Spin-Chirality-Driven Ferroelectricity on a Perfect Triangular Lattice Antiferromagnet

Magnetic field ($B$) variation of the electrical polarization $P_c$ ($\parallel c$) of the perfect triangular lattice antiferromagnet $\mathrm{RbFe}{({\mathrm{MoO}}_4)}_2$ is examined up to the saturation point of the magnetization for $B\perp c$. $P_c$ is observed only in phases for which chirality is predicted in the in-plane magnetic structures. No strong anomaly is observed in $P_c$ at the field at which the spin modulation along the $c$ axis, and hence the spin helicity, exhibits a discontinuity to the commensurate state. These results indicate that the ferroelectricity in this compound originates predominantly from the spin chirality, the explanation of which would require a new mechanism for magnetoferroelectricity. The obtained field-temperature phase diagram of ferroelectricity agree well with those theoretically predicted for the spin chirality of a Heisenberg spin triangular lattice antiferromagnet.

Figure 1

(a) Crystal structure of $\mathrm{RbFe}{({\mathrm{MoO}}_4)}_2$ (RFMO). Fe sites form simple-stacking perfect triangular lattice layers. Each Fe-Fe nearest-neighbor bond is equivalent. (b) Top view above $T_s$ (space group $P\overline{3}m1$). (c) Top view below $T_s$ (space group $P\overline{3}$), where threefold symmetry remains. Arrows indicate the 120° spin structure below $T_N$ with positive ($+$) and negative ($-$) chirality.

Figure 2

Contour plot of the magnetic Bragg intensity in the ($h$, $h$, $l$) scattering plane for (a) $P1$ phase ($B=0$) and (b) $P2$ phase at $B=3.8\mathrm{T}$ ($B\parallel [1\overline{1}0]$). (c) Field variation of $q_z$ (magnetic periodicity along $c$) in the ordering vector ($1/3$, $1/3$, $q_z$). Vertical solid line (dotted line) indicates the $P1\text{−}P2$ ($P2\text{−}P3$) phase boundary. All the data were taken at $T=2\mathrm{K}$.

Figure 3

(a) Magnetic field variation of the magnetization $M$ and the $c$ component of the electric polarization $P_c$ of RFMO for $B\parallel$ [110] ($a$ axis). Insets indicate the expected three-sublattice spin structures in the basal plane. (b) $P_c$ (open circles) and its field derivative $d{P}_c/dB$ (open triangles) in the low-field region measured under a pulsed magnetic field. Only the field-increasing data are shown for clarity. The upward arrow for $d{P}_c/dB$ near 3.8 T indicates a tiny anomaly observed at the $P1\text{−}P2$ transition. The dot-dashed line indicates the expected variation of $P_c(B)$ assuming $P_c\propto {\sigma }_t$ (chirality model), whereas the dashed line represents the case of $P_c\propto {\sigma }_h$ (helicity model). The latter exhibits a large jump across the $P1\text{−}P2$ transition where a jump in $q_z$ from $\sim 0.41$ to $1/3$ is observed. The zero-field extrapolation of the helicity with $q_z$ fixed to $1/3$ is 2.8 times larger than that for $q_z\approx 0.45$ ($P1$), as indicated by the dotted line.

Figure 4

(a) Phase diagram of RFMO for $B\parallel$ [110] ($a$ axis) determined from $P_c(B)$, $\epsilon (T,B)$, $M(T,B)$, and specific heat $C(T,B)$ measurements. The highlighted regions indicate the ferroelectric phases ($P1$ and $P2$). Insets depict the expected in-plane spin structures. (b) Spin arrangements along the $c$ axis for $P1$ and $P2$ phases.

Figure 5

Local electrical polarization in RFMO. (a) Paramagnetic state. Thick vertical arrows indicate local electrical polarizations due to the asymmetric arrangement of the ${\mathrm{MoO}}_4$ pyramids with respect to the triangular plane. As $i$ or $S_6$ lattice symmetry ensures equal magnitude of up- and down-pointing polarizations, no macroscopic polarization appears. (b) Positive (left triangle) and negative (right triangle) spin chirality may induce a change in the magnitude of the local electrical polarization, leading to a macroscopic polarization.