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Microscopic flexoelectricity in the canonical PMN relaxor

J. Hlinka

Abstract

Previously reported neutron scattering investigations of the canonical relaxor ferroelectric perovskite oxide with a chemical formula Pb(Mg(1/3)Nb(2/3))O3 (PMN) are revisited in order to appreciate the role of the intrinsic bulk flexoelectricity. Despite the outstanding electromechanical properties of lead-based relaxors, the magnitude of the flexoelectric coupling coefficient derived here directly from the PMN neutron diffuse scattering data, does not exceed the range of values typical for conventional perovskite ferroelectrics. We explain how these findings are related in the framework of the Ginzburg-Landau-Devonshire and the ferroelectric soft mode theory. We propose that the relaxor properties of PMN might be related to the suppression of the transverse correlation length of the flexoelectrically hybridized translational-polarization fluctuations due to its closeness to the Lifshitz-point regime.

Microscopic flexoelectricity in the canonical PMN relaxor

Abstract

Previously reported neutron scattering investigations of the canonical relaxor ferroelectric perovskite oxide with a chemical formula Pb(Mg(1/3)Nb(2/3))O3 (PMN) are revisited in order to appreciate the role of the intrinsic bulk flexoelectricity. Despite the outstanding electromechanical properties of lead-based relaxors, the magnitude of the flexoelectric coupling coefficient derived here directly from the PMN neutron diffuse scattering data, does not exceed the range of values typical for conventional perovskite ferroelectrics. We explain how these findings are related in the framework of the Ginzburg-Landau-Devonshire and the ferroelectric soft mode theory. We propose that the relaxor properties of PMN might be related to the suppression of the transverse correlation length of the flexoelectrically hybridized translational-polarization fluctuations due to its closeness to the Lifshitz-point regime.
Paper Structure (9 sections, 33 equations, 2 figures)

This paper contains 9 sections, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. "Phase shift" model of Hirota et al.
  3. Flexoelectric perspective
  4. Magnitude of the flexoelectric coupling
  5. Lattice-dynamics perspective
  6. Critical soft modes
  7. Lifshitz regime
  8. Tight binding phonon dispersion model
  9. Summary

Figures (2)

  • Figure 1: Phonon dispersion curves in a model with flexoelectrically induced Lifshitz limit. (a) dispersion curves at temperatures well above the criticality, (b) the same but when the soft mode is approaching the phase transition, (c) as previous, but with bare optic branch modified by admixing the second-neighbour interaction term. Dashed lines are bare TO and TA modes, full lines are eigenfrequencies of the dynamical matrix. The fill, dotted and dash-dotted lines in the panel (d) gives the fraction of the bare TO mode $|\langle {\rm TO}| \omega_-\rangle|^2$ in the lower-frequency eigenmode $| \omega_-\rangle$, defining its "opticity" for models of the panel (a),(b) and (c), respectively. Details are given in the main text.
  • Figure 2: Phonon dispersion with the interaction term $d$ increased by 10 percent with respect the Fig. 1. Panel (a) corresponds to a model with an antiferroelectric instability, $c= 20$ meV$^2$, $d= - 105.5$ meV$^2$, other parameters as in Fig. 1b. Panel (b) corresponds to a model with an incommensurate instability, $c= 3$ meV$^2$, $d= -105.5$ meV$^2$, other parameters as in Fig. 1c.