Correlation between Spin Helicity and an Electric Polarization Vector in Quantum-Spin Chain Magnet ${\mathrm{LiCu}}_2{\mathrm{O}}_2$

Measurements of polarized neutron scattering were performed on a $S=1/2$ chain multiferroic ${\mathrm{LiCu}}_2{\mathrm{O}}_2$. In the ferroelectric ground state with the spontaneous polarization along the $c$ axis, the existence of transverse spiral spin component in the $bc$ plane was confirmed. When the direction of electric polarization is reversed, the vector spin chirality as defined by ${\mathbf{C}}_{ij}={\mathbf{S}}_i\times {\mathbf{S}}_j$ ($i$ and $j$ being the neighboring spin sites) is observed to be reversed, indicating that the spin-current model or the inverse Dzyaloshinskii-Moriya mechanism is applicable even to this $e_g$-electron quantum-spin system. Differential scattering intensity of polarized neutrons shows a large discrepancy from that expected for the classical-spin $bc$-cycloidal structure, implying the effect of large quantum fluctuation.

Figure 1

(a) Crystal structure of ${\mathrm{LiCu}}_2{\mathrm{O}}_2$. (b) Schematic view of magnetic interactions between ${\mathrm{Cu}}^{2+}$ sites. (c),(d) Temperature dependence of magnetic susceptibility, electric polarization, and dielectric constant. All the quantities were measured in the warming process.

Figure 2

The experimental geometries for the polarized neutron diffraction: (a) ${\mathbf{S}}_n\perp \mathbf{Q}$ and (b) ${\mathbf{S}}_n\parallel \mathbf{Q}$. The labels “on” and “off” indicate the state of the neutron-spin flipper. (c) Schematic illustration of nuclear and magnetic Bragg positions in the reciprocal space. (d) The $k$-scan profiles of the (1.5, $+\delta$, 0) magnetic reflection in the ${\mathbf{S}}_n\perp \mathbf{Q}$ setup.

Figure 3

(a)–(d) The $k$-scan profiles of the (1.5, $\pm \delta$, 0) magnetic reflections in the ${\mathbf{S}}_n\parallel \mathbf{Q}$ setup. The labels on and off show the state of neutron-spin flipper. Solid lines show the result of the Gaussian fitting. (e),(f) The geometrical relationships between spin chirality (helicity) and electric polarization determined from the observed results.