on BaFe$_{2-x}$Co$_x$As$_2$ [@lester09] confirm that the commensurate AF order appears below the structural transition temperature and superconductivity coexists with AF order for $0.06\leq x\leq 0.102$. Neutron scattering measurements on BaFe$_{2-x}$Co$_x$As$_2$ with coexisting AF order and superconductivity reveal that the intensity of AF Bragg peaks actually decreases below $T_c$ without changing the spin-spin correlation lengths [@pratt09; @adchristianson09]. While these results indicate that the static AF order competes with superconductivity, it remains unclear whether the long-range AF order truly coexists microscopically with superconducting regions [@mywang; @mywang11b]. Recently, for electron-doped samples near optimal superconductivity it has been shown that the commensurate static AF order changes into transversely incommensurate short-range AF order that coexists and competes with superconductivity (see inset in Fig. 2b) [@dkpratt11; @hluo12]. Taking the temperature dependence of the orthorhombic lattice distortion of BaFe$_{2-x}$Co$_x$As$_2$ into account [@snandi10], the AF order, structure, and superconductivity phase diagrams for BaFe$_{2-x}T_x$As$_2$ are shown in Fig. 2b.

Although the superconducting transition temperature for hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ can reach up to $T_c=38$ K [@rotter] as compared to the $T_c\approx 25$ K for electron-doped BaFe$_{2-x}T_x$As$_2$ [@johnston; @stewart], those materials are much less studied because of the difficulty in growing high-quality single crystals. The initial transport and neutron scattering experiments on 