Structural phase transitions in the geometric ferroelectric $\mathrm{LaTa}{\mathrm{O}}_4$

The recent report of an intermediate incommensurately modulated orthorhombic phase in $\mathrm{LaTa}{\mathrm{O}}_4$ has prompted a re-examination of the phase transition sequence in $\mathrm{LaTa}{\mathrm{O}}_4$ as a function of temperature. With falling temperature, the sequence of phases examined is (orthorhombic) $Cmc{2}_1\left(\mathrm{C}\right)\leftrightarrow Cmc{2}_1\left(\mathrm{IC}\right)\leftrightarrow \left(\mathrm{monoclinic}\right)P{2}_1/c$, with C and IC denoting commensurate and incommensurate phases, respectively. The orthorhombic to monoclinic transition, $T_{\mathrm{m}-\mathrm{o}}$, is a first order reconstructive transition occurring at 440 K and $T_{\mathrm{IC}-\mathrm{C}}$ is a first-order displacive transition occurring at 500–530 K. Strain and elasticity data confirm a first-order transition between the basic and modulated $Cmc{2}_1$ phases, with similarities to the isostructural fluoride $\mathrm{BaMn}{\mathrm{F}}_4$. A Raman spectroscopic study of the $\mathrm{LaTa}{\mathrm{O}}_4$ phase transition indicates that the IC-C phase transition is driven by a soft zone-boundary phonon (unstable) of the commensurate orthorhombic ($Cmc{2}_1$) phase. The soft phonon is found to appear (underdamped) above 443 K and vanishes (overdamped) around 528 K. A large supercell of the monoclinic phase below $T_{\mathrm{m}-\mathrm{o}}$ is proposed based on the Raman spectroscopic results.

Figure 1

Structure of the parent Cmcm phase (middle) with the orthorhombic $Cmc{2}_1$ (left) and monoclinic $P{2}_1/c$ (right) subgroups. Grey, orange, and red spheres represent La, Ta and O atoms, respectively.

Figure 2

Dielectric data (at 400 kHz) as a function of temperature for: (a) Sample A (b) Sample B. The anomaly attributed to a $Cmc{2}_1\left(\mathrm{C}\right)\to Cmc{2}_1\left(\mathrm{IC}\right)$ transition in the data for Sample A occurs at ∼488 K during heating and ∼483 K during cooling. The related maximum in relative permittivity for Sample B occurs at ∼501 K during heating and ∼496 K during cooling. The anomaly in the Sample B data at ∼430 K (heating) is attributed to the $P2{/}_{1}c\to Cmc{2}_1$ (IC) transition. Due to the noise in the loss data (tan δ) for Sample A a 21-point moving average is included to guide the eye.

Figure 3

Strain analysis based on lattice parameters. (a)–(d) Lattice parameters for both Sample A and B. Data for the $P{2}_1/c$ structure are expressed in terms of the unit cell of the $Cmc{2}_1$ structure. Linear variations of the reference parameters, $a_{\mathrm{o}}, b_{\mathrm{o}}, c_{\mathrm{o}}, V_{\mathrm{o}}$, for calculation of spontaneous strains were obtained by fitting to data of Sample A (initially $o-\mathrm{LaTa}{\mathrm{O}}_4$ at ambient) in the temperature interval 573–773 K. Variations of lattice parameters of Sample B (initially $m\text{−}\mathrm{LaTa}{\mathrm{O}}_4$ at ambient) are closely similar to those of Sample A. (e) Variation of $\cos \gamma (\approx e_6)$ for the monoclinic structure of Sample B, where γ is the monoclinic angle of a cell aligned with that of the $Cmc{2}_1$ structure. (f) Variation of spontaneous strains defined with respect to the $Cmc{2}_1$ structure of Sample A. Curves are fits of Eq. (1) to the data, consistent with the view that the $Cmc{2}_1\to \mathrm{IC}$ transition is weakly first-order and has a transition temperature, $T_{\mathrm{tr}}$, between ∼510 and ∼520 K.

