Ferroelectrically Induced Weak Ferromagnetism by Design

We present a strategy to design structures for which a polar lattice distortion induces weak ferromagnetism. We identify a large class of multiferroic oxides as potential realizations and use density-functional theory to screen several promising candidates. By elucidating the interplay between the polarization and the Dzyaloshinskii-Moriya vector, we show how the direction of the magnetization can be switched between 180° symmetry equivalent states with an applied electric field.

Figure 1

Paraelectric $AB{\mathrm{O}}_3$, space group, $R\overline{3}c$. $A$-site: Wyckoff position 2a, site symmetry 32. $B$-site: Wyckoff position 2b, site symmetry $\overline{3}$. Oxygen-site (not shown): Wyckoff position 6d, site symmetry $\overline{1}$. Note, the unique point symmetries of the $A$ and $B$ sites are due to their location with respect to the O site.

Figure 2

Chiral nature of the $S_1\mathrm{\text{−}}\mathrm{O}\mathrm{\text{−}}{S}_2$ bonds; (left) Polarization-up and (right) Polarization-down. (middle) Paraelectric state showing two equivalent interplanar pathways, e.g., $S_1\mathrm{\text{−}}{\mathrm{O}}_A\mathrm{\text{−}}{S}_2$ and $S_1\mathrm{\text{−}}{\mathrm{O}}_B\mathrm{\text{−}}{S}_2$. Note: $\mathbf{D}\parallel \mathbf{P}$, $\mathbf{L}\perp \mathbf{M}\perp \mathbf{P}$.

Figure 3

Superexchange pathways, $S_1\mathrm{\text{−}}{\mathrm{O}}_A\mathrm{\text{−}}{S}_2$ and $S_1\mathrm{\text{−}}{\mathrm{O}}_B\mathrm{\text{−}}{S}_2$, between nearest neighbor spins. The net Dzyaloshinski-Moriya vector, ${\mathbf{D}}_{12}$, contains two contributions, ${\mathbf{D}}_A$ and ${\mathbf{D}}_B$, that cancel in the paraelectric phase.