Anisotropic optical properties of detwinned BaFe$_{2}$As$_{2}$

The optical properties of a large, detwinned single crystal of BaFe$_2$As$_2$ have been examined over a wide frequency range above and below the structural and magnetic transition at $T_{\rm N}\simeq 138$ K. Above $T_{\rm N}$ the real part of the optical conductivity and the two infrared-active lattice modes are almost completely isotropic; the lattice modes show a weak polarization dependence just above $T_{\rm N}$. For $T<T_{\rm N}$, the optical conductivity due to the free-carrier response is anisotropic, being larger along the $a$ axis than the $b$ axis below $\simeq 30$ meV; above this energy the optical conductivity is dominated by the interband contributions, which appear to be isotropic. The splitting of the low-energy infrared-active mode below $T_{\rm N}$ is clearly observed, and the polarization modulation of the new modes may be used to estimate that the crystal is $\simeq 70$% detwinned. The high-frequency mode, with a threefold increase in strength of the lower branch below $T_{\rm N}$ and nearly silent upper branch, remains enigmatic.