  From first-principles density functional theory calculations combined with
varying temperature Raman experiments, we show that AFe$_2$As$_2$ (A=Ba, Sr),
the parent compound of the FeAs based superconductors of the new structural
family, undergoes a spin-Peierls-like phase transition at low temperature. The
coupling between the phonons and frustrated spins is proved to be the main
cause of the structural transition from the tetragonal to orthorhombic phase.
These results well explain the magnetic and structural phase transitions in
AFe$_2$As$_2$(A=Ba, Sr) recently observed by neutron scattering.
