Determination of the phase diagram of the electron-doped superconductor $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$

Systematic measurements of the resistivity, heat capacity, susceptibility, and Hall coefficient are presented for single-crystal samples of the electron-doped superconductor $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$. These data delineate an $x\text{−}T$ phase diagram in which the single magnetic/structural phase transition that is observed for undoped ${\text{BaFe}}_2{\text{As}}_2$ at 134 K appears to split into two distinct phase transitions, both of which are rapidly suppressed with increasing Co concentration. Superconductivity emerges for Co concentrations above $x\sim 0.025$ and appears to coexist with the broken-symmetry state for an appreciable range of doping up to $x\sim 0.06$. The optimal superconducting transition temperature appears to coincide with the Co concentration at which the magnetic/structural phase transitions are totally suppressed, at least within the resolution provided by the finite-step size between crystals prepared with different doping levels. Superconductivity is observed for a further range of Co concentrations before being completely suppressed for $x\sim 0.18$ and above. The form of this $x\text{−}T$ phase diagram is suggestive of an association between superconductivity and a quantum critical point arising from suppression of the magnetic and/or structural phase transitions.

Figure 1

(Color online) Temperature dependence of the in-plane $\left({\rho }_{ab}\right)$ resistivity of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$. Data are shown normalized by the room-temperature resistivity ${\rho }_{ab}\left(300\text{K}\right)$ to remove uncertainty in estimates of the absolute value due to geometric factors. Successive data sets are offset vertically by 0.1 for clarity (except for $x=0$ data, which are offset by 1.4). Values of the Co concentration $x$ are listed in the legend and were determined by microprobe analysis for all concentrations except the specific sample with $x=0.070$, for which $x$ was estimated based on the observed linear relation between nominal and actual $x$.

Figure 2

(Color online) (a) Heat-capacity data for four representative Co concentrations ($x=0$, 0.016, 0.025, 0.036, and 0.061) showing the suppression of the structural/magnetic phase transitions with increasing Co concentration. (b) Superconducting anomaly for the sample with $x=0.061$ shown as $\Delta C/T$ vs $T$, where $\Delta C=C_S-C_N$ and $C_N$ is estimated as described in the text from the heat capacity measured in an applied field of 14 T. Data are shown for zero field and for applied fields of 1, 3, and 5 T along the $c$ axis.

Figure 3

(Color online) Resistivity [panels (a)–(c)] and heat-capacity [panels (d)–(f)] data for samples with $x=0$, 0.016, and 0.025 over a narrower temperature interval, showing the splitting of the single phase transition observed for $x=0$ into two distinct phase transitions for $x>0$.

Figure 4

(Color online) Comparison of heat-capacity, susceptibility, resistivity, and Hall-coefficient data for samples with (a) $x=0$, (b) $x=0.016$, and (c) $x=0.025$. In the upper panels, the heat capacity (right axis) is shown as $\Delta C$, having subtracted the background phonon contribution as described in the main text, together with the in-plane susceptibility ${\chi }_{ab}$ (left axis) and the derivative $d\left(\chi T\right)/dT$ (arb. units). In the lower panels, absolute values of the in-plane resistivity ${\rho }_{ab}$ (left axis) are shown together with the Hall coefficient $R_H$ (right axis) and the derivative $d\rho /dT$ (arb. units). Vertical dotted lines mark successive phase transitions evident in all four physical properties.

Figure 5

(Color online) Progression of the two successive phase transitions marked as $\alpha$ and $\beta$, as a function of Co concentration as observed in (a) heat capacity and (b) the derivative of the resistivity $-d\rho /dT$. Heat-capacity data are shown as $\Delta C$, having subtracted the background phonon contribution as described in the main text. Data for $x=0.025$ and 0.036 (marked by an asterisk in the legend) have been multiplied by factors of 3 and 5, respectively, for clarity.

Figure 6

(Color online) Phase diagram for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ showing the suppression of the two successive phase transitions $\alpha$ and $\beta$ with increasing Co concentration and the eventual SC “dome.” Data points for $T_{\alpha }$ and $T_{\beta }$ were obtained from heat-capacity, resistivity, Hall-coefficient, and susceptibility data for $x=0$, 0.016, 0.025, and 0.036 and from resistivity data alone for $x=0.045$ and 0.051. Superconducting $T_c$ values were obtained from resistivity data. Error bars indicate 10% and 90% of the resistive transition. Uncertainty in the Co concentration corresponds to less than the width of the data markers.

Figure 7

(Color online) Temperature dependence of susceptibility following zfc and fc cycles, for both single-crystal and powdered samples for three representative Co concentrations corresponding to $x=0.045$ (underdoped), $x=0.061$ (optimally doped), and $x=0.109$ (overdoped). Measurements were made in a field of 50 Oe applied parallel to the $ab$ plane of the single crystals.