Lyddane-Sachs-Teller Relation Research Articles

Infrared-active phonon modes and static dielectric constants in α-(AlxGa1−x)2O3 (0.18 ≤ x ≤ 0.54) alloys

We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(AlxGa1−x)2O3 alloys by far-infrared and infrared generalized spectroscopic ellipsometry. Single-crystalline high quality undoped thin-films grown on m-plane oriented α-Al2O3 substrates with x = 0.18, 0.37, and 0.54 were investigated. A single mode behavior is observed for all phonon modes, i.e., their frequencies shift gradually between the equivalent phonon modes of the isostructural binary parent compounds. We also provide physical model line shape functions for the anisotropic dielectric functions. We use the anisotropic high-frequency dielectric constants for polarizations parallel and perpendicular to the lattice c axis measured recently by Hilfiker et al. [Appl. Phys. Lett. 119, 092103 (2021)], and we determine the anisotropic static dielectric constants using the Lyddane–Sachs–Teller relation. The static dielectric constants can be approximated by linear relationships between those of α-Ga2O3 and α-Al2O3. The optical phonon modes and static dielectric constants will become useful for device design and free charge carrier characterization using optical techniques.

Semi-Experimental Determination of the Linear Clamped Electro-Optical Coefficients of Polar Crystals from Vibrational Spectroscopic Data

The present work highlights a new general method devoted to computations of the clamped linear electro-optical coefficients from the measured fundamental vibrational frequencies and the nonlinear dielectric susceptibility constants. The calculations are based on the formula analog to that of the Lyddane–Sachs–Teller relation, which is systematically used for the calculations of the clamped linear electro-optical coefficient of oxide ferroelectric crystals such as LiNbO3, LiTaO3, BaTiO3, PbTiO3, and KNbO3. The computed electro-optical coefficients are in good agreement with those obtained from direct measurements and the first-principles calculations or other semi-empirical models. In addition, the famous r51 or r42 coefficients of the tetragonal BaTiO3, PbTiO3, and KNbO3 crystals are finally calculated with high accuracy and discussed in connection with the soft mode behavior.

Optical phonon modes, static and high-frequency dielectric constants, and effective electron mass parameter in cubic In2O3

A complete set of all optical phonon modes predicted by symmetry for bixbyite structure indium oxide is reported here from a combination of far-infrared and infrared spectroscopic ellipsometry, as well as first principles calculations. Dielectric function spectra measured on high quality, marginally electrically conductive melt grown single bulk crystals are obtained on a wavelength-by-wavelength (also known as point-by-point) basis and by numerical reduction of a subtle free charge carrier Drude model contribution. A four-parameter semi-quantum model is applied to determine all 16 pairs of infrared-active transverse and longitudinal optical phonon modes, including the high-frequency dielectric constant, ε∞=4.05±0.05. The Lyddane–Sachs–Teller relation then gives access to the static dielectric constant, εDC=10.55±0.07. All experimental results are in excellent agreement with our density functional theory calculations and with previously reported values, where existent. We also perform optical Hall effect measurements and determine for the unintentionally doped n-type sample a free electron density of n=(2.81±0.01)×1017cm−3, a mobility of μ=(112±3)cm2/(Vs), and an effective mass parameter of (0.208±0.006)me. Density and mobility parameters compare very well with the results of electrical Hall effect measurements. Our effective mass parameter, which is measured independently of any other experimental technique, represents the bottom curvature of the Γ point in In2O3 in agreement with previous extrapolations. We use terahertz spectroscopic ellipsometry to measure the quasi-static response of In2O3, and our model validates the static dielectric constant obtained from the Lyddane–Sachs–Teller relation.

Soft mode theory of ferroelectric phase transitions in the low-temperature phase

Historically, the soft mode theory of ferroelectric phase transitions has been developed for the high-temperature (paraelectric) phase, where the phonon mode softens upon decreasing the temperature. In the low-temperature ferroelectric phase, a similar phonon softening occurs, also leading to a bosonic condensation of the frozen-in mode at the transition, but in this case the phonon softening occurs upon increasing the temperature. Here we present a soft mode theory of ferroelectric and displacive phase transitions by describing what happens in the low-temperature phase in terms of phonon softening and instability. A new derivation of the generalized Lyddane–Sachs–Teller (LST) relation for materials with strong anharmonic phonon damping is also presented which leads to the expression ɛ 0/ɛ ∞ = |ω LO|2/|ω TO|2. The theory provides a microscopic expression for T c as a function of physical parameters, including the mode specific Grüneisen parameter. The theory also shows that , and again specifies the prefactors in terms of Grüneisen parameter and fundamental physical constants. Using the generalized LST relation, the softening of the TO mode leads to the divergence of ϵ 0 and to a polarization catastrophe at T c. A quantitative microscopic form of the Curie–Weiss law is derived with prefactors that depend on microscopic physical parameters.

