Anisotropic Resistivities of Precisely Oxygen Controlled Single-Crystal ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{O}_{8+\mathit{\delta }}$: Systematic Study on ``Spin Gap'' Effect

The in-plane resistivity ${\rho }_a\left(T\right)$ and the out-of-plane resistivity ${\rho }_c\left(T\right)$ have been systematically measured for ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals with their oxygen contents precisely controlled. In the underdoped region, deviation from $T$-linear in-plane resistivity, which evidences the opening of the “spin gap,” is clearly observed, while the out-of-plane resistivity is well reproduced by the activation-type phenomenological formula ${\rho }_c\left(T\right)=(a/T)\exp (\Delta /T)+c$. In contrast to the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ system, we find that the onset of the semiconducting ${\rho }_c\left(T\right)$ does not coincide with the opening of the spin gap seen in the ${\rho }_a\left(T\right)$ in this ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ system.