Electron transport and anisotropy of the upper critical magnetic field in a $\mathrm{Ba_{0.68}K_{0.32}Fe_2As_2}$ single crystals

Early work on the iron-arsenide compounds supported the view, that a reduced dimensionality might be a necessary prerequisite for high-$T_{c}$ superconductivity. Later, however, it was found that the zero-temperature upper critical magnetic field, $H_{c2}(0)$, for the 122 iron pnictides is in fact rather isotropic. Here, we report measurements of the temperature dependence of the electrical resistivity, $\rho(T)$, in $\mathrm{Ba_{0.5}K_{0.5}Fe_{2}As_{2}}$ and $\mathrm{Ba_{0.68}K_{0.32}Fe_{2}As_{2}}$ single crystals in zero magnetic field and for $\mathrm{Ba_{0.68}K_{0.32}Fe_{2}As_{2}}$ as well in static and pulsed magnetic fields up to 60 T. We find that the resistivity of both compounds in zero field is well described by an exponential term due to inter-sheet umklapp electron-phonon scattering between light electrons around the $M$ point to heavy hole sheets at the $\Gamma$ point in reciprocal space. From our data, we construct an $H-T$ phase diagram for the inter-plane ($H\parallel {c}$) and in-plane ($H\parallel {ab}$) directions for $\mathrm{Ba_{0.68}K_{0.32}Fe_{2}As_{2}}$. Contrary to published data for underdoped {\textrm 122} FeAs compounds, we find that $H_{c2}(T)$ is in fact anisotropic in optimally doped samples down to low temperatures. The anisotropy parameter, $\gamma=H^{ab}_{c2}/H^{c}_{c2}$, is about $2.2$ at $T_{c}$. For both field orientations we find a concave curvature of the $H_{c2}$ lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism we perfectly can describe $H_{c2}$ and its anisotropy.