The lattice dynamics of ferroelectric relaxors and nanoparicles is still the subject of many theoretical and experimental investigations. In addition to the usual structural techniques, spectroscopic methods sensitive to vibrational modes are widely used to elucidate phase transition mechanisms. Numerous studies have been already performed using inelastic neutron scattering (INS), Raman scattering (RS) and infrared reflectivity (IR). Using all these techniques, it is very difficult to disclose neatly the behavior at very low frequencies in these materials. Hyper-Raman scattering is a non-linear optic spectroscopy where two incident photons scatter one photon after interaction with an excitation in the media. One major interest of this technique is its selection rules that are different from both IR and RS. For example, in the Pm3 ̅m simple cubic perovskite, the polar F1u modes are active both in IR and HRS, while the "silent" F2u mode is active only in HRS. This provides HRS as an experimental tool that can probe polar and non-polar excitations and that gives details about the spectral shape down to frequencies of a few cm−1. In this talk, recent HRS experimental studies reporting the lattice vibrations of prototypical ferroectric relaxors such as PMN and PMT [1-3] and of the well-known quantum paraelectric material strontium titanate (micro- and nano-particles) [4] will be discussed. Special attention will be given to the dynamics of the low-lying vibrations such as the ferroelectric soft modes. These results show that HRS can be a very useful tool for the investigation of the vibrations of ferroelectric materials. [1] A. Al-Zein, B. Hehlen, J. Rouquette, and J. Hlinka, Phys. Rev. B 78, 134113 (2008). [2] A. Al-Zein, J. Hlinka, J. Rouquette, and B. Hehlen, Phys. Rev. Lett. 105, 017601 (2010). [3] A. Al-Zein, J. Hlinka, J. Rouquette, A. Kania, and B. Hehlen, J. Appl. Phys. 109, 124114 (2011). [4] J. M. Kiat, C. Bogicevic, P. Geimener, F. Karolak, N. Guiblin, F. Porcher, A. Al-Zein, B. Hehlen, and R. Haumont, submitted to Phys. Rev. B.

Raman spectroscopy were used to study the temperature behavior of the polar optical modes of a set of strontium titanate ceramics with grain size ranging between about 20 nm and 1 µm. Diminishing the grain size yields to an enhancement of (normally forbidden) Raman polar modes with a strong reduction of dielectric permittivity. A progressive decoupling between the antiferrodistortive (AFD) order parameter and the spontaneous strain is observed. In addition, the soft mode of nano STO ceramic has been observed by Hyper-Raman spectroscopy. The obtained spectra shows no splitting of this vibration in the range between 25 K and 300 K. This is attributed to the weak tatragonality ratio c/a even at very low temperature. Moreover, the static dielectric constant calculated from the Lyddane-Sachs-Teller relation that resembles the intrinsic dielectric constant are in agreement with that obtained from dielectric measurements. These results were interpreted in comparison with the soft mode behavior of micronic grain size STO ceramic.

Hyper Raman scattering (HRS) is a non-linear optical spectroscopy in which two incident photons at frequency ωI give a scattered one at ωS after interaction with an excitation of frequency ω in the media. The main interest of this technique arises from its selection rules different from the classical Raman scattering and Infrared absorption. The hyper-Raman spectroscopy of vitreous silica has been performed and the results have been compared to Raman and Infrared absorption data. The spectral responses have been analyzed within a simple structural model considering motions of Si-O-Si bonds and of SiO4 tetrahedra. Most of the HRS bands can be assigned by motions from one or the other of these two elementary structural units. It includes the boson peak (BP), an excess of vibrational modes at low frequency, characteristic of the disordered state and whose origin remains strongly debated. The HRS BP has been successfully decomposed into libration motions of rigid tetrahedra and into motions originating from fluctuating charges in the glass. Interestingly, both contributions are different in shape and frequency. The former, which largely dominates the hyper-Raman signal, superposes the neutron BP while the latter mimics the Raman signal. This result clarifies the nature of the modes underlying the BP of v-SiO2 and gives a natural explanation for its different signatures in neutron and Raman. The spectroscopy also highlights a new polar component in the high frequency phonon spectrum of v-SiO2, and supports previous numerical simulations predicting that the modes associated to the lowest frequency polar band are strongly delocalized.

Fracture and stress corrosion mechanisms, densification of silica close to a Vickers indent observed by Brillouin scattering, and quantitative estimate of the ring structure and of the Si-O-SI angle in permanently densified silicas.

