Soft modes and phonon interactions in studied by means of neutron scattering

Abstract

This paper presents an inelastic neutron scattering study of the proper ferroelectric and elastic neutron scattering results on the satellite diffraction pattern which characterizes the modulated phase. The temperature dependences of the satellite intensities and modulation wavevector are in fair agreement with results from previous x-ray experiments. Close to the incommensurate-to-ferroelectric transition temperature , an unexpected intensity overshoot is observed, similar to that seen in birefringence and dilatation experiments. The relationship between the lattice dynamics and the observed phase transition sequence is examined. The dispersion of the ferroelectric soft optic phonon (-polarization) and of the acoustic phonons is followed along the and -directions. In the ferroelectric phase, the TO mode shows a considerable softening as the incommensurate phase is approached from below. In the paraelectric and incommensurate phases, the response from the TO (-polarization) and TA ( strain) branches has been investigated via a series of constant-q scans in the -direction (approximately the modulation wavevector direction). The combined inelastic line-shapes, as observed in a number of non-equivalent Brillouin zones, could all be analysed in terms of a coupled-mode damped harmonic oscillator model. In addition, a diverging, resolution-limited, central peak is observed close to . It is suggested that the TO-TA coupling lies at the origin of the incommensurate instability. A phenomenological free energy is developed, in the continuum approximation, in which the TO-TA interaction is included via a pseudo-Lifshitz term of the type .

THE PHASE TRANSITIONS CHARACTER AND MICROSCOPIC MODELS FOR Sn_2P_2S(Se)_6 FERROELECTRICS

“…In this regime, the ratio r of slopes of the temperature dependencies of the soft mode frequency could be high enough, depending on the actual form of the phonon dispersion. This agrees with scattering data value r ∼ −7 [12,13] experimentally estimated from inelastic neutron, and is also responsible for the large value of the ratio of Curie-Weiss constants, that is observed experimentally (figure 5) [8]. It can be also claimed that the quartic coefficient of the Landau potential for ferroelectric Sn 2 P 2 S 6 should be considered as temperature dependent on the temperature scales comparable with T 0 .…”

“…The crossover situation for Sn 2 P 2 S(Se) 6 ferroelectrics actually implies that these compounds should reveal a soft mode, which, however, does not soften completely, which is really observed in the experiment (figures 2 and 3) [6,12,13]. In this regime, the ratio r of slopes of the temperature dependencies of the soft mode frequency could be high enough, depending on the actual form of the phonon dispersion.…”

“…For a type II incommensurate phase, that was determined by symmetry for proper Sn 2 P 2 (Se x S 1−x ) 6 ferroelectrics, the PT instability appears to be off (but still near) the Brillouin zone center. A coupling of transverse optic (TO) and transverse acoustic (TA) phonon branches lies at the origin of this IC instability, that was clearly demonstrated by neutron scattering data (figure 4) [13]. We wonder which is more important for the mixed displacive-order/disorder type of the PT in the crystals considered, a dipolar coupling among the displacements of Sn 2+ cations, or the TO-TA coupling?…”

“…Soft mode behavior for the ferroelectric phase of Sn 2 P 2 Se 6 from a neutron scattering data at the (3 0 1) Brillouin zone center. The full lines are damped harmonic oscillator fits [13].…”

“…For Sn 2 P 2 S 6 and Sn 2 P 2 Se 6 in the Raman scattering spectra (figure 2) [6], and in the neutron scattering spectra (figures 3 and 4) [12,13], the soft optical mode is observed. According to the temperature dependence of a dielectric susceptibility [8] in the paraelectric phase of these compounds (figure 5) the Curie-Weiss constant is in the range of C = 0.5−0.7·10 5 K. Such characteristics are peculiar for the displacive type PT.…”