Helicoidal magnetic order in the spin-chain compound ${\mathrm{NaCu}}_2{\mathrm{O}}_2$

We report susceptibility, specific heat, and neutron diffraction measurements on ${\mathrm{NaCu}}_2{\mathrm{O}}_2$, a spin-$1∕2$ chain compound isostructural to ${\mathrm{LiCu}}_2{\mathrm{O}}_2$, which has been extensively investigated. Below 12 K, we find a long-range ordered, incommensurate magnetic helix state with a propagation vector similar to that of ${\mathrm{LiCu}}_2{\mathrm{O}}_2$. In contrast to the Li analog, substitutional disorder is negligible in ${\mathrm{NaCu}}_2{\mathrm{O}}_2$. We can thus rule out that the helix is significantly influenced by impurities. A spin Hamiltonian with frustrated longer-range exchange interactions provides a good description of both the ordered state and the paramagnetic susceptibility.

Figure 1

(Color online) (a) Crystal structure, and (b) proposed magnetic structure of ${\mathrm{NaCu}}_2{\mathrm{O}}_2$. In panel (b), the most important magnetic interactions within a chain pair are sketched.

Figure 2

(Color online) Temperature dependence of the static magnetic susceptibility of a powder sample of ${\mathrm{NaCu}}_2{\mathrm{O}}_2$ in a magnetic field $B=0.1\mathrm{T}$ (open circles). The thick red line is the result of a fit to the helix model described in the text, whereas the blue line (dot-dashed, mostly hidden by the red one) is the (exact) susceptibility of the 1D-Heisenberg chain $(J_2=85\mathrm{K})$ (Ref. 18). For comparison, the green line represents the result of a fit to a simpler $J_1\text{−}{J}_2$ helix model (see text). The inset shows the actually measured data, from which a Curie contribution ${\chi }_{\mathit{Cur}}=0.0105∕\mathrm{T}$ has been subtracted to obtain the data presented in the main panel. Note that the Curie tail is very weak, providing testimony to the high quality of the sample.

Figure 3

Single-crystal data for ${\mathrm{NaCu}}_2{\mathrm{O}}_2$ as a function of temperature. (a) Susceptibility taken with a magnetic field of 0.1 T applied along the principal crystallographic axes. (b) Specific heat for two applied magnetic fields: 0 T (open circles) and 9 T (full circles). The inset extends the temperature range.

Figure 4

Difference of neutron diffraction data collected at 2 and 20 K (open circles). The extra reflections at low temperature are all of magnetic origin. The solid line is a fit to a spiral model in the $bc$ plane with propagation vector $(0.5,\zeta ,0)$ with $\zeta =0.227$. The temperature dependence of the $(0.5,\zeta ,1)$ reflection is plotted in the inset together with a fit of the intensity to a power law.