Thermal expansion and anisotropic pressure derivatives of $T_c$ in $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ single crystals

Heat capacity and anisotropic thermal expansion were measured for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ $\left(x=0,0.038,0.074\right)$ single crystals. Thermal expansion is anisotropic and, in tetragonal phase, is significantly higher along the $c$ axis. Previously reported phase transitions, including possibly split structural and magnetic for $x=0.038$, are clearly seen in both measurements. Uniaxial pressure derivatives of the superconducting transition temperature inferred from the Ehrenfest relation have opposite signs for in-plane and $c$-axis pressures for both $\text{Ba}{\left({\text{Fe}}_{0.962}{\text{Co}}_{0.038}\right)}_2{\text{As}}_2$ and $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$, with the opposite sign of this anisotropy.

Figure 1

Temperature-dependent heat capacity of ${\text{BaFe}}_2{\text{As}}_2$ single crystal. Left inset: enlarged region near the structural/magnetic phase transition; right inset: low temperature $C_p/T$ as a function of $T^2$. Linear specific heat term, $\gamma$ is $\approx 15\text{mJ}/\text{mol}{\text{K}}^2$.

Figure 2

(Color online) Anisotropic, temperature dependent, (a) linear and volume thermal expansivities ($\Delta a/a_0$, $\Delta c/c_0$ and $\Delta V/V_0$, where the changes are taken relative to the values at 1.8 K) and (b) thermal expansion coefficients (${\alpha }_a$, ${\alpha }_c$ and $\beta$) of ${\text{BaFe}}_2{\text{As}}_2$ single crystal. Inset to (a): expanded low temperature part of the main graph. Inset to (b): expanded part of the main graph near the structural-magnetic phase transition. Note that at temperatures below the structural-magnetic phase transition the data marked as $a$ axis are some average of $a$ and $b$.

Figure 3

Temperature-dependent heat capacity of $\text{Ba}{\left({\text{Fe}}_{0.962}{\text{Co}}_{0.038}\right)}_2{\text{As}}_2$ single crystal. Insets: $C_p/T$ vs $T$ near the superconducting transition with the estimate of $\Delta C_p/T_c$ shown; temperature dependence of the derivative $d{C}_p/dT$. Arrows mark the phase transitions.

Figure 4

(Color online) (a) Linear and volume thermal expansivities (the changes are taken relative to the values at 1.8 K) of $\text{Ba}{\left({\text{Fe}}_{0.962}{\text{Co}}_{0.038}\right)}_2{\text{As}}_2$ single crystal; inset: enlarged low temperature part of the data. (b) Thermal expansion coefficients of $\text{Ba}{\left({\text{Fe}}_{0.962}{\text{Co}}_{0.038}\right)}_2{\text{As}}_2$ single crystal. (c) Enlarged, low temperature, part of the data in the panel (b), vertical lines mark structural-magnetic phase transitions; inset: enlarged low temperature part of the data including the superconducting transition, lines show how $\Delta {\alpha }_c$ was estimated. Note that at temperatures below the structural-magnetic phase transitions the data marked as $a$ axis are some average of $a$ and $b$.

Figure 5

Temperature-dependent heat capacity of $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$ single crystal. Insets: $C_p/T$ vs $T$ near the superconducting transition with the estimate of $\Delta C_p/T_c$ shown.

Figure 6

(Color online) (a) Linear and volume thermal expansivities (the changes are taken relative to the values at 1.8 K) of $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$ single crystal; inset: enlarged low temperature part of the data. (b) Thermal expansion coefficients of $\text{Ba}{\left({\text{Fe}}_{0.926}{\text{Co}}_{0.074}\right)}_2{\text{As}}_2$ single crystal; inset: enlarged low temperature part of the data including the superconducting transition.