Domain walls and ferroelectric reversal in corundum derivatives

Domain walls are the topological defects that mediate polarization reversal in ferroelectrics, and they may exhibit quite different geometric and electronic structures compared to the bulk. Therefore, a detailed atomic-scale understanding of the static and dynamic properties of domain walls is of pressing interest. In this work, we use first-principles methods to study the structures of ${180}^{\circ }$ domain walls, both in their relaxed state and along the ferroelectric reversal pathway, in ferroelectrics belonging to the family of corundum derivatives. Our calculations predict their orientation, formation energy, and migration energy and also identify important couplings between polarization, magnetization, and chirality at the domain walls. Finally, we point out a strong empirical correlation between the height of the domain-wall-mediated polarization reversal barrier and the local bonding environment of the mobile $A$ cations as measured by bond-valence sums. Our results thus provide both theoretical and empirical guidance for future searches for ferroelectric candidates in materials of the corundum derivative family.

Figure 1

Structure of ordered-LNO corundum derivatives $A_{2}B{B}^{\prime }{\mathrm{O}}_6$ and of LNO-type $AB{\mathrm{O}}_3$ corundum derivatives if $B^{\prime }=B$. Octahedra containing $A, B$, and $B^{\prime }$ cations are shown in violet, brown, and green, respectively. (a) Side view of the rhombohedral unit cell. ${\xi }_1$ (or ${\xi }_2$) is the vertical distance between an $A$ cation and the oxygen plane that it penetrates during the polarization reversal. (b) Top view of the $AB$ layer and (c) side view in the enlarged hexagonal-setting cell.

Figure 2

Illustration of domains and DWs in ordered-LNO materials. FE DWs are formed between $\mathrm{R}\Uparrow$ domains and $\mathrm{L}\Downarrow$ domains. The DW between adjacent thumbs represents ${\mathrm{DW}}_{\Downarrow \Uparrow }$, and the DW between adjacent little fingers represents ${\mathrm{DW}}_{\Uparrow \Downarrow }$. Left and right hands represent left (L) and right (R) chirality, and the direction in which the fingers point ($\Uparrow$ or $\Downarrow$) represents the polarization direction.

Figure 3

Structures of the X-wall in the 6+6 supercell (left) and the Y-wall in the 4+4 supercell (right). (a) and (b) Top views of the X-wall and Y-wall. The number in each octahedron is the unit-cell label. The X-wall lies in the $x-z$ or $\left(01\overline{1}0\right)$ plane and is located between the sixth and the seventh unit cells, as shown by the dashed yellow line. The Y-wall lies in the $y-z$ or $\left(2\overline{1}\overline{1}0\right)$ plane and is located between the fourth and the fifth unit cells. (c) and (d) Side views of the X-wall and Y-wall. Odd-number cells are behind even-number cells in the X-wall. (e) and (f) The ${\xi }_1+{\xi }_2$ displacement profile of an X-wall and a Y-wall.

Figure 4

Two possible magnetic orders at FE DWs in $A_{2}B{B}^{\prime }{\mathrm{O}}_6$. In ${\mathrm{Mn}}_3{\mathrm{WO}}_6$ the $A_1, A_2$, and $B$ cations are all Mn, and $B^{\prime }$ is W. The structure in the center has polarization and magnetization ($+\mathrm{P}, +\mathrm{M}$) with the magnetic order $udu$. The structures on the left and right both have polarization $-\mathrm{P}$, but the left one has the magnetic order $udu$, while the right one is $dud$. In case 1, the FE DW is formed between structures in the center and on the left. In case 2, the FE DW is formed by the central and rightward structures.

Figure 5

Illustration of magnetoelectric coupling at FE DWs when $udu-dud$ is favored. (a) Magnetization direction is coupled to the polarization direction in different FE domains. (b) When the polarization is reversed by an electric field, the magnetization reverses as well.

Figure 6

DW-mediated FE reversal in corundum derivatives. (a) and (b) Illustrations of DW motions in 4+4 and 3+4 supercells. The upward and downward arrows represent the polarization in each unit cell. The dashed blue line represents ${\mathrm{DW}}_{\Downarrow \Uparrow }$, and the solid green line is ${\mathrm{DW}}_{\Uparrow \Downarrow }$. The filled black arrows represent the polarization that is reversed during the DW motion. (c) Energy profile of the DW reversal in ${\mathrm{LiTaO}}_3$ and the evolution of ${\xi }_1$ and ${\xi }_2$. The dashed brown lines highlight the positions where ${\xi }_1=0$ and ${\xi }_2=0$. (d) Energy profiles of the DW reversal for selected corundum derivatives. The results of both ${\mathrm{DW}}_{\Downarrow \Uparrow }$ and ${\mathrm{DW}}_{\Uparrow \Downarrow }$ are included for ${\mathrm{Li}}_2{\mathrm{ZrTeO}}_6$. Energy units are meV per unit cell.

Figure 7

Scatterplot of DW-mediated reversal barrier versus normalized $A$-cation bond-valence sum (i.e., divided by valence charge). The linear fit is of the form $y=a+b(x-1)$, with $a=157$ meV and $b=1883$ meV.