Femtosecond laser excitation of coherent optical phonons in ferroelectricLuMnO3

Abstract

We have used femtosecond pump-probe spectroscopy to excite and probe coherent optical phonon vibrations in single crystals of hexagonal ferroelectric ${\text{LuMnO}}_{3}$. An optical phonon mode of ${A}_{1}$ symmetry was coherently excited with 25 fs pump-laser pulses $(\ensuremath{\lambda}\ensuremath{\approx}800\text{ }\text{nm})$. The phonon mode, involving Lu ion motion along the $c$ axis, was identified as the soft mode driving the ferroelectric transition. The excitation mechanism was determined to be purely displacive in nature due to resonant excitation of a narrow intra-atomic ${d}_{xy,{x}^{2}\ensuremath{-}{y}^{2}}\ensuremath{\rightarrow}{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ transition in Mn. The lifetime of the $\text{Mn}\text{ }{d}_{xy,{x}^{2}\ensuremath{-}{y}^{2}}\ensuremath{\rightarrow}{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ excitation was measured to be 0.8 ps. A remarkable reversal of the sign of the oscillation amplitude ($\ensuremath{\pi}$ phase shift) of the reflectivity curve was observed upon comparing longitudinal-optical (LO) with transverse-optical (TO) mode geometries. The phase reversal is attributed to the macroscopic electric depolarization field accompanying infrared-active longitudinal phonon modes but absent in TO modes. In addition to the direct effect of the ion motion on the optical properties, which is the same in LO and TO modes, the longitudinal depolarization field of the LO mode gives rise to an additional modulation of the refractive index via the linear electro-optic effect which dominates the optical response.