Polar modes in relaxor PbMg 1/3 Nb 2/3 O 3 by hyper-Raman scattering B. Hehlen, 1 G. Simon, 1 and J. Hlinka 2 1 Laboratoire des Colloides, Verres et Nanomateriaux (LCVN), University of Montpellier II, 34095 Montpellier, France 2 Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Praha 8, Czech Republic Received 8 November 2006; revised manuscript received 28 December 2006; published 16 February 2007 Phonon modes in PbMg 1/3 Nb 2/3 O 3 relaxor are studied by backward and near-forward hyper-Raman scatter- ing technique. Polar mode frequencies obtained from hyper-Raman experiment fully agree with results of infrared spectroscopy. An additional mode observed in cross-polarized spectra near 250 cm -1 is assigned as F 2u mode. Most surprisingly, experiments reveal i a strong enhancement of hyper-Raman scattering by longitu- dinal optic modes and ii remarkable correspondence between near-forward hyper-Raman scattering and imaginary part of the inverse dielectric function. DOI: 10.1103/PhysRevB.75.052104 PACS numbers: 78.30.-j, 77.80.-e, 63.50.+x, 63.20.Ls Mixed perovskites with diffuse ferroelectric transition, known as relaxor ferroelectrics, are recently attracting more and more attention. 1–5 Fundamental attribute of these relaxor materials is a characteristic frequency-temperature depen- dence of the dielectric response, different from the usual Curie-Weiss behavior. PbMg 1/3 Nb 2/3 O 3 PMN is a prototype example of a relaxor system: it shows high dielectric permit- tivity over broad temperature range at 1 kHz, more than 10 4 near T m  260–270 K, dipolar freezing behavior with Vogel-Fulcher temperature T VF  200 K and a broad distribu- tion of relaxation times from mHz to GHz range. 6,7 Obser- vations of a pronounced diffuse x-ray scattering and of an optical birefringence persisting up to T d  600–650 K Burns temperature 8 suggest existence of structural distor- tions at nanometric scales. Yet, from the standpoint of clas- sical x-ray diffraction techniques, the structure of the zero- field-cooled system remains cubic at all temperatures. 9 Spectroscopic methods sensitive to vibrational modes can often help to elucidate phase transition mechanisms or re- lated anharmonic phenomena. In case of PMN, there has been a considerable effort in studying lattice vibrations by inelastic neutron scattering INS, 10–13 Raman scattering RS 14–16 and infrared IR reflectivity 17–20 techniques. The Pm3 ¯ m simple cubic perovskite average structure of PMN have only five atoms in the ABO 3 unit cell and therefore, there are only 3 F 1u and 1 F 2u triply degenerate zone center optic modes. However, quantitative interpretation of experi- mental data usually requires to take into account the short- or medium-range inhomogeneities of the structure, associated for example with B-site “chemical” ordering and/or the “polar nanoregions” PNR. INS experiments focused mainly on the “soft” phonon branch associated with the lowest fre- quency transverse optic TO F 1u mode. It is a quite complex task because of strong anharmonic effects, coupling with acoustic modes, and mixing with diffuse scattering contribu- tions. The great sensitivity of RS to local structural inhomo- geneities stems from the fact that the first-order RS is symmetry-prohibited in the simple Pm3 ¯ m cubic perovskite structure. It is admitted that the observed RS intensity is caused by nanoclusters of the chemical and/or polar order PNR’s, but detailed quantitative understanding of RS spec- tra was not reached so far. Finally, the IR spectroscopy probes polar modes only. It was shown that the IR reflectiv- ity spectra of PMN in the phonon frequency region can be interpreted as due to the three F 1u modes, but their spectral response is modified by spatially fluctuating anisotropy of dielectric function, what leads to intriguing effects like the appearance of new, so-called geometrical resonances. 20 In this paper, still another experimental tool is employed to study phonon modes in PMN: hyper-Raman scattering HRS spectroscopy. This technique is based on a nonlinear optical effect where two incident photons produce one scat- tered photon after interaction with a phonon or other excitation. 21 Major interest of this technique is that its selec- tion rules are different from RS and IR ones. In the Pm3 ¯ m simple cubic perovskite, the polar F 1u modes are active both in IR and HRS, while the “silent” F 2u mode is active only in HRS. There were two HRS studies of materials similar to PMN presented so far, and both have brought very interesting and unexpected results. 22,23 The first paper 22 revealed that the spectrum of lead zirconate titanate PZT ceramics measured in HRS setup is similar to the conventional Raman spectrum except for the excess intensity located at the positions of LO mode frequencies. As the measurements were done in the ferroelectric phase, it is possible that the second harmonic generation is responsible for the generation of the conven- tional Raman background and that the proper HRS is just the excess intensity associated with LO modes. Such result is, however, quite surprising since the measurement was done in an almost backscattering geometry, where one would nor- mally expect scattering by TO modes only. The latter work 23 was focused on the low frequency HRS spectrum of PbMg 1/3 Nb 2/3  0.73 Ti 0.27 O 3 PMN-27PT crystal, and results suggest that the “silent” F 2u mode has frequency below 80 cm -1 and behaves as a soft mode. This challenging sce- nario is also very surprising since the first-principles based lattice dynamics calculations 18,24 for pure PMN do not indi- cate softening of this F 2u mode. To clarify both issues, we have chosen to perform polarized backscattering as well as near-forward HRS investigation of the model relaxor system—pure PMN crystal. For the experiment, we have used the same type of melt- grown PMN single crystal as used in the previous IR measurements. 6,20 HRS was excited by a pulsed YAG laser emitting at  = 1.064 m working at a frequency of 2000 Hz, PHYSICAL REVIEW B 75, 052104 2007 1098-0121/2007/755/0521044 ©2007 The American Physical Society 052104-1