  The effect of K, Co and P dopings on the lattice dynamics in the
BaFe$_2$As$_2$ system is studied by infrared spectroscopy. We focus on the
phonon at $\sim$ 253 cm$^{-1}$, the highest energy in-plane infrared-active
Fe-As mode in BaFe$_2$As$_2$. Our studies show that the Co and P dopings lead
to a blue shift of this phonon in frequency, which can be simply interpreted by
the change of lattice parameters induced by doping. In sharp contrast, an
unusual red shift of the same mode was observed in the K-doped compound, at
odds with the above explanation. This anomalous behavior in K-doped
BaFe$_2$As$_2$ is more likely associated with the coupling between lattice
vibrations and other channels, such as charge or spin. This coupling scenario
is also supported by the asymmetric line shape and intensity growth of the
phonon in the K-doped compound.

Superconductivity