Figure 4

Segments of RUS spectra from polycrystalline Sample A, collected in the second cooling sequence. They are stacked with offsets up the $y$ axis in proportion to the temperature at which they were collected. Resonance peaks which do not change frequency with changing temperature are from the alumina buffer rods. Blue lines are fits to resonance peaks of the sample in the temperature interval of elastic softening with decreasing temperature.

Figure 5

Variations of $f^2$ and $Q^{-1}$ from fitting of a single resonance peak in RUS spectra from a polycrystalline sample of Sample A, using an asymmetric Lorentzian function. The peak has frequency ∼345 kHz at 800 K. There is a rounded minimum in $f^2$ at ∼510 K and the small difference in values between heating and cooling has its maximum at the same temperature. There is a reduction in $Q^{-1}$ at ∼480 K and the onset of an increase below ∼310 K. Scatter in the data for $Q^{-1}$ between ∼500 and ∼600 K is, at least in part, an experimental artifact due to interaction of sample peaks with rod peaks.

Figure 6

Segments of RUS spectra from a polycrystalline sample of Sample B collected in the second cooling sequence. They are stacked with offsets up the $y$ axis in proportion to the temperatures at which they were collected. Resonance peaks which do not change frequency with changing temperature are from the alumina buffer rods. Blue lines are fits to a resonance peak from the sample which has frequency ∼500 kHz at 800 K and appears to trend towards ∼220 kHz at room temperature.

Figure 7

Variations of $f^2$ and $Q^{-1}$ from fitting of a resonance peak which has frequency ∼500 kHz at ∼800 K. Individual peaks from the sample became progressively weaker and harder to distinguish from buffer rod peaks below ∼430 K but the trend of elastic softening with falling temperature clearly continued below 350 K. A dashed line is shown at 510 K to mark the temperature at which a minimum in $f^2$ was seen in spectra from Sample A (Fig. 5).

Figure 8

Low frequency Raman data measured on Sample B on heating. (a) Raman spectra of $m\text{−}\mathrm{LaTa}{\mathrm{O}}_4$ sample measured at different temperatures from $T=298–583\mathrm{K}$ shows $T_{\mathrm{m}-\mathrm{o}}$ at ∼443 K and region of phase coexistence at associated with $T_{\mathrm{IC}-\mathrm{C}}$ at 493 - 528 K. Open circles are the experimental data. Continuous solid lines are fit for individual Raman bands and total Lorentzian fit to the data. The appearance of Raman modes are indicated by arrow and star symbols. (b) Temperature-dependent Raman mode frequencies of Sample B. Discontinuous changes of the mode frequencies are consistent with both transitions being first-order. A zone boundary soft mode of the $Cmc{2}_1$ (C) phase appears at $T_{\mathrm{m}-\mathrm{o}}=443\mathrm{K}$ with frequency $44\mathrm{c}{\mathrm{m}}^{-1}$ and continuously softens, disappearing at ∼528 K.

Figure 9

(a) Raman spectra of Sample B in the frequency range $10–1000\mathrm{c}{\mathrm{m}}^{-1}$, as measured at 298 K (monoclinic phase) and 460 K [$Cmc{2}_1$ (IC) phase]. The large number of almost equal spaced Raman lines with frequencies in the range $100–500\mathrm{c}{\mathrm{m}}^{-1}$ in the spectrum of the low temperature $P{2}_1/c$ phase (at 298 K) suggests that the this monoclinic phase involves at least a 4× multiplication of the primitive unit cell of the already modulated orthorhombic $Cmc{2}_1$ (IC) phase. (b) Low frequency Raman spectra deconvoluted to sum of Lorentzian peaks for monoclinic phase (298 K) and orthorhombic phase (460 K). Individual fitted peaks are also shown.