Electronic States and Magnetic Propertis of Edge-sharing Cu-O Chains

The electronic states and magnetic properties for the copper oxides containing edge-sharing Cu-O chains such as Li$_2$CuO$_2$, La$_6$Ca$_8$Cu$_{24}$O$_{41}$ and CuGeO$_3$ are systematically studied. The optical conductivity $\sigma(\omega)$ and the temperature dependence of the magnetic susceptibility $\chi(T)$ for single crystalline samples Li$_2$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 $\sigma(\omega)$ 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-$T_{c}$ 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.