Direct observation of multiferroic vortex domains in YMnO3

Abstract

Topological vortices with swirling ferroelectric, magnetic and structural anti-phase relationship in hexagonal RMnO3 (R = Ho to Lu, Y, and Sc) have attracted much attention because of their intriguing behaviors. Herein, we report the structure of multiferroic vortex domains in YMnO3 at atomic scale using state-of-the-art aberration-corrected scanning transmission electron microscopy (STEM). Two types of displacements were identified among six domain walls (DWs); six translation-ferroelectric domains denoted by α+, γ-, β+, α-, γ+ and β-, respectively, were recognized, demonstrating the interlocking nature of the anti-vortex domain. We found that the anti-vortex core is about four unit cells wide. In addition, we reconstructed the vortex model with three swirling pairs of DWs along the [001] direction. These results are very critical for the understanding of topological behaviors and unusual properties of the multiferroic vortex.

Figure 1. The models of ferroeletric, translation-ferroelectric unit cell and the topology of experimental anti-vortex.

a. Ferroelectric unit cell and its projection along the [001] and [100] directions, yellow and blue spheres represent Y_up and Y_down atoms, respectively. The grey spheres represent Mn atoms and the navy blue spheres represent O atoms. b. The translation relationship among three translation domains (α+, β+, γ+) are labeled by the three parallelograms along [001]. Six translation-ferroelectric unit cells with different origins and up-down configuration denoted by α+, β−, γ+, α−, β+and γ−, respectively. The yellow circles with a dot and blue circles with a cross represent Y_up and Y_down atoms, respectively. c. Dark-field image of the anti-vortex domains along the [100] direction observed in our experiments. Bright and dark contrasts indicate opposite polarizations. α+, γ−, β+, α−, γ+ and β− are used to characterize the anti-vortex topology. d. The domain walls structures of α+β− and β−α+ configurations along [001] and [100] directions. The α+ and β− domains are indicated by different background colors. The same polarized unit cells are marked by broken rectangles. Two types of domain walls (Type I and Type II) with different translations can be idenfied. A black ruler with lattice periodicity projected along the [100] direction are added to illustrate their translation relationship.

Figure 2. HAADF image of the anti-vortex domains.

Yellow and blue rectangles are used to mark the upward and downward polarized unit cells, respectively. The yellow upward and blue downward arrows indicate the different direction of polarization, respectively. Two white horizontal lines are superposed on the image to identify the relative translation relationship among α, β and γ domains. The DWs are marked by red dotted lines and the red circle is used to mark the region of the vortex core. The types of six DWs are also outlined by the white vertical lines, labeled by type-I and type-II. The schematics of the three translation domains are presented at the bottom. The broken rectangles are used to indicate the same polarized unit cells. The black ruler are scaled by the lattice periodicity projected along the [100] direction. The positions of the broken rectangles relative to the short vertical lines in the black ruler reflect their translation relationship.

Figure 3. The cartoon displaying the distribution of the vortex in three dimensions.

The anti-vortex α⁺-γ⁻-β⁺-α⁻-γ⁺-β⁻ along the [100] direction turns to be the vortex α⁺-β⁻-γ⁺-α⁻-β⁺-γ⁻ along the [001] direction. Yellow and blue regions represent upward and downward polarized domains. The red dotted line indicates the topology of the vortex in three dimensions.

Figure 4. The reconstructed model of the vortex domains along the [001] direction.

The red dotted lines and the circle indicate the locations of DWs and the core of the vortex, respectively. The yellow circles with a dot and the blue circles with a cross represent Y_up and Y_down atoms, respectively. The green circles represent Y atoms at the paraelectric position. Black parallelograms are used to outline the unit cell of translation domain in each domain, representing α+, β−, γ+, α−, β+ and γ−, respectively. TW_I + FEW and TW_II + FEW are used to label two types of translation-ferroelectric DWs.