Multigap superconductivity in single crystals of Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$: A calorimetric investigation

We investigate the electronic properties and the superconducting gap characteristics of a single crystal of hole-doped 122 Fe-pnictide Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$ by means of specific-heat measurements. The specific heat exhibits a pronounced anomaly around the superconducting transition temperature $T_c$ $=$ 29.4 K and a small residual part at low temperature. In a magnetic field of 90 kOe, the transition is broadened and $T_c$ is lowered insignificantly by an amount $\sim$1.5 K. We estimate a high electronic coefficient in the normal state with a value 57.5 mJ mol${}^{-1}$ K${}^{-2}$, being consistent with hole-doped 122 compounds. The temperature-dependent superconducting electronic specific heat cannot be described with single-gap BCS theory under the weak-coupling approach. Instead, our analysis implies a presence of two $s$-wave-like gaps with magnitudes ${\Delta }_1\left(0\right)/k_B{T}_c$ $=$ 1.06 and ${\Delta }_2\left(0\right)/k_B{T}_c$ $=$ 2.08 with respective weights of $48\%$ and 52%. While our results have qualitative similarities with other hole-doped 122 materials, the gap's magnitude and their ratio are quite different.

Figure 1

(a) The volume susceptibility ${\chi }_{\mathrm{vol}}$ after demagnetization correction has been plotted as function of temperature. The ${\chi }_{\mathrm{vol}}$ has been deduced from the dc magnetization measured with $H\left|\right|c$ $=$ 20 Oe following ZFC and FC protocols for Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$. The inset shows the similarly deduced ${\chi }_{\mathrm{vol}}$ with $H\left|\right|ab$ plane ($H$ $=$ 5 Oe). (b) The same data in the main panel of (a) have been plotted without demagnetization correction.

Figure 2

Temperature dependence of the specific heat $C/T$ measured in 0 and 90 kOe for Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$ and BaFe${}_2$As${}_2$. The inset shows $C/T$ vs $T^2$. The straight lines represent linear fits to $C/T$ $=$ $\gamma$ $+$ $\beta T^2$ (see text).

Figure 3

The electronic specific heat $C_{\mathrm{el}}/T$ as a function of temperature for the sample Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$. ${\gamma }_n$ and ${\gamma }_r$ represent the normal-state and residual electronic coefficients of the specific heat. The inset shows the entropy in the normal and superconducting states as a function of temperature.

Figure 4

The normalized superconducting electronic specific heat ($C_{\text{el-s}}/{\gamma }_{n}T$) of Ba${}_{0.65}$Na${}_{0.35}$Fe${}_2$As${}_2$ as a function of reduced temperature $t=T/T_c$. The dashed line represents the theoretical curve based on single-band weak-coupling BCS theory with the $s$-wave gap $\Delta \left(0\right)/k_B{T}_c$ $=$ 1.76, following Eq. (4) and (5). The solid lines represent the curves of the two $s$-wave gap models (see text).