Multiferroicity in Rare-Earth Nickelates $R{\mathrm{NiO}}_3$

We show that charge ordered rare-earth nickelates of the type $R{\mathrm{NiO}}_3$ ($R=\mathrm{Ho}$, Lu, Pr and Nd) are multiferroic with very large magnetically-induced ferroelectric (FE) polarizations. This we determine from first principles electronic structure calculations. The emerging FE polarization is directly tied to the long-standing puzzle of which kind of magnetic ordering is present in this class of materials: its direction and size indicate the type of ground-state spin configuration that is realized. Vice versa, the small energy differences between the different magnetic orderings suggest that a chosen magnetic ordering can be stabilized by cooling the system in the presence of an electric field.

Figure 1

Schematic view of the charge and magnetic ordered (a) $S$-type, (b) $T$-type, and (c) $N$-type noncollinear magnetic structure of $R{\mathrm{NiO}}_3$. ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Ni}}^{4+}$ are shown in red and orange. Arrows represent Ni spins. In (a) and (b), the zigzag spin chains are indicated. In (c), the FM planes perpendicular to [101] are highlighted. The vector $\mathbf{P}$ shows the direction of polarization obtained in our calculations.

Figure 2

Schematic arrangement of oxygen-induced dipoles and resulting FE polarization for the $P{2}_1/n$ crystal structure, in the top layer of Figs. 1a, 1b.

Figure 3

Ferroelectric polarization after an elementary translation along the $c$ axis, corresponding to the second layer Fig. 1, for (a) $S$- and (b) $T$-type magnetic ordering.