Determining the Short-Range Spin Correlations in the Spin-Chain ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ and ${\mathrm{CuGeO}}_3$ Compounds Using Resonant Inelastic X-Ray Scattering

We report a high-resolution resonant inelastic soft x-ray scattering study of the quantum magnetic spin-chain materials ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ and ${\mathrm{CuGeO}}_3$. By tuning the incoming photon energy to the oxygen $K$ edge, a strong excitation around 3.5 eV energy loss is clearly resolved for both materials. Comparing the experimental data to many-body calculations, we identify this excitation as a Zhang-Rice singlet exciton on neighboring ${\mathrm{CuO}}_4$ plaquettes. We demonstrate that the strong temperature dependence of the inelastic scattering related to this high-energy exciton enables us to probe short-range spin correlations on the 1 meV scale with outstanding sensitivity.

Figure 1

Experimental geometry for (left) ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ and (right) ${\mathrm{CuGeO}}_3$. (a) XAS measured at the oxygen $K$ edge for ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ with $\sigma$-polarized light at 20 K and (b) for ${\mathrm{CuGeO}}_3$ measured with $\pi$-polarized light at 40 K (using the total fluorescence yield). Preedge peaks are related to the upper Hubbard band. (c) RIXS spectra (on an energy loss scale) measured at the oxygen $K$ edge for ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ with $\sigma$ polarization at 20 K and (d) for ${\mathrm{CuGeO}}_3$ with $\pi$ polarization at 40 K. The incident energies used for the different spectra are indicated by full triangles on the corresponding XAS spectra in graphs (a) and (b). The RIXS spectra are normalized to the acquisition time.

Figure 2

Schematic illustration of how a ZRS exciton is created in the RIXS process at the oxygen $K$ edge. See text for detailed explanations. Unoccupied states are depicted with empty orbitals.

Figure 3

(a) Temperature dependent RIXS data for ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ measured with $\sigma$ polarization and an excitation energy of 530.1 eV and (b) for ${\mathrm{CuGeO}}_3$ measured with $\pi$ polarization and an excitation energy of 530.8 eV. The spectra are plotted in an energy loss scale. The spectra have been normalized to the area of the $dd$ excitations (see Supplemental Material [35]). The integrated intensity of the ZRS peaks as a function of temperature is displayed in the corresponding insets.

Figure 4

(a) Partial RIXS intensity ${\mathcal{I}}_i$ calculated from the ground state (black line) of a ${\mathrm{Cu}}_3{\mathrm{O}}_8$ cluster and the two excited states (red and green lines), respectively, for ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ and (b) for ${\mathrm{CuGeO}}_3$. Using the same color code, a schematic representation of the eigenstates and corresponding eigenenergies is shown. (c), Total RIXS signal $\mathcal{I}(T)$ as a function of temperature for ${\mathrm{Li}}_2{\mathrm{CuO}}_2$ and (d) ${\mathrm{CuGeO}}_3$ (Fig. S3 of the Supplemental Material shows analogous results for a ${\mathrm{Cu}}_5{\mathrm{O}}_{12}$ cluster for comparison).