Comprehensive Characterization of Superconductivity in Co-doped BaFe$_{2}$As$_{2}$

We have grown high-quality single crystals of Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ by self-flux method. Superconducting properties of these single crystals are characterized by measuring magnetization, resistivity, upper critical field, Hall coefficient, and magneto-optical images. A sharp drop of susceptibility is observed around 24 K for $x$=0.1. Irreversible magnetization shows fish-tail feature in a wide temperature range, indicating the presence of inhomogeneities in the crystal. The critical current density $J_{c}$ for $x$=0.1 is over 10$^{5}$ A/cm$^{2}$ at low temperatures up to 50 kOe. Upper critical field determined by resistive transition is anisotropic with anisotropic parameter $\sim $ 3.5. Hall effect measurements indicate that Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ is a multiband system with a dominant conduction by electron. Magneto-optical image for $x$=0.1 at 25 K reveals the presence of trapped vortices in a part of the crystal, which leads us to expect that bulk superconductivity above 25 K can be realized by fine tuning the Co-doping level.