Vibrational properties of ${\mathrm{LiNb}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_3$ mixed crystals

Congruent lithium niobate and lithium tantalate mixed crystals have been grown over the complete compositional range with the Czochralski method. The structural and vibrational properties of the mixed crystals are studied extensively by x-ray diffraction measurements, Raman spectroscopy, and density functional theory. The measured lattice parameters and vibrational frequencies are in good agreement with our theoretical predictions. The observed dependence of the Raman frequencies on the crystal composition is discussed on the basis of the calculated phonon displacement patterns. The phononic contribution to the static dielectric tensor is calculated by means of the generalized Lyddane-Sachs-Teller relation. Due to the pronounced dependence of the optical response on the Ta concentration, lithium niobate tantalate mixed crystals represent a perfect model system to study the properties of uniaxial mixed ferroelectric materials for application in integrated optics.

Figure 1

Room-temperature XRD spectra over a $2\mathrm{\Theta }$ range of $10-{80}^{\circ }$ for all grown samples. All peaks can be indexed in accordance with the Joint Committee on Powder Diffraction Standards (JCPDS) Card File 38-1252 for ${\mathrm{LiNb}}_{0.5}{\mathrm{Ta}}_{0.5}{\mathrm{O}}_3$. The spectra are labeled by the Ta concentration $y$ in the melt. For the sake of clarity, the plots have been separated by an artificial offset.

Figure 2

(a) Measured and (b) DFT LNT lattice parameters as a function of the Ta concentration. The red squares are the measured lattice parameters plotted with respect to the melt composition $y$. The solid line shows the crystal composition $x$ as extrapolated from Eq. (3).

Figure 3

Normalized Raman spectra obtained in $x(z,z)\overline{x}$ scattering geometry showing the behavior of $A_1$-TO modes in ${\mathrm{LiNb}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_3$ mixed crystals. For better visibility, the spectra have been separated by an artificial offset proportional to the Ta content $x$. Four $A_1$-TO modes predicted by the theory can be identified in all spectra. The inset shows the measured FWHM of the $A_1-{\mathrm{TO}}_4$ mode as a function of the Ta concentration, showing a clear decrease for Ta-rich crystals.

Figure 4

Experimentally measured phonon frequencies of the $A_1$-TO modes as a function of the (a) Ta concentration $x$ and (b) corresponding theoretical predictions. In (c), the experimental measured $A_1$-LO phonon frequencies are displayed, which are not covered by our model.

Figure 5

Eigenvectors of the transversal phonon modes with (a) $A_1$ symmetry and (b) $A_2$ symmetry. Nb/Ta atoms are in white, Li in gray, and O in red. The arrows represent the atomic displacement direction.

Figure 6

Normalized Raman spectra obtained in the $x(y,z)\overline{x}$ scattering geometry showing the $E$-TO modes in ${\mathrm{LiNb}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_3$ mixed crystals. The spectra have been separated with an artificial offset proportional to the Ta content $x$. Besides the $E$ modes, an $A_1-{\mathrm{TO}}_4$ leakage mode can be seen at high frequencies, resulting from an incomplete suppression of detection light. Peak assignment is carried following recent investigations [4, 43, 45].

Figure 7

Experimentally measured $E$-TO phonon frequencies in ${\mathrm{LiNb}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_3$ mixed crystals (a) as a function of the Ta concentration $x$ and (b) comparison with the calculated values. $E-{\mathrm{TO}}_5$ and $E-{\mathrm{TO}}_6$ can only be resolved in low-temperature Raman spectroscopy [43]. Recent literature data of this resonance are shown for comparison [43].

Figure 8

Eigenvectors of the transversal phonon modes with $E$ symmetry. Arrows represent the atomic displacement direction; color coding as in Fig. 5.

Figure 9

Experimentally measured $E$-LO phonon frequencies in ${\mathrm{LiNb}}_{1-x}{\mathrm{Ta}}_x{\mathrm{O}}_3$ mixed crystals as a function of the Ta concentration $x$. $E$-LO modes can only be detected in a single scattering configuration and are weak in intensity. For the sake of completeness, our results are complemented by recent literature data [43].

Figure 10

Detailed view of the frequency range between the $E-{\mathrm{TO}}_1$ and $E-{\mathrm{TO}}_2$ modes. A broad structure shifting to lower frequencies on Ta-rich samples is labeled by a dagger. This spectral feature is related to a two-phonon process and heavily depends on stoichiometry [42, 46]. Small variations in stoichiometry explain the slightly varying shapes obtained for different compositions.

Figure 11

(a) Closeup of the spectral range from 535 to 770 ${\mathrm{cm}}^{-1}$ in $z(y,y)\overline{z}$. The spectra have been normalized to the $E{-\mathrm{TO}}_8$ mode intensity to warrant comparability. (b) Lorentzian fits of the represented spectral range, which highlight the shift of the features in the 600–620 ${\mathrm{cm}}^{-1}$ range. (c) Shift of the central frequency of the $E-{\mathrm{TO}}_8$ and possible $A_1-{\mathrm{TO}}_4$-like mixed mode.

Figure 12

Calculated frequencies of the $A_2$ phonons with respect to Ta concentration $x$.

Figure 13

The compositional dependence of the static dielectric permittivity estimated by Eq. (4). The extraordinary permittivity ${\varepsilon }_{zz}$ shows a strong dependence on the Ta content, while the ordinary permittivity ${\varepsilon }_{xx}$ is almost constant.