Polar vibrational and dielectric properties of monolayer transition metal dichalcogenides from macroscopic equations

Long wavelength polar vibrations in monolayer (ML) transition metal dichalcogenides (TMDs) are systematically studied for in-plane and out-of-plane motions, using two pairs of macroscopic equations deduced from a microscopic dipole lattice model accounting for local field effects (LFEs) and electronic polarization (EP). Longitudinal and transverse optical modes and out-of-plane modes are derived, and the analytical expressions describe previous first-principles calculations very well. Owing to the LFEs, the in-plane dielectric susceptibilities of ML TMDs are one order of magnitude greater than the out-of-plane susceptibilities. Furthermore, the effects of the dielectric environment on the polar vibrations are studied. Both EP and LFEs should be accounted for obtaining an accurate evaluation of dielectric susceptibility and key lattice-dynamical properties such as Born charge and phonon dispersion. A two-dimensional (2D) Lyddane–Sachs–Teller relation and a frequency–susceptibility relation are derived for in-plane and out-of-plane motions, relating the 2D dielectric functions or susceptibilities to the polar phonon frequencies. The results are also compared in detail with those of ML hexagonal boron nitride.

Strain-Induced Increase of Dielectric Constant in EuO Thin Film

Recently, lattice dynamics of the highly strained Europium monoxide, as a promising candidate for strong ferroelectric-ferromagnet material, applied in the next-generation storage devices, attracted huge attention in the solid-state electronics. Here, the authors investigate the effect of tensile strain on dielectric properties of pulsed laser deposited EuO thin films from 10 to 200 K. A nearly 3% out-of-plane lattice compression is observed as the film thickness was reduced to ∼8 nm, which could originate from the lattice mismatch between film and a LaAlO3 substrate. The temperature and frequency dependence of capacitance and loss factor of the films reveals the dominant role of electronic and ionic polarization below 100 K. The interdigitated capacitor fabricated on strained film shows almost 50% increase of capacitance compared to the relaxed one, which corresponds to a considerable increase of dielectric constant induced by in-plane tensile strain. Softening of the in-plane polarized transverse optical (TO) phonon modes of EuO lattice due to tensile strain might have the major contribution to this behavior according to the Lyddane–Sachs–Teller relation.

The optical characteristics of the nonlinear optical single crystal CdSiP2 in the terahertz and infrared ranges

Experimental study of mechanisms forming absorption of Terahertz (THz) radiation in the advanced nonlinear-optical crystal CdSiP2 has been performed by backward-wave oscillator, time-domain and infrared spectroscopy. The classical oscillator model and Lyddane–Sachs–Teller relation were used to calculate the dispersion parameters of phonon modes. The spectra of complex permittivity and absorption coefficient have been determined based on the calculated dispersion parameters. The application of the Fresnel formulas for the absorption analysis in the THz region together with the results of the fit of the phonon modes made it possible to obtain quantitative data on the magnitude of the additional radiation losses in the THz range. Additional loss mechanisms give rise to increase the total absorption by at least one order of magnitude compared to the phonon contribution. The increase of the polariton absorption in the low-frequency dispersion branch is typical for crystals with ionic and ion-covalent bond and is composed of extrinsic losses and difference multi-particle processes. The level of total losses in the THz region in CdSiP2 single crystal is comparable to the values in other nonlinear-optical crystals, which makes this material promising for nonlinear-optical conversion of the infrared radiation into the THz region.

Synthesis and optical properties of La1−XCeXMnO3 studied by infrared reflectivity measurements

The bulk polycrystalline La1−xCexMnO3 (0.0 ≤ x ≤ 0.8) manganites were synthesized through citrate sol-gel auto-combustion method for a wide range of composition 0.0 ≤ x ≤ 0.8. The x-ray diffraction (XRD) analysis suggests the single phase rhombohedral (R-3c) symmetry for parent LaMnO3 compound, however a secondary cubic (Fm-3 m) phase of cerium oxide (CeO2) is appeared when Ce is incorporated into the LaMnO3. A detailed XRD study of these materials were discussed, and specifically the infrared reflectivity measurements on La1−xCexMnO3 materials are discussed in this study for the first time. The phonon softening and hardening was observed for different modes but softening was found to be more pronounced which implied strong electron–phonon coupling. The most affected phonon mode was appeared for the doping range 0.2 ≤ x ≤ 0.4, in which the largest softening was observed. The Lyddane–Sachs–Teller relation is verified by experimental FTIR data.

