Ferroelectricity in corundum derivatives

The search for new ferroelectric (FE) materials holds promise for broadening our understanding of FE mechanisms and extending the range of application of FE materials. Here we investigate a class of $AB{\mathrm{O}}_3$ and $A_{2}B{B}^{\prime }{\mathrm{O}}_6$ materials that can be derived from the $X_2{\mathrm{O}}_3$ corundum structure by mixing two or three ordered cations on the $X$ site. Most such corundum derivatives have a polar structure, but it is unclear whether the polarization is reversible, which is a requirement for a FE material. In this paper, we propose a method to study the FE reversal path of materials in the corundum derivative family. We first categorize the corundum derivatives into four classes and show that only two of these allow for the possibility of FE reversal. We then calculate the energy profile and energy barrier of the FE reversal path using first-principles density functional methods with a structural constraint. Furthermore, we identify several empirical measures that can provide a rule of thumb for estimating the energy barriers. Finally, the conditions under which the magnetic ordering is compatible with ferroelectricity are determined. These results lead us to predict several potentially new FE materials.

Figure 1

Structure of corundum derivatives. The unit cell in the rhombohedral setting is shown at the left; an enlarged hexagonal-setting view is shown at right. The cations $\alpha ,\beta ,\gamma$, and $\delta$ are all identical in the $X_2{\mathrm{O}}_3$ corundum structure. For the LNO-type $AB{\mathrm{O}}_3,\beta =\delta =A,\alpha =\gamma =B$; for the ilmenite $AB{\mathrm{O}}_3,\beta =\gamma =A,\alpha =\delta =B$; for the ordered-LNO $A_{2}B{B}^{\prime }{\mathrm{O}}_6,\beta =\delta =A,\gamma =B,\alpha =B^{\prime }$; for the ordered-ilmenite $A_{2}B{B}^{\prime }{\mathrm{O}}_6,\beta =\gamma =A,\delta =B,\alpha =B^{\prime }$. At left, ${\xi }_1$ (or ${\xi }_2)$ is the distance between $\beta$ (or $\delta )$ and the oxygen plane that it penetrates during the polarization reversal.

Figure 2

Structural evolution along the polarization reversal path of the LNO-type and the ordered-LNO corundum derivatives. “Before” and “After” are the initial and final structures on the reversal path with symmetry R3c for the LNO-type and R3 for the ordered-LNO corundum derivatives; “Midpoint” denotes the structure halfway between these and exhibits $\mathrm{R}\overline{3}$ structural symmetry in both cases.

Figure 3

Movements of $A$ cations in LNO-type (red, here $\mathrm{LiNb}{\mathrm{O}}_3)$ and ordered-LNO (blue, here ${\mathrm{Mn}}_2\mathrm{FeW}{\mathrm{O}}_6)$ corundum derivatives along the polarization reversal path. ${\xi }_1$ and ${\xi }_2$ are the distances from $A$ atoms to the oxygen planes that are penetrated during the polarization reversal, here rescaled to a range between $-1$ and 1. The symmetry at an arbitrary $({\xi }_1,{\xi }_2)$ point is R3; on the ${\xi }_1={\xi }_2$ and ${\xi }_1=-{\xi }_2$ diagonals it is raised to R3c and $\mathrm{R}\overline{3}$, respectively; and at the origin $\left({\xi }_1={\xi }_2=0\right)$ it reaches $\mathrm{R}\overline{3}\mathrm{c}$. Green diamonds denote the midpoint structure in the parameter space. In the LNO-type case “path1” and “path2” (filled and open red square symbols) are equivalent and equally probable, while the ordered-LNO system deterministically follows “path1” (full blue line), which becomes “path2” (dashed blue) under a relabeling ${\xi }_1\leftrightarrow {\xi }_2$.

Figure 4

The polarization reversal energy profile for $\mathrm{LiNb}{\mathrm{O}}_3,\mathrm{LiTa}{\mathrm{O}}_3,{\mathrm{Mn}}_2\mathrm{FeW}{\mathrm{O}}_6,{\mathrm{Zn}}_2\mathrm{FeOs}{\mathrm{O}}_6$, and ${\mathrm{Li}}_2\mathrm{ZrTe}{\mathrm{O}}_6$.

Figure 5

Empirical proportionality between the coherent FE energy barrier and $P_{\mathrm{S}}^2$. The red curve is the fitting polynomial $E_{\mathrm{barrier}}=(\mu /2)P_{\mathrm{S}}^2$, with $\mu /2$ = 0.057 meV ${\mathrm{cm}}^4/\mu {\mathrm{C}}^2$.

Figure 6

Empirical correlation between the spontaneous polarization and the reaction coordinate $\xi$ in the ground state. The red curve is the fitting polynomial $P_{\mathrm{S}}=m{\xi }_{\mathrm{S}}+n{\xi }_{\mathrm{S}}^3$ with $m=13.3\times {10}^8\mu \text{C}$/${\mathrm{cm}}^3$ and $n=19.0\times {10}^{24}\mu \text{C}$/${\mathrm{cm}}^5$.