Liu Guangxiu, Pi Maocai, Zhou Long, Liu Zhehong, Shen Xudong, Ye Xubin, Qin Shijun, Mi Xinrun, Chen Xue, Zhao Lin, Zhou Bowen, Guo Jia, Yu Xiaohui, Chai Yisheng, Weng Hongming, Long Youwen
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
Nat Commun. 2022 May 2;13(1):2373. doi: 10.1038/s41467-022-29764-w.
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 AMnCrO (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.
拓扑学作为数学的一个重要分支，是描述拓扑态和相变的理想理论工具。许多拓扑概念在由拓扑不变量确定的实空间或倒易空间中找到了它们的物理实体，这些拓扑不变量通常定义在可定向曲面上，如环面和球面。研究更有趣的不可定向曲面的可能物理实现是很自然的。在此，我们表明立方钙钛矿氧化物AMnCrO（A = La和Tb）中自旋诱导的铁电极化集存在于拓扑罗马曲面上——一种通过将莫比乌斯带边缘缝到圆盘边缘而形成的不可定向二维流形。诱导极化可能会沿着不可定向的莫比乌斯带或可定向的圆盘循环传播，这取决于由外部磁场控制的自旋演化。在实验中，极化的周期性可以与旋转磁场的周期性相同或为其两倍，这分别与圆盘和莫比乌斯带的可定向性一致。这种依赖路径的拓扑磁电效应提供了一种检测表面全局几何形状的方法，并加深了我们对数学和物理中拓扑学的理解。
