Impurity effects on the normal-state transport properties of ${\mathrm{Ba}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$ superconductors

We investigated the normal-state resistivity ${\rho }_{xx}\left(T\right)$ and the Hall effect in Zn- and Co-doped ${\mathrm{Ba}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single-crystalline microbridges. A crossover temperature $T^{*}$ was observed in the temperature dependency of the longitudinal resistivity ${\rho }_{xx}\left(T\right)$, which separates ${\rho }_{xx}\left(T\right)$ into temperature-linear and temperature-nonlinear regions. Above $T^{*}$, the carriers in ${\mathrm{Ba}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$ and Co-doped ${\mathrm{Ba}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_{1.94}{\mathrm{Co}}_{0.06}{\mathrm{As}}_2$ demonstrate electronlike behavior and an anomalous nonlinear magnetic field dependence of the Hall voltage with a sign reversal. By contrast, the Zn-doped ${\mathrm{Ba}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_{1.94}{\mathrm{Zn}}_{0.06}{\mathrm{As}}_2$ behaves like a hole type and the Hall coefficient is independent of the magnetic field. The field-induced sign reversal of the Hall coefficient of undoped and Co-doped samples depends on the field modification on the mobility and hole/electron concentration ratio. The $T^2$-dependent Hall angle of a nonmagnetic Zn-doped crystal is observed as a nearly parallel shift from that of the impurity-free crystal in the low-temperature region, indicating that the Zn induces a weak change of the spinons excitations, while increasing the number of scattering centers. The Co works as a nonmagnetic impurity as well, while it provides both spinons excitations and impurity scattering.

Figure 1

A SEM image of a typical microbridge. The magnetic field was initially applied along the c axis, then the sample was rotated along the axis of longitudinal current $I_{xx}$. Thus, the effective magnetic fields can be adjusted and the change of Lorentz force can be avoided as well.

Figure 2

Temperature dependencies of ${\rho }_{xx}$ for BK, BKZn, and BKCo. The blue dotted lines indicate the T-linear fitting for $\rho \left(T\right)$ as $\rho \left(T\right)={\rho }_0+kT$, and the red lines correspond to the T-nonlinear $\rho \left(T\right)$ fitting as $\rho \left(T\right)={\rho }_0+A{T}^n$. The fitting parameters are given in Table 1.

Figure 3

Magnetoresistivity ${\rho }_{xx}\left(H\right)$ for (a) BKZn and (b) BKCo. The pulsed magnetic field was up to 45 T, and applied along the c axis.

Figure 4

Magnetic field dependence of ${\rho }_{xy}$ for BK, BKZn, and BKCo; ${\rho }_{xy}$ was calculated as ${\rho }_{xy}\left(H\right)=[{\rho }_{xy}\left(H^{+}\right)-{\rho }_{xy}\left(H^{-}\right)]/2$ from the deviation from longitudinal resistances under positive and negative fields.

Figure 5

Contour plots of $R_H$ for BK, BKZn, and BKCo as a function of magnetic field and temperatures. The white dotted line separates regions demonstrating field-dependent (right) and field-independent (left) regions for $R_H\left(H\right)$.

Figure 6

Contours of $n_{\mathrm{eff}}$ for BK, BKZn, and BKCo as a function of magnetic field and temperature. The $n_{\mathrm{eff}}$ per Fe ion is estimated from $n_{\mathrm{eff}}=nV$, where $V$ is the volume per Fe ion and $n=1/e{R}_H$ is the carrier density. The white dotted line separates field-dependent (right) and field-independent (left) regions for $n_{\mathrm{eff}}\left(H\right)$.

Figure 7

Cotangent of the Hall angle cot${\Theta }_H={\rho }_{xx}/{\rho }_{xy}$ for a systematic set of BK, BKZn, and BKCo samples. The low-temperature data ($<$140 K) can be fitted by a square law cot${\Theta }_H$ = $\alpha T^2+C$ and are given by dotted lines in (b).