Optical cystallography and ferroelectric domain imaging of BaTiO$_3$ nanocrystals with tip-enhanced phonon Raman spectroscopy

The capability of probing phase transitions, stress, electron-phonon coupling, or doping via their effect on the vibrational structure of crystals has positioned phonon Raman spectroscopy as a powerful tool for the study of semiconductors and dielectrics. In extending the technique to the near-field, the symmetry selectivity of the phonon Raman response allows for optical crystallography on the nanoscale in tip-enhanced Raman spectroscopy taking advantage of the local field enhancement provided by the nanometer size apex of a plasmonic scanning probe tip. The general selection rules that provide the necessary degrees of freedom are derived as a superposition of the crystal Raman tensor, momentum conservation for phonon and light emission, and the symmetry of the near-field tip scattering geometry. The capabilities are demonstrated for the spectrally and spatially resolved identification of intrinsic ferroelectric domains of individual BaTiO$_3$ nanocrystals by probing the A$_1$ TO and E TO phonon modes with nanometer spatial resolution.