Phase diagrams of K- and Na - doped BaFe$_2$As$_2$ as probed by heat capacity and hydrostatic pressure*

Many iron-arsenide based superconductors present a simple scaling of the jump in specific heat at superconducting transition temperature $T_c$ with the value of $T_c$, $\Delta C_p \propto T_c^3$ (so called BNC scaling). A comprehensive study of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ over the whole range of K - concentrations showed clear deviation from the BNC scaling for $x > 0.7$. At the same concentrations anomalous behavior was observed in NMR and thermal conductivity measurements. This observation suggests change of the superconducting state for $x > 0.7$. The pressure dependence of $T_c$ (up to $\sim 1$ GPa) is linear or close to linear for all measured K-concentrations In contrast, the data for the large portion of Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ ($0.2 \leq x \leq 0.9$) series follow the BNC scaling. In addition, the pressure dependence of $T_c$ (measured up to $\sim 1$ GPa) have clear non-linearities for Na concentration in 0.2-0.25 region, that may be consistent with an emergent, narrow, tetragonal $C4$ phase.\footnote{S. Avci et al., PRB 88, 094510 (2013).}