Incommensurate Spin-Density Modulation in a Copper Oxide Chain Compound with Commensurate Charge Order

Neutron diffraction has been used to determine the magnetic structure of ${\mathrm{Na}}_8{\mathrm{Cu}}_5{\mathrm{O}}_{10}$, a stoichiometric compound containing chains based on edge-sharing ${\mathrm{CuO}}_4$ plaquettes. The chains are doped with $2/5$ hole per Cu site and exhibit long-range commensurate charge order with an onset well above room temperature. Below $T_N=23\mathrm{K}$, the neutron data indicate long-range collinear magnetic order with a spin-density modulation whose propagation vector is commensurate along, and incommensurate perpendicular to, the chains. Competing interchain exchange interactions are discussed as a possible origin of the incommensurate magnetic order.

Figure 1

(a) Nuclear unit cell and spin structure of ${\mathrm{Na}}_8{\mathrm{Cu}}_5{\mathrm{O}}_{10}$. (b) Cut of the lattice structure along the $ab$ plane, showing inequivalent copper sites and superexchange parameters, as explained in the text.

Figure 2

High-resolution neutron powder diffraction pattern of ${\mathrm{Na}}_8{\mathrm{Cu}}_5{\mathrm{O}}_{10}$ at room temperature. The upper line shows the result of the Rietveld refinement discussed in the text. The positions of nuclear Bragg reflections are indicated. The bottom curve gives the difference between the calculated and measured intensities.

Figure 3

Low-angle segment of the high-flux powder diffraction pattern measured at 1.4 K (red points). The upper line shows the results of the Rietveld refinement discussed in the text. The upper (lower) marks indicate the positions of nuclear (magnetic) Bragg reflections. The bottom curve gives the difference between the calculated and measured intensities. The inset shows the result of a refinement based on a commensurate spin structure.

Figure 4

Integrated intensities of the $(\mp 0.5\mp \alpha ,1,\pm 0.5\pm \beta )-$ and ($0.5-\alpha$, 0, $0.5+\beta$) magnetic Bragg reflections as a function of temperature. The line is the result of a power-law fit.