[Paper Review] Soft Phonon Anomalies in Relaxor Ferroelectrics

G. Shirane, P. M. Gehring|arXiv (Cornell University)|Nov 7, 2000

Ferroelectric and Piezoelectric Materials1 references3 citations

TL;DR

This paper investigates soft phonon anomalies in relaxor ferroelectrics, particularly the 'waterfall' dispersion feature in PZN-PT and PZN, using neutron inelastic scattering. The anomaly—where transverse optic phonons abruptly drop into the acoustic branch at q ≈ 0.2 Å⁻¹—arises from nanoscale polar micro-regions (PMRs), with the phenomenon diminishing at low temperatures as PMRs grow and long-wavelength optic modes reappear.

ABSTRACT

A review is given of the phonon anomalies, which have been termed ``waterfalls,'' that were recently discovered through a series of neutron inelastic scattering measurements on the lead-oxide relaxor systems PZN-xPT, PMN, and PZN. We discuss a simple coupled-mode model that has been used successfully to describe the basic features of the waterfall, and which relates this unusual feature to the presence of polar micro-regions.

Motivation & Objective

• To understand the origin of the soft phonon anomaly, known as the 'waterfall,' in relaxor ferroelectrics like PZN-PT and PZN.
• To investigate how polar micro-regions (PMRs) influence phonon dispersion and damping in the cubic phase of relaxors.
• To compare phonon behavior in PMN, PZN, and PZN-8%PT to identify universal features of relaxor dynamics.
• To examine the evolution of the waterfall anomaly through the cubic-to-rhombohedral phase transition at ~410 K in PZN.
• To explore the effect of external electric fields on PMRs and low-q phonons using neutron scattering.

Proposed method

• Neutron inelastic scattering was performed on high-quality single crystals of PZN, PZN-8%PT, and PMN using the BT2 triple-axis spectrometer at the NIST Center for Neutron Research.
• Constant-energy (E) and constant-Q (Q) scans were acquired at various temperatures, including 500 K (above Tc) and 150 K (below Tc), to map phonon dispersions and linewidths.
• Scattering intensity was analyzed using a logarithmic color scale in contour maps to visualize the waterfall feature near q ≈ 0.14 rlu.
• The linewidth Γ₁ of the TO mode was extracted and modeled to relate its q-dependence to PMR size and distribution.
• A coupled-mode model was applied to interpret the anomalous phonon dispersion, particularly the sharp drop in energy at finite q.
• Comparative analysis was conducted between PZN, PZN-8%PT, and PMN to assess differences in PMR dynamics and phonon behavior.

Experimental results

Research questions

• RQ1 What causes the 'waterfall' phonon dispersion feature observed in PZN-8%PT and PZN, where TO modes drop abruptly into the acoustic branch?
• RQ2 How do polar micro-regions (PMRs) influence the soft mode behavior and phonon damping in relaxor ferroelectrics?
• RQ3 Why does the waterfall anomaly vanish at low temperatures (e.g., 150 K) in PZN, and what does this imply about PMR size and long-wavelength mode propagation?
• RQ4 How does the high-temperature behavior of phonons in PZN compare to that in PMN, especially in the regime above the Burns temperature?
• RQ5 What is the effect of an external electric field on the PMR structure and the associated phonon anomalies?

Key findings

• The 'waterfall' anomaly in PZN-8%PT and PZN is observed as a sharp drop in transverse optic (TO) phonon energy at q ≈ 0.2 Å⁻¹ (0.14 rlu), forming a distinct vertical feature in neutron scattering maps.
• The anomaly is centered at q_wf ≈ 0.2 Å⁻¹ and is most prominent at 500 K, with constant-energy scans at -6 and -8 meV showing peak intensity at the same q, indicating a non-dispersive, anomalous mode.
• At higher energy transfer (-12 meV), scattering shifts to higher q, indicating recovery of a normal propagating TO mode outside the waterfall region.
• The waterfall feature diminishes through the cubic-to-rhombohedral phase transition at ~410 K and nearly disappears at 150 K, where a normal optic mode reappears at q ≈ 0 with energy ~11 meV.
• The linewidth Γ₁ of the TO mode increases sharply at q_wf, indicating strong damping and coupling to PMR fluctuations.
• The absence of a normal soft mode at low q above Tc in PZN suggests that PMRs suppress long-wavelength ferroelectric fluctuations, while their growth at low T allows propagation of long-wavelength optic modes.