Electronic states and magnetic properties of edge-sharing Cu-O chains

The electronic states and magnetic properties for the copper oxides containing edge-sharing Cu-O chains such as ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$, ${\mathrm{La}}_{6}{\mathrm{Ca}}_{8}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$, and ${\mathrm{CuGeO}}_{3}$ are systematically studied. The optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ and the temperature dependence of the magnetic susceptibility $\ensuremath{\chi}(T)$ for single-crystalline samples ${\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$ are measured as a reference system and analyzed by using the exact diagonalization method for small Cu-O clusters. It is shown that the spectral distribution of $\ensuremath{\sigma}(\ensuremath{\omega})$ is different between edge-sharing and corner-sharing Cu-O-Cu bonds. The charge transfer gap in edge-sharing chains is larger than that of high-${T}_{\mathrm{c}}$ cuprates. The exchange interaction between nearest-neighbor copper ions in edge-sharing chains ${J}_{1}$ depends sensitively on the Cu-O-Cu bond angles. In addition to ${J}_{1}$, the exchange interaction between next-nearest-neighbor copper ions ${J}_{2}$ has sufficient contribution to the magnetic properties. We calculate ${J}_{1}$ and ${J}_{2}$ for all the copper oxides containing edge-sharing Cu-O chains and discuss the magnetic properties.