Collapsed tetragonal phase in Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ stabilized by pressure: Structural studies using single-crystal neutron diffraction

Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals with concentration $x=0.032$, 0.051, and 0.063 were investigated by means of neutron diffraction under hydrostatic pressure. The region of existence of the high-temperature tetragonal, low-temperature orthorhombic, and pressure-induced collapsed tetragonal phases have been determined and the corresponding $p$-$T$ phase diagrams for the three compositions have been constructed. Structural details of the tetragonal phases at various conditions have been determined. The anomaly marking the orthorhombic-to-tetragonal structural phase transition temperature $T_S$ decreases with increasing Co substitution. Similarly to that, the critical pressure of the tetragonal (or orthorhombic)-to-collapsed-tetragonal transition also decreases with increasing Co doping level. The behavior is highly hysteretic and the differences in critical pressures with increasing and decreasing branches eventually makes the collapsed tetragonal phase stable down to ambient pressure and enables structural studies under identical conditions. Within the error bars on the fourth digit, no modification of the As structural positional parameter is found. Such a result suggests that the change of the As-As bond is caused solely by the reduction of the $c$-axis lattice parameter.

Figure 1

Observed versus calculated nuclear structure factors squared after correction for absorption and extinctions for the Ca(Fe${}_{0.968}$Co${}_{0.032}$)${}_2$As${}_2$ (a) and Ca(Fe${}_{0.937}$Co${}_{0.063}$)${}_2$As${}_2$ (b) single crystals. Schematic representation of the ThCr${}_2$Si${}_2$ crystal structure is shown in the inset.

Figure 2

Color map showing the pressure dependence of a portion of the diffraction pattern taken at 100 K within the range of (200) and (002) structural reflections [(a) and (b), respectively] of a Ca(Fe${}_{0.968}$Co${}_{0.032}$)${}_2$As${}_2$ sample with increasing pressure (counts per monitor are color coded in insets). Panels (c) and (d) show the same diffraction ranges with decreasing pressure. White arrows denote whether the pressure has been increased or removed in the course of the experiment.

Figure 3

2D scan profiles of the (002) reflection recorded with increasing pressure at 100 K at nearly ambient pressure (a) and at 0.32 GPa (b), 0.38 GPa (c), and 0.50 GPa (d). On the horizontal axis is the diffraction angle $2\theta$ on the vertical axis is the angular opening $\nu$ of the detector. The color coding corresponds to recorded diffracted intensity (red is the highest count rate).

Figure 4

The pressure dependence of the $c$-lattice constants for various structural phases in the Ca(Fe${}_{0.968}$Co${}_{0.032}$)${}_2$As${}_2$ sample upon increasing the pressure measured at 125 K (a), 100 K (b), 75 K (c), and 50 K (d). Red (medium gray), blue (light gray), and magenta (dark gray) vertical bars denote pressure intervals, at which O and T, T and cT, and O and cT phases coexist, respectively.

Figure 5

Color map showing the pressure dependence of a portion of the diffraction pattern taken at 50 K within the range of (200) and (002) structural reflections [(a) and (b), respectively] of a Ca(Fe${}_{0.937}$Co${}_{0.063}$)${}_2$As${}_2$ sample with increasing pressure (counts per monitor are color coded in insets). Panels (c) and (d) show the same diffraction ranges with decreasing pressure. White arrows denote whether the pressure has been increased or removed in the course of the experiment.

Figure 6

Pressure-temperature phase diagram for Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, $x=0.032$, 0.051, and 0.063, samples measured with increasing pressure. Experimental points were determined from midpoints of phase-transition regions (coexistence regions) between O, T, and cT phases. The light gray dashed line denotes approximately the temperature below which helium solidifies.

Figure 7

Observed versus calculated nuclear structure factors squared after correction for absorption and extinctions for the Ca(Fe${}_{0.949}$Co${}_{0.051}$)${}_2$As${}_2$ single crystal at 100 K and under hydrostatic pressure of 0.30 GPa before the application of elevated pressures (being in the T phase) (a) and under identical conditions after exposing it to 0.50 GPa (being in the cT phase) (b).