Multiple Soft-Mode Vibrations of Lead Zirconate

Abstract

Polarized Raman, IR and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibration of Pb and/or oxygen octahedra librations and their relation to particular 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. The most remarkable finding is the considerably enhanced frequency renormalization of the y-polarized polar modes, resulting in a pronounced low temperature dielectric anisotropy. Results are discussed in terms of contemporary phenomenological theory of antiferroelectricity.PACS numbers: 77.80.Bh, 77.84.Cg Although the ferroelectric and antiferroelectric materials have a lot in common, the latter have been much less investigated. An obvious reason is the absence of the direct linear coupling of the antiferroelectric (AF) order parameter to the macroscopic electric field.At the same time, a nonlinear coupling to the macroscopic electric field is still present. Therefore, AF materials actually do provide interesting functionalities, as well. In fact, the AF oxides are promising materials for high-energy storage capacitors, high-strain actuators and perhaps even for electrocaloric refrigerators [1][2][3]. The interest in the improvement of our understanding of AF oxides has been expressed recently [1,2,4,5].Lead zirconate, PbZrO 3 , is the best known example of an AF oxide -it is an end-member of technologically relevant solid solutions with PbTiO 3 (piezoelectric PZTs) [1,2,4,[6][7][8]. The parent paraelectric phase is a simple cubic perovskite with a 5-atom unit cell (P m3m, Z=1). Below the AF phase transition (T C ∼ 500 K), it goes over into an orthorhombic P bam (Z=8) structure [10,11]. The space-group symmetry change can be well understood[1] as a result of the condensation of two order parameters [1,4,9,12]. One of them is a polarization wave of a propagation vector Q Σ = (0.25, 0.25, 0) pc , the other order parameter is a Q R = (0.5, 0.5, 0.5) pc oxygen octahedra tilt mode (here pc stands for pseudocubic lattice, see Figs. 1-2).Superpositions of Q Σ , Q R include also Γ, X, M and Q S = (0.25, 0.25, 0.5) pc cubic-phase Brillouin zone points. All of these points become Brillouin zone centers in the P bam phase (see Fig. 2). Nevertheless, recent inelastic X-ray scattering experiments [4] have clearly demonstrated that the critical scattering occurs only in the vicinity of the Γ-point. Based on this experimental result, it was proposed that the AF phase transition is driven by a single mode, the Γ-point ferroelectric soft mode [4]. Within this model, the condensation of the Q Σ -point mode can be ascribed to the flexoelectric coupling with the ferroelectric mode, and the condensation of the Q R -point mode can be explained as due to a biquadratic coupling with the Q Σ m...

Dynamics of antipolar distortions

“…It is also worthwhile to realize that the present work and model most likely are not fully applicable to PbZrO 3 (which is often considered to be the prototype of antiferroelectrics), even if a trilinear energy coupling has been documented there as well. 37,38 This is because it was recently proposed 39 that the unusual Pbam ground state of PbZrO 3 arises from an original bilinear coupling between antipolar motions and oxygen octahedral tiltings. As a result, Eqs.…”

Elastic anomalies associated with the antiferroelectric phase transitions of PbHfO3 single crystals

“…PbZrO3 is the most representative antiferroelectric perovskite oxide. Recent lattice dynamic studies on this compound revealed rich information associated with the nature of the antiferroelectric phase transition [3][4][5][6]. In spite of the fact that the microscopic nature of the antiferroelectric phase transition in PbZrO3 is still under debate, it seems evident that more detailed and thorough investigations into the lattice dynamics over the whole momentum space in the Brillouin zone are indispensable for our better understanding of this archetypal antiferroelectrics.…”

Atomistic mechanism leading to complex antiferroelectric and incommensurate perovskites

“…The first of these modes is labeled R + 4 according to its symmetry, and is rather simple: it features the typical antiphase tilting of the O 6 octahedra in the perovskite lattice. This mode is therefore associated with the zone-boundary 2π/a lat (1/2,1/2,1/2) k-point of the cubic first-Brillouin zone, where a lat is the lattice con- Recent works [6][7][8] suggest that a trilinear coupling between the predominant R (anti)polar displacements of the A cations in the perovskite lattice (Pb in PZO's case) and rotations of the O 6 octahedra. Remarkably, they can also explain and hold the key to understand many other non-trivial antipolar states (see e.g.…”

“…PZO's ground state displays the P bam symmetry and is mostly characterized by two strongly unstable soft phonon modes [6][7][8][9]12 . The first of these modes is labeled R + 4 according to its symmetry, and is rather simple: it features the typical antiphase tilting of the O 6 octahedra in the perovskite lattice.…”