Thermal expansion of CaFe${}_2$As${}_2$: Effect of cobalt doping and postgrowth thermal treatment

We report thermal expansion measurements on Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals with different thermal treatment, with samples chosen to represent four different ground states observed in this family. For all samples, thermal expansion is anisotropic with different signs of the in-plane and $c$-axis thermal expansion coefficients in the high temperature, tetragonal phase. The features in thermal expansion associated with the phase transitions are of opposite signs as well, pointing to a different response of transition temperatures to the in-plane and the $c$-axis stress. These features, and consequently the inferred pressure derivatives, are very large, clearly and substantially exceeding those in the Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ family. For all transitions the $c$-axis response is dominant.

Figure 1

(a) The temperature-dependent change in $c$-axis dimension normalized with respect to the 300 K value $(\Delta c/c_{300\mathrm{K}}=[c\left(T\right)-c(300$ K$\left)\right]/c(300$ K$))$ for as-grown Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ ($x\le 0.059$). (b) Temperature-dependent $c$-axis thermal expansion coefficients, ${\alpha }_c$ for the same samples. Inset: temperature of the cT transition for samples with different cobalt concentrations, as determined by position of the peaks in ${\alpha }_c$.

Figure 2

(a) Temperature-dependent, anisotropic dilation with respect to 1.8 K $[\Delta L_i/L_{i,1.8\mathrm{K}}=[L_i\left(T\right)-L_i(1.8$ K$\left)\right]/L_i(1.8$ K$)]$ of as-grown CaFe${}_2$As${}_2$; (b) temperature-dependent, anisotropic thermal expansion coefficients ${\alpha }_i$ of as-grown CaFe${}_2$As${}_2$.

Figure 3

$T-T_{\mathrm{anneal}/\mathrm{quench}}$ phase diagram for Ca(Fe${}_{0.977}$Co${}_{0.023}$)${}_2$As${}_2$ (after Ref. 19, filled symbols). AFM/ORTHO, SC, and cT label antiferromagnetic and orthorhombic, tetragonal and superconducting, and nonmoment bearing collapsed tetragonal phases, respectively. Arrows mark the concentrations used in this work and transition temperatures determined from the thermal expansion data are shown as half-filled symbols.

Figure 4

(a) Temperature-dependent, anisotropic dilation with respect to 300 K $[\Delta c/c_{300\mathrm{K}}=[c\left(T\right)-c(300$ K$\left)\right]/c(300$ K$)]$ of Ca(Fe${}_{0.977}$Co${}_{0.023}$)${}_2$As${}_2$ with different thermal treatment. AFM/ORTHO, SC/TET, and cT label antiferromagnetic and orthorhombic, tetragonal and superconducting, and collapsed tetragonal and paramagnetic phases, respectively. (b) Low-temperature, $c$-axis thermal expansion coefficient, ${\alpha }_c$, of Ca(Fe${}_{0.977}$Co${}_{0.023}$)${}_2$As${}_2$ annealed for 7 days at 500${}^{\circ }$C. $T_c$ is approximately determined using the same criterion as in Ref. 25.

Figure 5

$T-x$ phase diagram for Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, $x\le 0.058$, annealed at 400${}^{\circ }$C for 7 days (after Ref. 19, filled symbols). AFM/ORTHO, SC, and TET label antiferromagnetic and orthorhombic, tetragonal and superconducting, and tetragonal and paramagnetic phases, respectively. Arrows mark the concentrations used in this work and transition temperatures determined from the thermal expansion data are shown as half-filled symbols.

Figure 6

(a) Temperature-dependent, $c$-axis dilation with respect to 300 K $[\Delta c/c300\text{K}=\left[c\right(T)-c(300$ K$\left)\right]/c(300$ K$)]$ of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, $x\le 0.058$, annealed at 400${}^{\circ }$C for 7 days. Inset: low-temperature part of the data plotted with respect to the values at 1.8 K. (b) Temperature-dependent, $c$-axis thermal expansion coefficients ${\alpha }_c$ for the same samples.

Figure 7

(a) Temperature-dependent, anisotropic dilation with respect to 1.8 K $[\Delta L_i/L_{i,1.8\mathrm{K}}=[L_i\left(T\right)-L_i(1.8$ K$\left)\right]/L_i(1.8$ K$)]$ of Ca(Fe${}_{0.973}$Co${}_{0.027}$)${}_2$As${}_2$, annealed at 400${}^{\circ }$C for 7 days; (b) temperature-dependent, anisotropic thermal expansion coefficients ${\alpha }_i$ of the same sample.

Figure 8

Temperature-dependent, anisotropic thermal expansion coefficients, ${\alpha }_i$, of (a) Ca(Fe${}_{0.971}$Co${}_{0.029}$)${}_2$As${}_2$, annealed at 400${}^{\circ }$C for 7 days; (b) Ca(Fe${}_{0.942}$Co${}_{0.058}$)${}_2$As${}_2$, annealed at 400${}^{\circ }$C for 7 days.

Figure 9

(a) Temperature-dependent, anisotropic thermal expansion coefficients ${\alpha }_i$ of Ca(Fe${}_{0.971}$Co${}_{0.029}$)${}_2$As${}_2$, annealed at 400${}^{\circ }$C for 7 days below 50 K. (b) Heat capacity, plotted as $C_p/T$ of Ca(Fe${}_{0.971}$Co${}_{0.029}$)${}_2$As${}_2$, annealed at 400${}^{\circ }$C for 7 days below 50 K.