Multiple Soft-Mode Vibrations of Lead Zirconate

J. Hlinka, T. Ostapchuk, E. Buixaderas, C. Kadlec, P. Kuzel, I. Gregora, J. Kroupa, M. Savinov, A. Klic, J. Drahokoupil, I. Etxebarria, and J. Dec

Phys. Rev. Lett. 112, 197601 – Published 12 May 2014

Abstract

Polarized Raman, IR, and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals have yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibrations of Pb ions and librations of oxygen octahedra. Their relation to phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. Analysis of the results yields insight into the phase transition mechanism, involving a soft ferroelectric branch coupled by a trilinear term to another two oxygen octahedra tilt modes.

Received 21 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.197601

Authors & Affiliations

J. Hlinka^*, T. Ostapchuk, E. Buixaderas, C. Kadlec, P. Kuzel, I. Gregora, J. Kroupa, M. Savinov, A. Klic, and J. Drahokoupil

Institute of Physics, Academy of Sciences of the Czech Republic Na Slovance 2, 182 21 Prague 8, Czech Republic

I. Etxebarria

Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea, P.K. 644, 48080 Bilbao, Spain

J. Dec

Institute of Materials Science, University of Silesia, Bankowa 12, PL-40-007 Katowice, Poland

^*hlinka@fzu.cz

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Vol. 112, Iss. 19 — 16 May 2014

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Figure 1
Crystal structure of ${PbZrO}_{3}$ in its (a) high-temperature cubic phase and (b) in its low-temperature orthorhombic phase. The orthorhombic $P b a m$ elementary unit cell is projected along its $z ∥ c$ axis, the $a = (1, - 1, 0)_{pc} / \sqrt{2}$ and $b = (1, 1, 0)_{pc} \sqrt{2}$ lattice vectors defining the $x$ and $y$ axes are indicated in the figure. Note that the $x$ components of the AFE displacements of the Pb ions 1 and 2 are opposite to those of 3 and 4. This displacement pattern forms a $Σ_{3}$ symmetry mode associated with $Q_{Σ} = b^{*}$ propagating vector.
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Figure 2
Brillouin zone points involved in the phase transition and low-frequency phonon branches of cubic ${PbZrO}_{3}$ . Panel (a) indicates $Γ, X, R, M, Q_{Σ}$ and $Q_{S}$ Brillouin zone points of cubic ${PbZrO}_{3}$ ; panel (b) shows corresponding phonon frequencies estimated from the available ${PbTiO}_{3}$ and ${PbTiO}_{3} − {PbZrO}_{3}$ spectroscopic data. Indices of the symmetry labels denoting phonon branches are those of Ref. [24].
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Figure 3
Typical low-frequency phonon spectra of ${PbZrO}_{3}$ . Panels (a) and (b) shows polarized Raman spectra at 80 K. The scattering geometry is indicated using standard Porto notation. Panel (c) shows the real part of the low-frequency conductivity spectra, as obtained from a combined fit to the spectra of IR reflectivity and time-domain THz spectroscopy, showing peaks at the transverse optic mode frequencies of the $B_{1 u} (z)$ , $B_{2 u} (y)$ , and $B_{3 u} (x)$ modes. The $x, y$ , and $z$ labels correspond to the crystallographic axes of the orthorhombic $P b a m$ structure.
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Figure 4
Temperature dependence of squared frequencies of Raman active (a)–(d) and IR active (e)–(g) modes of AFE ${PbZrO}_{3}$ . Panel (h) shows inverse static permittivity multiplied by the square of the plasma frequency of the Last mode ( $Ω_{Last} = 618 {cm}^{- 1}$ ). It provides an estimate of the squared oscillator frequency of the bare Last mode. Values of $ε (0)$ are taken from the joint THz-IR fit (point symbols). Independently measured 900 kHz data (available only along the $c$ axis) are shown by the continuous line. The yellow-shaded region indicates soft oxygen octahedra libration modes.
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Figure 5
Different kinds of soft-mode driven phase transitions. Panels (a)–(d) show schematically phonon dispersion of the polarization branch at $T > T_{C}$ , $T \approx T_{C}$ , and $T < T_{C}$ (traced in the parent-phase Brillouin zone) for a typical FE phase transition (a), hypothetical AFE phase transition (b), incommensurate transition (c), and in ${PbZrO}_{3}$ , as inferred from the present study (d). Panel (e) shows a phase diagram of the model described by Eqs. (1)–(2) with $β = 1$ , $B = 1$ , $J = 0.1$ , $A = 1$ [49].
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