Surface lattice dynamics of the 122-type iron pnictides*

We present a systematic High Resolution Electron Energy Loss Spectra (HREELS) study of the surfaces lattice dynamics of the cleaved single crystals of the parent compounds AFe$_{2}$As$_{2}$ (A=Ba, Ca) as a function of temperature and sample treatment. The different phonon signatures on the competing surface reconstructions 1$\times $2 phase and ($\surd $2x$\surd $2)R45$^{^{\circ}}$ phase are studied. For Ba there are two optical phonon modes are observed at 18 and 29 meV, which can be identified as the $A_{1g}$ and $B_{1g}$ vibrations of the As and Fe atoms, respectively. A detailed discussion is given in terms of the interplay between the spin and lattice in this novel system