Using methods of efficient model analysis and first-principles to study chiral noncoplanar antiferromagnetic systems, they found that the magneto-optical signal, that is, topological magneto-optical effects, can still be present in the absence of two necessary conditions -- band exchange splitting and spin-orbit coupling (figure 1), which was totally different from the conventional magneto-optical effects. In addition, topological magneto-optical effects can be quantized in the low frequency limit, that is, topological quantum magneto-optical effects. Topological and quantum topological magneto-optical effects represent new topological light-matter interactions, opening up a new research direction in the field of magneto-optical effects. The findings were published in Nature Communications 11, 118 (2020).

Figure 1 (a) topological magneto-optical effects induced by scalar spin chirality. (b) noncoplanar antiferromagnetic spin structures in three-dimensional face-centered cubic lattices. (c) noncoplanar antiferromagnetic spin structures in two-dimensional triangular lattices. (d) the unit sphere formed after four noncoplanar spins are transported in parallel.

Magneto-optical effects are one of the most basic experimental phenomena in solid-state physics, showing that when light interacts with magnetism, the polarization state of light will change. In 1846, Michael Faraday discovered the first magneto-optical phenomenon, that is, when linearly polarized light passes through a set of glass slices placed in an external magnetic field, the polarization plane of the transmitted light deflects at an angle to the incident light；then in 1877 John Kerr discovered that the polarized plane of reflected light on the surface of iron will undergo a similar deflection. Magneto-optical effects, represented by the Faraday and Kerr effects, not only helped in establishing Maxwell‘s theory of electromagnetism in the late 19th century but also promoted the application for an exquisite technology for modern high-density data storage since the 1950s of last century. At present, magneto-optical effects are a kind of widely used spectral analysis technology, which can be used to detect magnetic domain motion, dynamically manipulate magnetic sequence, measure cruise magnetism in two-dimensional materials and so on.

Magneto-optical effects have been known for more than 150 years, the physical origin of which has been always thought to be band exchange splitting and spin-orbit coupling, both of which are indispensable. Band exchange splitting is essentially due to the Zeeman effect of spontaneous magnetization in external magnetic field or magnetic material, then the spin-orbit coupling further splits the bands so that the orbital motion of spin-polarized electrons couples to incident polarized light. In the past, it was thought that band exchange splitting and spin-orbit coupling must exist simultaneously in order to allow for different degrees of absorption of left-handed and right-polarized light in magnetic materials, resulting in a series of magneto-optical phenomena such as Faraday and Kerr effects.

In this work, through effective model analysis and first-principles calculations, we theoretically found that in spin noncoplanar antiferromagnets (such as FeMn alloy and K0.5RhO2), the occurrence of magneto-optical effects can be independent of band exchange splitting and spin-orbit coupling. Analogous to Topological Houle effect, we called this novel magneto-optical effect "topological magneto-optical effects". Topological magneto-optical effects and conventional magneto-optical effects can be identified by integrating specific physical quantities such as Kerr Point, Cape Faraday, and the real part of magneto-optical conductivity. Specifically, the spectrum integral of topological magneto-optical effects is proportional to the chirality of scalar spin; the spectrum integral of the traditional magneto-optical effects is proportional to the anisotropic energy of the magnetic crystal. In addition, we found in the two-dimensional noncoplanar antiferromagnets that topological magneto-optical effects can be quantized under the low-frequency limit, namely "quantum topological magneto-optical effect", which is expressed as: Kerr rotational angle is exactly 90 degrees, the Faraday rotation angle amounts to the product of Chen number and fine structure constant. The physical origin of topological and quantum topological magneto-optical effects is the nonzero scalar spin chirality, which represents a new topological interaction between light and matter, completely different from the conventional light-matter interaction. The current experimental conditions can fully realize the experimental measurement of topological and quantum topological magneto-optical effects. It is expected that some experimental work will confirm our theoretical prediction in the near future.

The work was supported by National Natural Science Foundation of China and the National Key Research and Development Program of Ministry of Science. In particular, the research team would like to thank professor Stefan Blügel, associate professor Yuriy Mokrousov, Dr.Jan-Philipp Hanke of Juelich Research Center, Germany, professor Guo Guangyu of National Taiwan University and other collaborators for their strong support and cooperation.

[1] Wanxiang Feng, Jan-Philipp Hanke, Xiaodong Zhou, Guang-Yu Guo, Stefan Blugel, Yuriy Mokrousov, and Yugui Yao. “Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets”. Nature Communications 11, 118 (2020).

**Article link: **https://www.nature.com/articles/s41467-019-13968-8

**News Source: **School of Physics

**Editor: **News Agency of BIT, Liu Lirui

**Translation: ** News Agency of BIT