Diverse topological defects arise in hexagonal manganites, such as ferroelectric vortices, as well as neutral and charged domain walls. The topological defects are intriguing because their low symmetry enables unusual couplings between structural, charge, and spin degrees of freedom, holding great potential for novel types of functional 2D and 1D systems. Despite the considerable advances in analyzing the different topological defects in hexagonal manganites, the understanding of their key intrinsic properties is still rather limited and disconnected. In particular, a rapidly increasing number of structural variants is reported without clarifying their relation, leading to a zoo of seemingly unrelated topological textures. Here, we combine picometer-precise scanning-transmission-electron microscopy with Landau theory modeling to clarify the inner structure of topological defects in Er_1–xZr_xMnO₃. By performing a comprehensive parametrization of the inner atomic defect structure, we demonstrate that one primary length scale drives the morphology of both vortices and domain walls. Our findings lead to a unifying general picture of this type of structural topological defects. We further derive novel fundamental and universal properties, such as unusual bound-charge distributions and electrostatics at the ferroelectric vortex cores with emergent U(1) symmetry.

中文翻译：

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六方锰矿中的拓扑缺陷：内部结构和新兴的静电学。

六方锰矿中会出现各种拓扑缺陷，例如铁电涡旋以及中性和带电畴壁。拓扑缺陷之所以令人着迷，是因为它们的低对称性使结构，电荷和自旋自由度之间出现异常耦合，为新型2D和1D功能型系统提供了巨大的潜力。尽管在分析六方锰矿中不同的拓扑缺陷方面取得了长足的进步，但是对它们的关键内在特性的理解仍然相当有限且不连贯。特别是，报道了数量迅速增加的结构变体而未弄清它们之间的关系，从而导致了看似无关的拓扑结构的动物园。这里，_{1– x} Zr _x MnO ₃。通过对内部原子缺陷结构进行全面的参数化，我们证明了一个主要的长度尺度驱动了涡旋和畴壁的形态。我们的发现导致对这种类型的结构拓扑缺陷的总体了解。我们进一步得出新颖的基本和通用特性，例如异常的束缚电荷分布和具有U（1）对称性的铁电涡流核上的静电。