Resonant inelastic light scattering studies in the fractional quantum Hall regime, and of phase transitions in relaxor ferroelectrics

This dissertation presents inelastic light scattering results that probe low energy physics in quantum liquids and in materials with novel contemporary applications. Two areas are considered: (a) low-lying excitations in two dimensional structures under the extreme conditions that occur in the fractional quantum Hall regime (FQH), (b) low energy vibrational modes in relaxor ferroelectrics.; In the FQH regime we concentrate in the region 1/2 ≥ nu ≥ 1/3. We discovered new spin-flip excitations that provide insight into composite fermions (CF) energy level spacings and interactions. In the filling factor region 2/5 ≥ nu ≥ 1/3 we uncover new excitations that extend to filling factors between the main fractions of the FQH effect and can be associated to transitions between different CF Landau levels. These results provide information on residual interactions between the CFs. We find that residual interactions are not negligible and could lead to novel behaviors.; An analysis of the density dependence of CF energy levels at filling factors nu = 1/3 and nu = 2/5 based on simple energy level models is presented. The main assumptions are that the splitting between quasiparticle levels and spin reversal energies are proportional to the Coulomb energy. Energy level structures of CF quasiparticles are also probed by means of light scattering experiments with spin-flip excitations at nu = 3/7 and nu = 4/9.; Measurements of spin excitations in the limit of nu → 1/2 uncover a delicate balance between spin reversal and Fermi energies. The interactions are exposed in low-lying spin-flip excitations that have marked sensitivity to the state of spin polarization of the system when nu → 1/2. We are able to determine the boundaries between full and partial spin polarization, these, together with the observation of spin-flip rotons reveal spin reversal energies much larger than the bare Zeeman splitting.; Inelastic light scattering by optical phonons (Raman scattering) in relaxor ferroelectrics probe the structural, morphotropic, phase transition that occurs with changes in composition of solid solutions. These experiments uncover the impact of acoustic-optic mode coupling on the morphotropic phase transition and its possible link to the enhancement of the piezoelectric responses that take place at the morphotropic phase boundary.