Comprehensive study of out-of-plane transport properties in BaFe$_{2}$As$_{2}$: Three-dimensional electronic state and effect of chemical substitution

We investigated the out-of-plane transport properties of parent and chemically substituted BaFe$_{2}$As$_{2}$ for various types of substitution. Based on the studies of Hall coefficient and chemical-substitution effect, we have clarified the origin for the unusual temperature dependence of out-of-plane resistivity $\rho_c(T)$ in the high-temperature paramagnetic-tetragonal phase. Electron (hole) carriers have an incoherent (coherent) character, which is responsible for non-metallic (metallic) $\rho_c(T)$. Although both of electron and hole contributions are almost comparable, a slightly larger contribution comes from electrons at high temperatures, while from holes at low temperatures, resulting in a maximum in $\rho_c(T)$. In the low-temperature antiferromagnetic-orthorhombic phase, the major effect of substitution is to increase the residual-resistivity component, as in the case for the in-plane transport. In particular, Co atoms substituted for Fe give rise to strong scattering with large $\mathit{ac}$ anisotropy. We found that K substitution induces a non-metallic behavior in $\rho_c(T)$ at low temperatures, which is likely due to a weakly localized nature along the $c$-axis direction.