Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice

Guangxiu Liu, Maocai Pi, Long Zhou, Zhehong Liu, Xudong Shen, Xubin Ye, Shijun Qin, Xinrun Mi, Xue Chen, Lin Zhao, Bowen Zhou, Jia Guo, Xiaohui Yu, Yisheng Chai (), Hongming Weng () and Youwen Long ()
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Guangxiu Liu: Institute of Physics, Chinese Academy of Sciences
Maocai Pi: Chongqing University
Long Zhou: Institute of Physics, Chinese Academy of Sciences
Zhehong Liu: Institute of Physics, Chinese Academy of Sciences
Xudong Shen: Institute of Physics, Chinese Academy of Sciences
Xubin Ye: Institute of Physics, Chinese Academy of Sciences
Shijun Qin: Institute of Physics, Chinese Academy of Sciences
Xinrun Mi: Chongqing University
Xue Chen: Chongqing University
Lin Zhao: Institute of Physics, Chinese Academy of Sciences
Bowen Zhou: Institute of Physics, Chinese Academy of Sciences
Jia Guo: Institute of Physics, Chinese Academy of Sciences
Xiaohui Yu: Institute of Physics, Chinese Academy of Sciences
Yisheng Chai: Chongqing University
Hongming Weng: Institute of Physics, Chinese Academy of Sciences
Youwen Long: Institute of Physics, Chinese Academy of Sciences

Nature Communications, 2022, vol. 13, issue 1, 1-8

Abstract: Abstract Topology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn3Cr4O12 (A = La and Tb) reside on the topological Roman surface—a non-orientable two-dimensional manifold formed by sewing a Möbius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Möbius strip or orientable disc, depending on the spin evolution as controlled by an external magnetic field. Experimentally, the periodicity of polarization can be the same or twice that of the rotating magnetic field, which is consistent with the orientability of the disc and the Möbius strip, respectively. This path-dependent topological magnetoelectric effect presents a way to detect the global geometry of a surface and deepens our understanding of topology in both mathematics and physics.

Date: 2022
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DOI: 10.1038/s41467-022-29764-w

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