Figure 1

(a) Ground-state $P{2}_1/n$ structure and (b) the ferroelectric $R3$ structure of the double perovskites Bi${}_2$MnReO${}_6$ and Bi${}_2$NiReO${}_6$. Bi${}^{3+}$ cations are depicted as the large (brown) spheres and ${\mathrm{O}}^{2-}$ as the small (red) spheres. Re${}^{4+}$ and Mn${}^{2+}$ (Ni${}^{2+}$) are alternating in the shaded octahedra, in a three-dimensional checkerboard manner (this is indicated by the color of the octahedra). While in the $P{2}_1/n$ symmetry the Bi${}^{3+}$ cations form an “antipolar” pattern, their coherent shift along the [111] direction can be clearly seen in the $R3$ structure.Reuse & Permissions

Figure 2

(a) Distorted Bi${}_2$MnReO${}_6$ and Bi${}_2$NiReO${}_6$ obtained from the $R3$ (red circles) and $P{2}_1/n$ (blue triangles) structure by constraining the two in-plane lattice vectors to be equal and the angle between them to 90${}^{°}$. The out-of-plane parameter and the ionic positions were relaxed. The energies are positioned with respect to the bulk unconstrained $P{2}_1/n$ ground state (blue squares). The red diamonds show the energies for the unconstrained $R3$ structure. A crossover between the antipolar (AP) and the ferroelectric (FE) state occurs at 1.8% (with respect to the minimum of the FE curve) of compressive strain in Bi${}_2$MnReO${}_6$. Note that the energy of the $R3$ state lies on the strain curve for Bi${}_2$MnReO${}_6$, but is somewhat lower for Bi${}_2$NiReO${}_6$, due to the choice of a square in-plane lattice: the rhombohedral angle in $R3$ phase of Bi${}_2$MnReO${}_6$ is 60${}^{°}$, while in Bi${}_2$NiReO${}_6$ it is 61${}^{°}$. (b) Similar to (a), with an addition of a Hubbard $U$ on Mn (3 eV) and Ni (6 eV) $3d$ states. The shaded area shows the AP-FE crossover region.Reuse & Permissions

Figure 3

Density of states (DOS) of the ferroelectric phase of Bi${}_2$MnReO${}_6$ (a) and Bi${}_2$NiReO${}_6$ (b). The local magnetic moments on Mn/Ni and Re are antialigned. Thin black line, total DOS; green dashed line, Re; orange solid line, Mn/Ni.Reuse & Permissions