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; Youwen Long

doi:10.1038/s41467-022-29764-w

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

Nat Commun. 2022 May 2;13(1):2373. doi: 10.1038/s41467-022-29764-w.

Authors

Guangxiu Liu^#^{1

2}, Maocai Pi^#^{3

4}, Long Zhou¹, Zhehong Liu^{1

2}, Xudong Shen^{1

5}, Xubin Ye^{1

2}, Shijun Qin^{1

2}, Xinrun Mi^{3

4}, Xue Chen^{3

4}, Lin Zhao^{1

2}, Bowen Zhou^{1

2}, Jia Guo^{1

2}, Xiaohui Yu^{1

2}, Yisheng Chai^{6

7}, Hongming Weng^{8

9

10}, Youwen Long^{11

12

13}

Affiliations

¹ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
² School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
³ Center of Quantum Materials and Devices, Chongqing University, Chongqing, China.
⁴ Low Temperature Physics Laboratory and Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China.
⁵ Songshan Lake Materials Laboratory, Dongguan, Guangdong, China.
⁶ Center of Quantum Materials and Devices, Chongqing University, Chongqing, China. yschai@cqu.edu.cn.
⁷ Low Temperature Physics Laboratory and Chongqing Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics, Chongqing University, Chongqing, China. yschai@cqu.edu.cn.
⁸ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China. hmweng@iphy.ac.cn.
⁹ School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China. hmweng@iphy.ac.cn.
¹⁰ Songshan Lake Materials Laboratory, Dongguan, Guangdong, China. hmweng@iphy.ac.cn.
¹¹ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China. ywlong@iphy.ac.cn.
¹² School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China. ywlong@iphy.ac.cn.
¹³ Songshan Lake Materials Laboratory, Dongguan, Guangdong, China. ywlong@iphy.ac.cn.

^# Contributed equally.

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.