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 $\sigma \left(\omega \right)$ and the temperature dependence of the magnetic susceptibility $\chi \mathrm{}\left(T\right)\mathrm{}$ 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 $\sigma \left(\omega \right)$ 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.

• Received 29 August 1997

DOI:https://doi.org/10.1103/PhysRevB.57.5326