Soft-mode spectroscopy in cubic BaTiO3by hyper-Raman scattering

Abstract

Hyper-Raman scattering from cubic BaTi03 is studied to clarify the controversies about the low-frequency dielectric response in this material. Applying the Auctuation-dissipation theorem, we obtain the imaginary part e"(0) of the dielectric function in the wave-number range from 3 to 150 cm '. e"(0) can be adequately described by a classical singleoscillator dispersion formula. In approaching the Curie temperature, we find a continuous decrease of the mode frequency 00. The relative damping constant y/Qo exceeds 2, so that the mode may be referred to as intermediate between oscillator and relaxator. Because of the high damping e"(0) can be formally written as the sum of two overdamped oscillator contributions. This would lead to the concept of a soft-mode saturation and an extra dispersion mechanism as has been recently inferred from the far-infrared reflectivity spectrum. However, we do not find any evidence for this mode splitting and, so far, regard it as artificial.

Picosecond View of Microscopic-Scale Polarization Clusters in ParaelectricBaTiO3

“…As measured by HyperRaman spectroscopy [5,6], a relaxational dynamics was also observed in the paraelectric BaTiO 3 near T c . NMR experiment [7] has recently shown that Ti ion in the paraelectric phase of BaTiO 3 flutters among off-center sites, claiming the coexistence of order-disorder and displacive characters in phase transition of BaTiO 3 as that predicted by simulation [8].…”

“…The cluster is a dynamic correlated region where unit cells polarize coherently. NMR experiment [7] showed a relaxation time of Ti ion at each off-center site to be about 10 ns at a temperature of 5 C. On the other hand, hyper-Raman experiment [5] showed the relaxation time of the overdamped phonon to be an order of several hundreds of picoseconds in the same temperature region. Thus, an order of nanoseconds might be a measure of the relaxation time of cluster.…”

“…Although experiments such as neutron scattering [10], x-ray scattering [4,11], and optical birefringence [12,13] showed strongly fluctuating polarizations existing in paraelectric phase of BaTiO 3 near T c , however, such clusters have never been directly observed to date. The reason lies in the fact that the relaxation time of a particular cluster, around an order of nanoseconds [5,7], is too short compared to the general measuring time in practice. Traditional diffuse x-ray scattering or neutron scattering cannot be used to observe the dynamic correlation length, since where the spatial correlation has been averaged by the much longer time for measurement.…”

Doping and temperature-dependent optical properties of oxygen-reducedBaTiO3−δ

“…It saturates at ω T O1 ≈ 31 cm −1 upon approaching T C = 403 K. 19 According to the displacive model of the phase transition, it is this (soft) mode that is responsible for the ferroelectric instability in BaTiO 3 . 42,43 On the other hand, the Last (ω T O2 ≈ 180 cm −1 ) and the Axe (ω T O4 ≈ 498 cm −1 ) modes are nearly T -independent in a wide temperature range.…”

“…15 In fact, disorder in the form of microscopic clusters of orthorhombic Ti off-center displacements exists already in rhombohedral phase as revealed by Mn 4+ electron paramagnetic resonance (EPR). 16,17 Evidence of both order-disorder and displacive character of the phase transitions in BaTiO 3 has been found by variety of techniques including nuclear magnetic resonance 18 (NMR), extended x-ray-absorption fine structure (EX-AFS), x-ray-absorption near-edge structure 15 (XANES), Raman 19 and IR 20 spectroscopy. It becomes obvious, therefore, that both resonant (optical phonons) and nonresonant (relaxation) modes have to be considered in the problem of electron-lattice interaction in BaTiO 3 .…”