Fig. 1: Symmetry and topological properties of h-DyMnO3.
From: Three-dimensional imaging of topologically protected strings in a multiferroic nanocrystal
a Illustration of the crystal structure of h-DyMnO3 in the paraelectric phase, shown with 4 × 1 unit cells. A single unit cell is highlighted by the shaded green region. b Crystal structure of the centrosymmetric paraelectric phase of h-DyMnO3 projected normal to the c-axis. Arrows indicate the resulting displacement of oxygen ions due to tilting of MnO5 polyhedra during the trimerisation transition into the low temperature ferroelectric phase. Tilting occurs collectively either toward (+) or away (−) from one of the central dysprosium ions (α, β or γ) leading to six symmetry-equivalent trimerisation states corresponding to the six equivalent minima of the Mexican-hat-like potential energy surface (c). Each minimum in c corresponds to the ferroelectric phase, while the high symmetry paraelectric phase is represented by the central peak. d Illustration of three-dimensional topological domains forming a vortex (front)—antivortex (back) pair connected by a topologically protected string.
