Electronic structure, magnetic, and dielectric properties of the edge-sharing copper oxide chain compound ${\text{NaCu}}_2{\text{O}}_2$

We report an experimental study of ${\text{NaCu}}_2{\text{O}}_2$, a Mott insulator containing chains of edge-sharing ${\text{CuO}}_4$ plaquettes, by polarized x-ray absorption spectroscopy (XAS), resonant magnetic x-ray scattering (RMXS), magnetic susceptibility, and pyroelectric current measurements. The XAS data show that the valence holes reside exclusively on the ${\text{Cu}}^{2+}$ sites within the copper-oxide spin chains and populate a $d$ orbital polarized within the ${\text{CuO}}_4$ plaquettes. The RMXS measurements confirm the presence of incommensurate magnetic order below a Néel temperature of $T_N=11.5\text{K}$, which was previously inferred from neutron powder-diffraction and nuclear-magnetic-resonance data. In conjunction with the magnetic-susceptibility and XAS data, they also demonstrate an “orbital” selection rule for RMXS that is of general relevance for magnetic-structure determinations by this technique. Dielectric property measurements reveal the absence of significant ferroelectric polarization below $T_N$, which is in striking contrast to corresponding observations on the isostructural compound ${\text{LiCu}}_2{\text{O}}_2$. The results are discussed in the context of current theories of multiferroicity.

Figure 1

(Color online) Sketch of the orthorhombic crystal structure of ${\text{NaCu}}_2{\text{O}}_2$ (space group $Pnma$). The room-temperature lattice parameters are $a=6.2087\text{Å}$, $b=2.9343\text{Å}$, and $c=13.0548\text{Å}$ (Ref. 30).

Figure 2

(Color online) Polarization-dependent x-ray absorption spectra around the Cu $L_3$- and $L_2$-absorption edges of ${\text{NaCu}}_2{\text{O}}_2$. $\theta$ denotes the angle between the incident wave vector and the sample surface, which was parallel to the $ab$ plane (see lower right inset). The origins of the peaks $P_1$, $P_2$, and $P_3$ are discussed in the text. The inset shows the $\theta$ dependence of the intensity of peak $P_2$ on an larger scale.

Figure 3

(Color online) Temperature dependence of the magnetic susceptibility along the principal crystallographic axes measured with a magnetic field $H=1000\text{Oe}$. The inset highlights the data at low temperature.

Figure 4

(Color online) (a) Temperature dependence of the intensity of the magnetic Bragg reflection at $\mathbf{Q}=\left(0.5\xi 0\right)$, extracted from fits to RMXS data. (b) $b$-axis component of $\mathbf{Q}$ as a function of temperature.

Figure 5

Energy dependence of the scattered intensity at the (0.5 0.227 0) magnetic reflection near the Cu $L_3$-absorption edge. The data were taken at $T=3\text{K}$. The dotted lines at 931.6 and 934.3 eV represent the energies of the ${\text{Cu}}^{2+}$ and ${\text{Cu}}^{1+}$ absorption edges, which were extracted from the widths of longitudinal momentum scans through the magnetic reflection.

Figure 6

(Color online) (a) Longitudinal reciprocal-space scans through the $\mathbf{Q}=\left(0.5\xi 0\right)$ reflection taken with horizontal (H) and vertical (V) polarization of the incident x-ray beam. The data for V polarization were multiplied by 100. (b) Azimuthal-angle $\left(\Psi \right)$ dependence of the ratio of Bragg-peak intensities measured with V- and H-polarized incident beams. The line is the result of a fit to the function $A{\text{sin}}^2\Psi$, as discussed in the text. A small offset in $\Psi$ was also included in the fit in order to account for imperfect sample alignment. The inset illustrates the definition of $\Psi$ and the scattering geometry of $\Psi =0°$.

Figure 7

(Color online) (a) Electrical polarization and (b) dielectric constant measured along the $c$ axis for $\mathbf{H}=0$ and 14 T applied along the three principal crystallographic directions. The data in panel (b) were shifted vertically by arbitrary amounts $<5\mathrm{\%}$ for clarity, and in order to take into account small changes in the electrode connections.