Hyper-Raman scattering is used to investigate the vibrations in two prototypical relaxors, PbMg(1/3)Nb(2/3)O(3) and PbMg(1/3)Ta(2/3)O(3) (PMT). First-order scattering from polar modes is clearly observed. Most of the triply-degenerate cubic vibrations are split into doublets and their frequencies compare very well to that of PbTiO(3) in its tetragonal phase. Their shape and scattering intensities are sensitive to the local chemical ordering and ferroelectric distortions. For example, the tendency toward 1: 1 local ordering on the B-site in PMT is clearly evidenced. These results demonstrate the strong potentiality of hyper-Raman scattering as structural probe of complex perovskites.

High resolution hyper-Raman spectroscopy (HRS) of single crystals of the relaxor PbMg1/3Nb2/3O3 has been performed. The temperature dependence of the three F1u-symmetry polar modes is investigated between 20 K and 800 K. The soft mode is clearly observed above 520 K (Fig. 1) [1]. It is splitted into a doublet up to the highest temperature investigated. The high frequency component (A1) appears to be underdamped even hundred of degrees below the Burns temperature Td  620 K in PMN. Its frequency nicely matches with previous high resolution neutron scattering experiments (Fig. 2) but is too high to explain the behaviour of the dielectric constant of PMN. This is the reason why the search of a lower-frequency vibration was subject to numerous experimental studies, but still, a clear understanding of the soft mode dynamics of relaxors was lacking. This vibration, labelled E1 in Figure 1, is clearly observed in HRS. It is underdamped at high temperature and becomes overdamped near Td and below. Its frequency 0 as well as its "relaxational" frequency rel = 02/, (, full width at half maximum) extrapolate to zero at the Curie-Weiss temperature T0  400 K (Fig. 2). Moreover, the static dielectric constant calculated from the Lyddane-Sachs-Teller relation nicely mimics the behaviour of that obtains from dielectric measurements. These observations strongly suggest that this vibration corresponds to the "primary" soft mode of PMN. Similar observations have been made in others relaxor-type compounds, thus suggesting a universal behaviour of the low-frequency dynamics of cubic relaxors.

The hyper-Raman spectroscopy (HRS) of three single crystals of the relaxor PbMg1/3Nb2/3O3 has been performed [1,2]. The temperature dependence of the three F1u-symmetry polar modes was investigated between 20 K and 800 K. In addition, the relative scattering intensities obtained for the band near 250 cm−1 in various polarization geometries are fully compatible with the hyper-Raman tensor of the nonpolar F2u 'silent' mode of the parent Oh cubic structure. From a structural point of view, the results reveal that the HRS response is sensitive to the B-site distortions and that oxygen atoms play a minor role in the structural changes, at least between 300 K and 800 K. The advantage of HRS for the measurement of zone-center soft modes is apparent from Fig. 1a. The very good instrumental resolution combined with a very weak second harmonic generation signal at high temperature (narrow band at w=0 in Fig. 1a) allows measurements of polar modes by HRS down to a few cm-1. Figure 1b shows a series of spectra measured between 520 and 750 K. Clearly, the soft- TO-mode is splitted into a doublet over the whole temperature range explored. The high frequency component (A1) appears to be underdamped even hundred of degrees below the Burns temperature Td @ 620 K in PMN. Its frequency nicely matches with previous high resolution neutron scattering experiments [3] (Fig. 2) but is too high to explain the behaviour of the dielectric constant of PMN. This is the reason why the search of a lower-frequency vibration was subject to numerous experimental studies [4], but still, a clear understanding of the soft mode dynamics of relaxors was lacking. This vibration, labelled E1 in Figure 1, is clearly observed in HRS [5]. It is underdamped at high temperature and becomes overdamped near Td and below. Its frequency w0 as well as its "relaxational" frequency wrel = w0 2/G, (G, full width at half maximum) extrapolate to zero at the Curie- Weiss temperature T0 @ 400 K [6], as shown in Figure 2. Moreover, the static dielectric constant calculated from the Lyddane-Sachs-Teller relation nicely mimics the behaviour of the experimental one [6] (inset of Fig. 2). These observations strongly suggest that this vibration corresponds to the "primary" soft mode of PMN. In addition, the intensity of the soft TO-doublet exhibits a step-like anomaly around Td, a behaviour which might relate to the growth of a local polarization-related order parameter. Similar observations have been made in others relaxor-type compounds, thus suggesting a universal behaviour of the low-frequency dynamics of cubic relaxors.