Evidence for multiple gaps in the specific heat of LiFeAs crystals

The zero-field specific heat of LiFeAs was measured on several single crystals selected from a bulk sample. A sharp $\Delta C_{\text{p}}/T_{\text{c}}$ anomaly $\approx 20\text{mJ}/\text{mole}{\text{K}}^2$ was observed. The value appears to be between those of $\text{SmFeAs}\left({\text{O}}_{0.9}{\text{F}}_{0.1}\right)$ and $\left({\text{Ba}}_{0.6}{\text{K}}_{0.4}\right){\text{Fe}}_2{\text{As}}_2$ but bears no clear correlation with their Sommerfeld coefficients. The electronic specific heat below $T_{\text{c}}$ further reveals a two-gap structure with the narrower one only on the order of 0.7 meV. While the results are in rough agreement with the $H_{\text{c}1}\left(T\right)$ previously reported on both LiFeAs and $\left({\text{Ba}}_{0.6}{\text{K}}_{0.4}\right){\text{Fe}}_2{\text{As}}_2$, they are different from the published specific-heat data of a $\left({\text{Ba}}_{0.6}{\text{K}}_{0.4}\right){\text{Fe}}_2{\text{As}}_2$ single crystal.

Figure 1

(a) XRD pattern of LiFeAs bulk sample that exhibits preferred orientation along (001). The data were collected with $\text{Cu}K\alpha$ lines. The small impurity peaks belong to ${\text{FeAs}}_2$. (b) Magnetization of similar LiFeAs single crystals selected from the bulk samples.

Figure 2

The reproducibility of the data with error bars representing the standard deviations of 4–8 sequential repeat measurements. The small dots and large open circles are the data of the first run and the second run (1 day later) on the crystals, respectively. The solid line represents the data of a large piece of the parent sample. Inset: the deviations of the above individual data points from their smoothed average.

Figure 3

The observed $C_{\text{p}}/T$ (triangles with error bars representing the standard deviations of 4–8 sequential repeat measurements) and entropy $S$ (inverted triangles) of a LiFeAs single crystal. Solid line: the expected normal-state $C_{\text{p},\mathit{n}}/T$ from the fitting. Inset: the $C_{\text{p}}/T$ observed up to 160 K with error bars representing the standard deviations of 4–8 sequential repeat measurements. The thick lines are the fits from Eq. (1). The upper and lower thin dashed lines are the Debye and Einstein contributions, respectively.

Figure 4

(a) The $C_{\text{p}}/T$ observed between 2.2 and 5 K (open circles with error bars representing the standard deviations of 4–8 sequential repeat measurements) and the data below 2.2 K (solid circles with error bars representing the standard deviations of 4–8 sequential repeat measurements), which may be less reliable due to the small crystal mass (see text). The solid line is the linear fit of ${\gamma }_0+{\beta }_3^{\prime }{T}^2$ below 4 K and the dot-dashed line assumes no electronic contribution below $T_{\text{l}}$. (b) The $\Delta C_{\text{p}}/T$ below $T_{\text{c}}$. A thermodynamic $T_{\text{c}}\approx 15.4\text{K}$ and a jump $\Delta C_{\text{p}}/T\approx 20\text{mJ}/\text{mole}{\text{K}}^2$ around $T_{\text{c}}$ are estimated through linear extrapolations (solid lines).

Figure 5

Comparison of the electronic $C_{\text{p},\mathit{e}}/\left(\gamma -{\gamma }_0\right)T$ observed with models. Circles with error bars representing the standard deviations of 4–8 sequential repeat measurements: data; solid lines: the $\alpha$ model fits with two $s$-wave gaps; dashed lines: fits with single $s$-wave gap; dot-dashed line: the expected low-$T$ approximation of single $d$-wave gap in Ref. 21. (a) At ${\gamma }_0=3\text{mJ}/\text{mole}{\text{K}}^2$. (b) At ${\gamma }_0=0\text{mJ}/\text{mole}{\text{K}}^2$. (c) At ${\gamma }_0=6.2\text{mJ}/\text{mole}{\text{K}}^2$.