Control of magnetic, nonmagnetic, and superconducting states in annealed Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

We have grown single-crystal samples of Co substituted CaFe${}_2$As${}_2$ using an FeAs flux and systematically studied the effects of annealing/quenching temperature on the physical properties of these samples. Whereas the as-grown samples (quenched from 960${}^{\circ }$C) all enter the collapsed tetragonal phase upon cooling, annealing/quenching temperatures between 350 and 800${}^{\circ }$C can be used to tune the system to low-temperature antiferromagnetic/orthorhomic or superconducting states as well. The progression of the transition temperature versus annealing/quenching temperature ($T$-$T_{\mathrm{anneal}}$) phase diagrams with increasing Co concentration shows that, by substituting Co, the antiferromagnetic/orthorhombic and the collapsed tetragonal phase lines are separated and bulk superconductivity is revealed. We established a 3D phase diagram with Co concentration and annealing/quenching temperature as two independent control parameters. At ambient pressure, for modest $x$ and $T_{\mathrm{anneal}}$ values, the Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ system offers ready access to the salient low-temperature states associated with Fe-based superconductors: antiferromagnetic/orthorhombic, superconducting, and nonmagnetic/collapsed tetragonal.

Figure 1

Temperature-dependent anisotropic magnetic susceptibility with a magnetic field of 1 T applied perpendicular and parallel to the $c$ axis for (a) the $x=0.00/T_{\mathrm{anneal}}=350{}^{\circ }$C sample, as an example of the antiferromagnetic/structural transition, and (b) the $x=0.00/$as-grown sample, as an example of the collapsed tetragonal phase transition.

Figure 2

Criteria used to determine the transition temperatures of (a) the antiferromagnetic/structural phase, (b) the superconducting phase, and (c) the collapsed tetragonal phase transitions. Inferred transition temperature is indicated by arrow in each figure.

Figure 3

Room-temperature $c$-lattice parameter of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$, determined via the diffraction from platelike samples described in the Experimental Methods section, (a) of as-grown samples and samples annealed/quenched at selected temperatures as a function of measured Co concentration, $x$, and (b) of pure samples and Co substituted samples with $x=0.022$, 0.028, and 0.059, as a function of annealing temperature $T_{\mathrm{anneal}}$. In (a), for comparison, data of Sn grown sample under pressure are also presented.[30, 39]

Figure 4

Temperature-dependent (a) magnetic susceptibility with a field of 1 T applied parallel to the $c$ axis and (b) normalized electrical resistance of as-grown Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples. For clarity, susceptibility data in (a) have been offset by $2\times {10}^{-4}$ emu/mole from each other and resistance data in (b) have been offset by 0.2 from each other.

Figure 5

Values for (a) the $a$-lattice paramter, (b) the $c$-lattice parameter, and (c) unit-cell volume as a function of temperature for Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ for $x=0.00$ (square)[39] and $x=0.059$ (circle) as-grown samples determined from single crystal x-ray diffraction measurements.

Figure 6

Temperature-dependent magnetic susceptibility with a field of 1 T applied perpendicular to the $c$ axis of $x=0.019$ samples annealed at 350${}^{\circ }$C for different amount of time varying from 1 day to 14 days. Susceptibility data have been offset by $1\times {10}^{-4}$ emu/mole from each other for clarity.

Figure 7

Temperature-dependent (a) magnetic susceptibility with a field of 1 T applied perpendicular to the $c$ axis, (b) low-field magnetic susceptibility measured upon zero-field cooling (ZFC) with a field of 0.01 T applied perpendicular to the $c$ axis, and (c) normalized electrical resistance of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 350${}^{\circ }$C. Low-temperature resistance of superconducting samples are presented in (d).

Figure 8

(a) Temperature-dependent specific heat data of the $x=0.033/T_{\mathrm{anneal}}=350{}^{\circ }$C sample, measured in zero field and a field of 9 T applied parallel to the $c$ axis, and (b) the difference between of the two sets of data presented as $\Delta$$C_P/T$. The red dashed lines represent the isoentropic construction used to determine the jump in $C_P$ at $T_c$ (see text).

Figure 9

Phase diagram of transition temperature $T$ vs Co concentration $x$ of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 350${}^{\circ }$C. The size of filled triangle ($T_c$-$M$) schematically represents size of low-temperature diamagnetic fraction. The filled symbols are inferred from magnetization ($M$) data, the open symbols are inferred from resistance ($R$) data.

Figure 10

Temperature-dependent (a) magnetic susceptibility with a field of 1 T applied perpendicular to the $c$ axis, (b) low-field magnetic susceptibility measured upon ZFC with a field of 0.01 T applied perpendicular to the $c$ axis, and (c) normalized electrical resistance of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 400${}^{\circ }$C, together with (d) the specific heat data for the $x=0.028/T_{\mathrm{anneal}}=400{}^{\circ }$C sample (see text). Low-temperature resistance of superconducting samples are presented in the inset of (c).

