Effect of annealing on the specific heat of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

We report on the effect of annealing on the temperature and field dependencies of the low-temperature specific heat of the electron-doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ for under- ($x$ $=$ 0.045), optimally ($x$ $=$ 0.08), and over- ($x$ $=$ 0.105 and 0.14) doped regimes. We observed that annealing significantly improves some superconducting characteristics in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$. It considerably increases $T_c$, decreases ${\gamma }_0$ in the superconducting state, and suppresses the Schottky-like contribution at very low temperatures. The improved sample quality allows for a better identification of the superconducting gap structure of these materials. We examine the effects of doping and annealing within a self-consistent framework for an extended $s$-wave pairing scenario. At optimal doping our data indicate that the sample is fully gapped, while for both under- and overdoped samples significant low-energy excitations remain, possibly consistent with a nodal structure. The difference of sample quality offers a natural explanation for the variation in low-temperature power laws observed by many techniques.

Figure 1

The temperature dependence of the heat capacity of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ before (red circles) and after (blue squares) annealing for $x=$ (a) 0.045, (b) 0.08, (c) 0.105, and (d) 0.14. Arrows mark the superconducting transitions. Inset: low-temperature part of the electronic specific heat of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$.

Figure 2

The temperature dependence of the electronic fraction of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ normalized by normal state specific heat (circles, $x$ $=$ 0.045; triangles, $x$ $=$ 0.105; squares, $x$ $=$ 0.08). Empty and full symbols represent unannealed and annealed data, respectively.

Figure 3

The low-temperature dependence of the specific heat of the unannealed and annealed samples measured at different magnetic fields for $H\Vert c$. The data are presented in the form of $C/T$ vs $T^2$ (see text).

Figure 4

(a) The magnetic field dependence of the low-temperature specific heat of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ (circles, $x$ $=$ 0.045; triangles, $x$ $=$ 0.105; squares, $x$ $=$ 0.08). Empty and full symbols represent unannealed and annealed data, respectively. (b) The same data as in (a) presented as $\Delta \gamma (H)/({\gamma }_n-{\gamma }_0)$ vs $H/H_{c2}$. The dotted, solid, and dashed lines described the field dependencies of the low-temperature specific heat according to clean $s$- (Ref. 48), anisotropic $s$- (Ref. 49), and clean $d$-wave (Ref. 50) models, respectively.

Figure 5

(a) Optimal doping, $x=0.08$. Theoretical fits (lines) to experimental data for annealed sample. (b) Overdoped regime, $x=0.105$. Theoretical fits (lines) to experimental data for unannealed (open symbols) and annealed (filled symbols) sample.

Figure 6

The temperature dependencies of normalized electrical resistivity of unannealed (squares) and annealed (circles) Ba(Fe${}_{0.955}$Co${}_{0.045}$)${}_2$As${}_2$. Arrows mark the antiferromagnetic phase transition. Inset: low temperature part of the resistivity.

Figure 7

The temperature dependencies of magnetic susceptibility of unannealed (empty symbols) and annealed (filled symbols) Ba(Fe${}_{0.895}$Co${}_{0.105}$)${}_2$As${}_2$. The ZFC measurements have been performed on the same sample with the filed parallel to the ab plane of the crystal.