Heat capacity jump at $T_c$ and pressure derivatives of superconducting transition temperature in the Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($0.2\le x\le 1.0$) series

We present the evolution of the initial (up to $\sim$10 kbar) hydrostatic pressure dependencies of $T_c$ and of the ambient pressure jump in the heat capacity associated with the superconducting transition as a function of K doping in the Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ family of iron-based superconductors. The pressure derivatives show a weak but distinct anomaly near $x\sim 0.7$. In the same concentration region, $\Delta C_p{|}_{T_c}$ deviates from the $\Delta C_p\propto T^3$ scaling found for most BaFe${}_2$As${}_2$-based superconductors. These results are consistent with a possible significant modification of the superconducting state, occurring near $x\sim 0.7$.

Figure 1

Example of temperature-dependent magnetization (zero-field-cooled, taken in 25 Oe applied magnetic field) of Ba${}_{0.4}$K${}_{0.6}$Fe${}_2$As${}_2$ measured at 1.5, 3.9, 6.5, and 11.1 kbar. The criterion for $T_c$ (for $P=11.1$ kbar curve as an example) used in this work is shown by the arrow. Superconducting transitions in Pb used as a pressure gauge are seen near 7 K.

Figure 2

Summary plot of the pressure dependence of $T_c$ for the samples studied in this work. Dashed lines are linear fits to the data except for the $x=0.2$ where the fit is a second-order polynomial. These lines are extended to $P=0$. Stars are the $T_c$ values obtained in the analysis of the ambient pressure heat capacity data below.

Figure 3

$d\left(\ln T_c\right)/dP$, $d{T}_c/dP$, and $T_{c0}$ (top to bottom) as a function of K concentration in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$. Symbols: stars are the data of this work, triangle are the data for KFe${}_2$As${}_2$ from Ref. 44, and circles are the data for four underdoped samples obtained by linear fits of the first three-four data points under pressure in Ref. 47. $T_{c0}$ values are taken from the linear fits of $T_c\left(P\right)$. Two symbols for $x=0.6$ correspond to measurements on two samples of slightly differing quality. Dashed line is a guide for the eye.

Figure 4

K concentration dependence of the normalized pressure derivatives, $d\left(\ln T_c\right)/dP=\frac{1}{T_{c0}}d{T}_c/dP$ (left axis, circles), and the normalized concentration derivatives, $d\left(\ln T_c\right)/dx=\frac{1}{T_{c0}}d{T}_c/dx$ (right axis, triangles) of the superconducting transition temperatures. Dashed line corresponds to the shared zero on $Y$ axes.

Figure 5

Temperature-dependent heat capacity of Ba${}_{0.2}$K${}_{0.8}$Fe${}_2$As${}_2$ plotted as $C_p/T$ vs $T$. Criteria for $T_c$ and $\Delta C_p{|}_{T_c}$ (isoentropic construct) are shown.

Figure 6

$\Delta C_p$ at the superconducting transition vs $T_c$ for the Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ series, plotted together with literature data for various FeAs-based superconducting materials. Updated plot[44] is used to show the literature data. The line corresponds to $\Delta C_p\propto T_c^3$. Numbers near the symbols are K concentration $x$. Two symbols for $x=0.6$ correspond to measurements on two samples of slightly differing quality.