Figure 11

Phase diagram of transition temperature $T$ vs Co concentration $x$ of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 400${}^{\circ }$C. The size of filled triangle ($T_c$-$M$) schematically represents size of low-temperature diamagnetic fraction. Filled symbols are inferred from magnetization ($M$) data, open symbols are inferred from resistance ($R$) data.

Figure 12

Temperature-dependent (a) magnetic susceptibility with a field of 1 T applied perpendicular to the $c$ axis, (b) low-field magnetic susceptibility measured upon ZFC with a field of 0.01 T applied perpendicular to the $c$ axis, (c) normalized electrical resistance, and (d) phase diagram of transition temperature $T$ vs Co concentration $x$ of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 500${}^{\circ }$C. Low-temperature resistance of superconducting samples are presented in the inset of (c). In (d), the size of filled triangle ($T_c$-$M$) schematically represents size of low-temperature diamagnetic fraction. Filled symbols are inferred from magnetization ($M$) data, open symbols are inferred from resistance ($R$) data.

Figure 13

Temperature-dependent (a) magnetic susceptibility with a field of 1 T applied parallel to the $c$ axis, (b) low-field magnetic susceptibility measured upon ZFC with a field of 0.01 T applied parallel to the $c$ axis, (c) normalized electrical resistance, and (d) phase diagram of transition temperature $T$ vs Co concentration $x$ of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 600${}^{\circ }$C. The inset of (c) presents the resistance data of 1.9$\%$ sample measured upon warming up and cooling down. For clarity, susceptibility data in (a) have been offset by $2\times {10}^{-4}$ emu/mole from each other and resistance data in (b) have been offset by 0.2 from each other. In (d), the filled symbols are inferred from magnetization ($M$) data, the open symbols are inferred from resistance ($R$) data.

Figure 14

Temperature-dependent (a) magnetic susceptibility with a field of 1 T applied parallel to the $c$ axis, (b) low-field magnetic susceptibility measured upon ZFC with a field of 0.01 T applied parallel to the $c$ axis, (c) normalized electrical resistance, and (d) phase diagram of transition temperature $T$ versus Co concentration $x$ of Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples for an annealing/quenching temperature of 700${}^{\circ }$C. For clarity, susceptibility data in (a) have been offset by $1\times {10}^{-4}$ emu/mole from each other and resistance data in (b) have been offset by 0.1 from each other. In (d), the filled symbols are inferred from magnetization ($M$) data, the open symbols are inferred from resistance ($R$) data.

Figure 15

Phase diagram of transition temperature $T$ vs annealing/quenching temperature $T_{\mathrm{anneal}}$ for Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ for (a) $x=0.00$, (b) 0.010, (c) 0.019, (d) 0.022, (e) 0.028, (d) 0.038, and (e) 0.059. The size of filled triangle ($T_c$-$M$) schematically represents size of low-temperature diamagnetic fraction. Filled symbols are inferred from magnetization ($M$) data, open symbols are inferred from resistance ($R$) data.

Figure 16

Width of transition of as-grown Ca(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ samples as a function of measured Co concentration $x$.

Figure 17

Temperature-dependent resistance data of the $x=0.033/T_{\mathrm{anneal}}=350{}^{\circ }$C sample, measured in zero field and applied field up to 1 T.

Figure 18

$\Delta$$C_P$ vs $T_c$ for the $x=0.033/T_{\mathrm{anneal}}=350{}^{\circ }$C sample and the $x=0.028/T_{\mathrm{anneal}}=400{}^{\circ }$C sample, plotted together with literature data for various FeAs-based superconducting materials.[48, 49, 50]

Figure 19

Temperature-dependent (a) resistance data of the $x=0.028/T_{\mathrm{anneal}}=400{}^{\circ }$C sample, measured in applied field parallel to the $c$ axis for $H=0$, 2, 4, 6, 8, 10, 12, and 14 T and (b) anisotropic $H_{c2}$ data determined from $R$($T$) data. Inset to (b) shows $\gamma =H_{c2}^{\perp c}$/$H_{c2}^{\parallel c}$ for $10K<T<16K$.

Figure 20

Temperature-dependent magnetic susceptibility of the $x=0.025/T_{\mathrm{anneal}}=400{}^{\circ }$C sample, measured upon warming up and cooling down.

Figure 21

Three-dimensional phase diagram with substitution level $x$, annealing/quenching temperature $T_{\mathrm{anneal}}$, and transition temperature $T$, as three axes. Red (antiferromagnetic/orthorhombic), green (superconducting), and blue (collapsed tetragonal) spheres represent data. Transparent colored surfaces are guides to the eyes. Black dashed lines are $T$-$x$ lines for different $T_{\mathrm{anneal}}$ and yellow dashed lines are $T$-$T_{\mathrm{anneal}}$ lines for different $x$. Solid colored areas on the $T_{\mathrm{anneal}}$-$x$ plane are low-temperature ground states. Note that dark green area (from magnetization data) represents the bulk superconducting region, whereas light green area (from resistance data) represents the zero-resistance region.