Spin-Driven Ferroelectricity in Triangular Lattice Antiferromagnets $A{\mathrm{CrO}}_2$ ($A=\mathrm{Cu}$, Ag, Li, or Na)

The correlation between the dielectric and magnetic properties is investigated on the triangular-lattice antiferromagnets $A{\mathrm{CrO}}_2$ ($A=\mathrm{Cu}$, Ag, Li, or Na) with a 120-degree spiral structure. For the $A=\mathrm{Cu}$ and Ag compounds with a delafossite structure, the ferroelectric polarization emerges with a spiral-spin order, implying strong coupling between ferroelectricity and the spiral-spin structure. For the $A=\mathrm{Li}$ and Na compounds with an ordered rock salt structure, on the other hand, no spontaneous polarization is discerned, while the clear anomaly in the dielectric constant can be observed upon the transition to the spiral-spin ordered state. This feature can be ascribed to the possible antiferroelectric state induced by the alternate stacking of the Cr-spin sheet with opposite vector spin chirality.

Figure 1

Crystal structure of $A{\mathrm{CrO}}_2$ : (a) delafossite structure ($A=\mathrm{Cu}$ or Ag) and (b) ordered rock salt structure ($A=\mathrm{Li}$ or Na).

Figure 2

Temperature dependence of magnetic susceptibility $\chi$, dielectric constant $\epsilon$, and electric polarization $P$ for (a)–(c) ${\mathrm{CuCrO}}_2$ and (d)–(f) ${\mathrm{AgCrO}}_2$ with delafossite structure. (g)–(i) Magnetic field dependence of magnetization $M$, dielectric constant, and electric polarization for ${\mathrm{CuCrO}}_2$. For (i), electric poling was performed at 0T. In (c), (f), and (i), the magnitude and sign of poling electric field are also indicated. $H_{\parallel }$ and $H_{\perp }$ indicate the magnetic field parallel and perpendicular to the direction of electric field.

Figure 3

(a) Symmetry elements in the $A{\mathrm{CrO}}_2$ system with space group $R\overline{3}m$: twofold rotation axis (2), reflection mirror ($m$), and threefold rotation axis along the $c$-axis with inversion center (triangle with small circle). ${\mathrm{O}}^{2-}$ site above (below) the ${\mathrm{Cr}}^{3+}$ layer is indicated as closed (open) circle. (b), (c) Symmetry elements compatible with the 120° spin structure with (b) (110) spiral plane or (c) ($1\overline{1}0$) spiral plane. The thick bars (orange online, left panel) indicate the spin-spiral plane. Electric polarization expected from the spin-current model along each chain is also indicated, such as $\pm P_0$ and $-(\alpha /2)P_0$ (see text).

Figure 4

Temperature profiles of specific heat capacity $C$, dielectric constant $\epsilon$, and electric polarization $P$ for (a)–(c) ${\mathrm{LiCrO}}_2$ and (d)–(f) ${\mathrm{NaCrO}}_2$ with ordered rock salt structure.