Thermoelectric power of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ and Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$: Possible changes of Fermi surface with and without changes in electron count

Temperature-dependent, in-plane, thermoelectric power (TEP) data are presented for Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ ($0⩽x⩽0.36$) single crystals. The previously outlined $x-T$ phase diagram for this system is confirmed. The analysis of TEP evolution with Ru doping suggests significant changes in the electronic structure, correlations, and/or scattering occurring near $~$$7\%$, $~$$30\%,$ and possibly $~$$20\%$ of Ru-doping levels. These results are compared with an extended set of TEP data for the electron-doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ series for which initial angle-resolved photoemission spectroscopy and transport studies have identified $x~0.02$ as the concentration at which the Lifshitz transition takes place. In addition to $x~0.02$ the Co levels of $x\approx 0.11$ and 0.22 are identified as concentrations at which similar changes occur.

Figure 1

In-plane TEP of the Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ ($0⩽x⩽0.36$) single crystals. The plot is divided into three panels for clarity. The curves for $x=0.073$ and $x=0.21$ are each repeated on two panels for continuity.

Figure 2

(a) Derivatives $\mathit{dS}/\mathit{dT}$ for representative concentrations, with the structural/magnetic transition temperatures marked with arrows. The data for $x=0.060$ and $x=0.126$ are shifted along the y axis by 0.4 and 0.8 $\mu$V/K${}^2$ for clarity. (b) Low temperature $S(T)$ curves for $0.21⩽x⩽0.36$ with the $T_c$ criteria marked with arrows (see text for details).

Figure 3

(a) $x-T$ phase diagram for Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ obtained from the TEP measurements. $T_s/T_m$ denotes the structural/magnetic transition, and $T_c$, the superconducting transition. The lines through the experimental points are guides for the eye. The criteria used are explained in the text. The open triangles show $T_c$ from $S=0$ criterion. The horizontal lines correspond to 25, 50, and 150 K. (b) $x$-dependent TEP of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ at fixed, 25, 50, 150, and 200 K temperatures. Arrows mark the regions of anomalous $S(x)|{}_{T=\mathrm{const}}$ behavior. (c) Low-temperature values of $S/T$ for non-superconducting Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ samples. Error bars correspond to $\pm \sigma$ (standard deviation) in Ru concentration as determined by WDS. The $\sigma$ values vary from $0.5\times {10}^{-3}$ for low Ru dopings to $0.025$ at high Ru dopings. See Ref. 31 for details.

Figure 4

Low temperature part of in-plane TEP of the non-superconducting Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ ($0⩽x⩽0.161$) single crystals.

Figure 5

In-plane TEP of the Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ ($0.13⩽x⩽0.42$) single crystals.

Figure 6

(a) $x-T$ phase diagram for Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ obtained from the TEP measurements. $T_s/T_m$ denotes the structural/magnetic transitions shown here, schematically as a single line; $T_c$ denotes the superconducting transition. Lines through the experimental points are guides for the eye. The criteria used are explained in the text. The horizontal lines correspond to 25, 50, and 150 K. (b) $x$-dependent TEP of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ at fixed, 25, 50, 150, and 200 K temperatures. Arrows mark the regions of anomalous $S(x)|{}_{T=\mathrm{const}}$ behavior. (c) Low-temperature values of $S/T$ for non-superconducting Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples.