Hall Effect and Resistivity Study of the Magnetic Transition, Carrier Content, and Fermi-Liquid Behavior in $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$

The negative Hall constant $R_H$ measured all over the phase diagram of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ allows us to show that electron carriers always dominate the transport properties. The evolution of $R_H$ with $x$ at low doping ($x<2\%$) indicates that important band structure changes happen for $x<2\%$ prior to the emergence of superconductivity. For higher $x$, a change with $T$ of the electron concentration is required to explain the low $T$ variations of $R_H$, while the electron scattering rate displays the $T^2$ law expected for a Fermi liquid. The $T=0$ residual scattering is affected by Co disorder in the magnetic phase, but is rather dominated by incipient disorder in the paramagnetic state.

Figure 1

Temperature dependence of the in-plane resistivity $\rho (T)$ of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ single crystals. For the sake of clarity, the data for the undoped parent and low doped non SC samples, which evolve differently than for higher Co content, are plotted with dashed lines. Notice the singularities associated with the SDW transitions.

Figure 2

$T$ variation of the Hall number $|n_H|$ for a selected set of samples. Here, $n_H$ $(e/\mathrm{Fe})=0.32\times {10}^{-9}/R_H({\mathrm{m}}^3/\mathrm{C})$. For the undoped compound, the drop below $T_{\mathrm{SDW}}$ occurs in two steps, the value on the plateau indicated by an arrow being $0.074e/\mathrm{Fe}$. Inset: Raw data for the magnetic samples showing the drops of $R_H$ at $T_{\mathrm{SDW}}$. The data for the most overdoped sample have been kept for comparison.

Figure 3

Phase diagram of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ where $T_{SDW}$ (▾) has been taken at the minimum of $d\rho /dT$[27]. (■): values of $n_e$ determined at low $T$ for $x\ge 4\%$. The linear fit (full line) extrapolates for x=0 to 0.07, close to the value (●) of the intermediate plateau of $|n_H(T)|$ (arrow in Fig. 2). Extrapolations from the paramagnetic phase (▴), assuming $T^2$ variations for $n_H(T)$ as found for higher $x$, allow us to conjecture the evolution of $n_e$ (dash line) which would take place below $x=0.03$ in the absence of magnetic ordering.

Figure 4

(a) $T$ variation of $\cot ({\Theta }_H=\rho /|R_H|)$ at 1 T. (b) This quantity, which reduces to $(m_e/m_0/)/\tau$ if ${\sigma }_h\ll {\sigma }_e$, is plotted versus $T^2$ in the paramagnetic phase for $x\gtrsim 4$%. This evidences a Fermi-liquid behavior for $T\le 150\mathrm{K}$. Inset: Coefficient $B$ of the $T^2$ variation versus $n_e$ in logarithmic scales. The line corresponds to $B\propto 1/n_e$.