Beyond anharmonicity: signature of spin-phonon coupling at the surface of BaFe$_{2}$As$_{2}$

High Resolution Electron Energy Loss Spectroscopy (HREELS) has been used to investigate the temperature dependence of the lattice dynamics of cleaved single crystals of BaFe$_{2}$As$_{2}$, one of the parent compounds of Fe-based superconductors. Both the phonon frequency as well as phonon linewidth of the intense 32 meV out-of-plane Fe/As mode (A$_{2u})$ and the 24 meV out-of-plane As vibration mode (A$_{1g})$ show a dramatic temperature dependence and anomalous behavior below $\sim $150K. The anomalous behavior is associated with the coupled elasto-magnetic transition in the bulk but occurs appreciably higher at the surface than in the bulk ($\sim $138 K). The anharmonicity at the surface is considerably larger than that in the bulk for the orthorhombic phase, but is significantly less in the tetragonal phase. A detailed discussion is given in terms of the interplay between the spin and lattice in this novel system.