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We study systematically transport, susceptibility and heat capacity forBaFe$_{2-x}$Co$_x$As$_2$ single crystals. In the underdoped region, spindensity wave (SDW) transition is observed in both resistivity andsusceptibility. The magnetic susceptibility shows unusual T-linear dependenceabove SDW transition up to 700 K. With Co doping, SDW ordering is graduallysuppressed and superconductivity emerges with a dome-like shape. Electricaltransport, specific heat and magnetic susceptibility indicate that SDW andsuperconductivity coexist in the sample BaFe$_{2-x}$Co$_x$As$_2$ around x =0.17, being similar with (Ba,K)Fe$_2$As$_2$. When x$>$0.34, thesuperconductivity completely disappears. A crossover from non-Fermi-liquidstate to Fermi-liquid state is observed with increasing Co doping. A detailedelectronic phase diagram about evolution from SDW to superconducting state isgiven.

Abnormal T-linear susceptibility and Phase diagram of BaFe$_{2-x}$Co$_x$As$_2$ single crystals