Electric polarization induced by a proper helical magnetic ordering in a delafossite multiferroic $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$

We have established the relationship between the electric polarization vector and the local spin arrangement including vector spin chirality in delafossite multiferroic $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$. The results of polarized neutron diffraction and pyroelectric measurements demonstrate that proper helical magnetic ordering in $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$ induces a spontaneous electric polarization parallel to the vector spin chirality. This result cannot be explained by the Katsura-Nagaosa-Balatsky model, which successfully explains the ferroelectricity in recently explored ferroelectric helimagnets, such as $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$. We thus conclude that $\mathrm{Cu}{\mathrm{Fe}}_{1-x}{\mathrm{Al}}_x{\mathrm{O}}_2$ is another type of multiferroic.

Figure 1

(Color online) Schematic illustrations of the experimental configurations and the relationship between the direction of the poling electric field $E$ and the proper helical magnetic structure in the FEIC phase for (a) the $E_{\parallel \left[110\right]}$ sample and (b) the $E_{\parallel \left[1\overline{1}0\right]}$ sample.

Figure 2

(Color online) (a) The hexagonal basis represented on the ${\mathrm{Fe}}^{3+}$ triangular lattice layer. The open and filled blue circles denote ${\mathrm{O}}^{2-}$ ions located above and below the ${\mathrm{Fe}}^{3+}$ layer, respectively. (b) The location of the magnetic reflections surveyed in the present measurement in the $\left(HHL\right)$ zone. [(c-1)–(f-2)] The diffraction profiles of $(H,H,\frac{3}{2})$ reciprocal lattice scans for the $(q,q,\frac{3}{2})$ and $(\frac{1}{2}-q,\frac{1}{2}-q,\frac{3}{2})$ magnetic Bragg reflections at $T=2\mathrm{K}$ in the FEIC phase.

Figure 3

(Color online) (a) The relationship between the vector spin chirality and the direction of the electric polarization. (b) The temperature variations of the electric polarization along the [110] and $\left[1\overline{1}0\right]$ axes measured after cooling with a poling electric field parallel to the [110] and $\left[1\overline{1}0\right]$ directions, respectively. (c) The temperature dependence of $I_{\text{on}}-I_{\text{off}}$ measured on heating after cooling with a poling electric field $(120\mathrm{kV}∕\mathrm{m})$ parallel to the [110] axis. [(d) and (e)] The schematic drawings of the distributions of the RH- (filled arrows) and LH- (open arrows) helical orderings among magnetic domains with three equivalent propagation wave vectors, $(q,q,\frac{3}{2})$, $(-2q,q,\frac{3}{2})$, and $(q,-2q,\frac{3}{2})$, when the macroscopic electric polarization emerges along (d) the [110] axis and (e) the $\left[1\overline{1}0\right]$ axis. The directions of the arrows denote the (001) projection of the three modulation wave vectors. The size of the arrows shows the fractions of the RH- or LH-helical orderings.

Figure 4

(Color online) (a) Temperature variations of the electric polarization along the [110] axis measured after cooling under various poling electric fields along the [110] axis. [(b)–(d)] The poling electric field dependence of (b) the spontaneous electric polarization, (c) $(I_{\text{on}}-I_{\text{off}})∕(I_{\text{on}}+I_{\text{off}})$, and (d) $(I_{\text{on}}+I_{\text{off}})$ at $T=2\mathrm{K}$. The colored solid lines are guides for the eyes.