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

Systematic measurements of the resistivity, heat capacity, susceptibility and Hall coefficient are presented for single crystal samples of the electron-doped superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. These data delineate an $x-T$ phase diagram in which the single magnetic/structural phase transition that is observed for undoped BaFe$_2$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 up to $x \sim 0.06$. The optimal T$_c$ appears to coincide with the Co concentration at which the magnetic/structural phase transitions are totally suppressed. 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 $x-T$ 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.