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Recently we initiated a research project at the Swiss Neutron Spallation Source SINQ at PSI in collaboration with other laboratories to investigate the chemical structure and low-frequency atomic motions in classical and relaxor ferroelectrics. We found that an additional QE component coexisting with an elastic central peak is present in both PMT and PMN relaxors [1]. From diffraction studies, it appears that this scattering can be related with atomic displacements, mainly due to Pb ions [2]. However, this unexpected quasi-elastic scattering is still not understood. We only point out that as anharmonicity effects are important in relaxors, it is a priori possible that this quasi-elastic mode originates from strong coupling between TA and heavily damped TO phonon modes. From recent neutron work at SINQ in PMN, we found that the transverse acoustic and the lowest transverse optic phonons are strongly coupled at all temperatures. However, because, the lowest optic branch is underdamped and does not exhibit any noticeable softening in the temperature range 300 K<T<670 K where quasi-elastic scattering is strongest, we conclude that quasi-elastic scattering does not originate from the combined effects of coupling between TA and TO phonons with an increase of the damping of the TO phonon [3]. In addition we found that the susceptibility associated with the quasi-elastic scattering mirrors the temperature dependence of the real part of dielectric permittivity quite well. This suggests that the relaxational mode is involved in the formation of the dielectric anomaly in PMN. We remember that displacive phase transitions in ferroelectrics are described by soft-mode theory that connects the transverse optic frequency to the dielectric susceptibility through the Lydanne-Sachs-Teller relationship. It is however at moment an open issue to understand the origin of the relaxation mode and to link it with the formation of the ferroelectric state in PMN and other relaxors.

Neutron scattering investigations were carried out in PMT and BaMg_1/3Ta_2/3O₃ (BMT) complex perovskites. Whereas the temperature dependence of the lattice parameter of BMT follows the classical expectations, the lattice parameter of relaxor ferroelectric PMT exhibits anomalies. One of these anomalies is observed in the same temperature range as the peak in the dielectric susceptibility. Below T=180 K PMT exhibits very small thermal expansion, similar to invar alloys. We find that in PMT, lead ions are displaced from the ideal positions in the perovskite structure at all temperatures. Consequently short-range order is present. This induces strong diffuse scattering with an anisotropic shape in wavevector space. The temperature dependences of the diffuse neutron scattering intensity and of the amplitude of the lead displacements are similar.

• [1] S. N. Gvasaliya, B. Roessli and S. G. Lushnikov, Europhys. Lett. 63, 303 (2003); S. N. Gvasaliya, S. Lushnikov and B. Roessli, Crystal. Rep. 49, 108 (2004); S. N. Gvasaliya, S. G. Lushnikov and B. Roessli, Phys. Rev. B 69, 092105 (2004).
• [2] S. N. Gvasaliya, B. Roessli, D. Sheptiakov, S. G. Lushnikov and T.A. Shaplygina, Eur. Phys. J. B 40, 235 (2004).
• [3] S. N. Gvasaliya, B. Roessli, R. A. Cowley, P. Hubert, S. G. Lushnikov, J. Phys.: Condens. Matter 17, 4343-4359 (2005).

We initiated a similar study in the classical ferroelectric KNbO₃. ABO₃ perovskites form a class of important materials, in part because of potential technical applications but also as fundamental interest in the physics of phase transitions [1]. At sufficiently high temperatures many of these perovskites have cubic symmetry and structural phase transitions can take place as the temperature is lowered. Well-known examples are e.g. the cubic-tetragonal phase transition in SrTiO₃ (T_C=105 K) or in BaTiO₃ (T_C=425 K). There are, however, ABO₃ perovskites which were less studied. An example is the first-order cubic-tetragonal phase transition in KNbO₃ which occurs at T_C=680 K when cooling the crystal from above the transition temperature [3]. The mechanism of the cubic-tetragonal (C-T) phase transition in KNbO₃ is still controversial. Whereas well-defined soft phonon modes with frequency varying with temperature have been detected in many materials close to TC, only an over-damped excitation has been observed in cubic KNbO₃ with neutron scattering and it was suggested that the nature of the C-T phase transition in that compound is similar to the displacive C-T transition in BaTiO₃. On the other hand, two coexisting and essentially uncoupled modes are inferred from analysis of optical data in the cubic phase of KNbO₃: a relaxation mode and soft phonon, with the relaxation process driving the C-T phase transition [4]. We re-investigated the low energy part of the vibration spectrum in KNbO₃ under improved resolution conditions first to try to elucidate the mechanism of the phase transition in this crystal and second to check whether the diffuse scattering found by X-rays is of static or dynamic origin. The inelastic cold-neutron scattering measurements were performed with the three-axis spectrometer TASP, located at the neutron spallation source SINQ. We found a coexistence of a static and a quasi-elastic component. The static component appears to correspond with static disorder in the cubic cell and is temperature independent in agreement with X-rays results [5]. The quasi-elastic component is coupled with the acoustic phonon branch and its intensity follows the Curie-Weiss law well indicating that order-disorder phenomena play a significant role in the dynamics of C-T phase transition in KNbO₃ [6].

• [1] G. A. Smolenskii et al., Ferroelectrics and Related Materials (New York, Gordon and Breach, 1984).
• [2] A. D. Bruce anf R. A. Cowley, Structural phase transitions (London, Taylor & Francis), 1981.
• [3] G. Shirane, H. Danner, A. Pavlovic, and R. Pepinsky, Phys. Rev. 93, 672 (1954).
• [4] M. D. Fontana, A. Ridah, G. E. Kugel and C. Carabatos-Nedelec, J. Phys. C 21, 5853 (1988).
• [5] R. Comes, M. Lambert and A. Guinier, Acta Crystallogr. A 26, 244 (1970).
• [6] S. N. Gvasaliya, B. Roessli, R. A. Cowley, S. G. Lushnikov, A. Choubey and P. Gunter, JETP Lett. 80, 355 (2004).

Funding: SNF, Others

Partners:
ETH Zürich, Switzerland, http://www.ethz.ch/
Ioffe Institute, St. Petersburg, Russia, http://www.ioffe.rssi.ru/index_en.html
Oxford University, UK, http://www.ox.ac.uk/
Tohoku University, Sendai, Japan, http://www.tohoku.ac.jp/english/index.html

Contact: bertrand.roessli@psi.ch, Bertrand Roessli