Doping dependence of the specific heat of single-crystal BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$

We present specific heat measurements on a series of BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ single crystals with phosphorous doping ranging from $x$ $=$ 0.3 to $x$ $=$ 0.55. Our results reveal that BaFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ follows the scaling $\Delta C/T_c\approx T_c^2$ remarkably well. The clean-limit nature of this material imposes additional restraints on theories aimed at explaining the scaling. Furthermore, we find that the Ginzburg-Landau parameter decreases significantly with doping whereas the superconducting anisotropy is $\Gamma$ ≈ 2.6, independent of doping.

Figure 1

Temperature dependence of the specific heat of ${\mathrm{BaFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2$, $x=0.3$. The dashed line indicates the extrapolation of the normal state background. Lower inset: Temperature dependence of the magnetization of the crystals measured in 1 G∥$c$ after cooling in zero field. Top inset: Picture of a cleaved single crystal displaying a shiny and flat surface.

Figure 2

Temperature dependence of the eletronic specific heat of BaFe${}_2$(As${}_{0.7}$P${}_{0.3}$)${}_2$ (a), (b) and BaFe${}_2$(As${}_{0.5}$P${}_{0.5}$)${}_2$ (c), (d) near the superconducting transition in various fields applied parallel to the $c$ axis and parallel to the $ab$ plane. The solid lines in (a) illustrate the entropy conserving construction used to determine the transition temperature.

Figure 3

Dependence of the superconducting anisotropy parameter $\Gamma$ and the $c$-axis Ginzburg-Landau parameter ${\kappa }_c$ on $T_c$.

Figure 4

Dependence of the upper critical field slope and of the specific heat anomaly on $T_c^2$.

Figure 5

Compilation of $\Delta C$/$T_c$ vs $T_c$ values of various Fe-based superconductors plotted on log-log scales (reference numbers are in brackets). The line indicates a quadratic dependence. See also Refs. 5, 6, and 22.