A Quasi-Global Approach to Improve Day-Time Satellite Surface Soil Moisture Anomalies through the Land Surface Temperature Input

Passive microwave observations from various spaceborne sensors have been linked to the soil moisture of the Earth’s surface layer. A new generation of passive microwave sensors are dedicated to retrieving this variable and make observations in the single theoretically optimal L-band frequency (1–2 GHz). Previous generations of passive microwave sensors made observations in a range of higher frequencies, allowing for simultaneous estimation of additional variables required for solving the radiative transfer equation. One of these additional variables is land surface temperature, which plays a unique role in the radiative transfer equation and has an influence on the final quality of retrieved soil moisture anomalies. This study presents an optimization procedure for soil moisture retrievals through a quasi-global precipitation-based verification technique, the so-called Rvalue metric. Various land surface temperature scenarios were evaluated in which biases were added to an existing linear regression, specifically focusing on improving the skills to capture the temporal variability of soil moisture. We focus on the relative quality of the day-time (01:30 pm) observations from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), as these are theoretically most challenging due to the thermal equilibrium theory, and existing studies indicate that larger improvements are possible for these observations compared to their night-time (01:30 am) equivalent. Soil moisture data used in this study were retrieved through the Land Parameter Retrieval Model (LPRM), and in line with theory, both satellite paths show a unique and distinct degradation as a function of vegetation density. Both the ascending (01:30 pm) and descending (01:30 am) paths of the publicly available and widely used AMSR-E LPRM soil moisture products were used for benchmarking purposes. Several scenarios were employed in which the land surface temperature input for the radiative transfer was varied by imposing a bias on an existing regression. These scenarios were evaluated through the Rvalue technique, resulting in optimal bias values on top of this regression. In a next step, these optimal bias values were incorporated in order to re-calibrate the existing linear regression, resulting in a quasi-global uniform LST relation for day-time observations. In a final step, day-time soil moisture retrievals using the re-calibrated land surface temperature relation were again validated through the Rvalue technique. Results indicate an average increasing Rvalue of 16.5%, which indicates a better performance obtained through the re-calibration. This number was confirmed through an independent Triple Collocation verification over the same domain, demonstrating an average root mean square error reduction of 15.3%. Furthermore, a comparison against an extensive in situ database (679 stations) also indicates a generally higher quality for the re-calibrated dataset. Besides the improved day-time dataset, this study furthermore provides insights on the relative quality of soil moisture retrieved from AMSR-E’s day- and night-time observations.

Raman scattering in sodium nitrite crystals near the phase transition

Optical Raman spectra of a ferroelectric sodium nitrite crystal have been detected in a wide spectrum range at various temperatures, including the region of the ferroelectric phase transition. A manifestation of a transverse soft polar mode of the A 1(z) type responsible for the ferroelectric phase transition has been discovered in the spectrum at room temperature. This mode has been found to become overdamped even far from the ferroelectric phase transition temperature. This mode also appears as a central peak under heating. It has been found that the pseudoscalar mode of the A 2 type has the highest intensity in the Raman spectrum of sodium nitrite. The frequency corresponding to the maximum intensity of this mode in the Raman spectrum varies from 130 cm–1 at 123 K to 106 cm–1 at T = 513 K. A fair agreement of the experimental data for the A 1(z) mode with the Lyddane–Sachs–Teller relation has been established. The polariton curves for the A 1(z) polar mode and the dispersion curves for axinons has been plotted.

Temperature-dependent far-infrared properties of Bi12GeO20 single crystal

Far-infrared reflectivity spectra of bismuth germanium oxide (Bi12GeO20) single crystals are measured from room temperature down to 10 K. All the reflectivity spectra are fitted to a complex dielectric function ∊(ω) in the factorised form. Phonon modes at low frequency are found to develop upon decreasing temperature and gain considerable spectrum weight below 150 K. The temperature-dependent static dielectric constants are obtained from the Lyddane–Sachs–Teller relation based on the obtained oscillator parameters. The dielectric constants are found to increase upon decreasing temperature, which is attributed to the charge transfer among the ions in the unit cell with the temperature varying.

Characterization of Dielectric Property of Nanosized (Pb0.7Sr0.3)TiO3 Powders Studied by Raman Scattering

Nanosized perovskite (Pb0.7Sr0.3)TiO3 powders have been studied by Raman scattering to characterize the dielectric property derived from the particle size effect. All the optical phonons were assigned while referring to previously reported Raman spectra of PbTiO3. The frequencies of the soft E(1TO) and A1(1TO) modes show a slight hardening with a decrease in particle size. The size dependences of the clamped dielectric constants along the a and c axes characterized by the effect of the phonon confinement are evaluated by the Lyddane–Sachs–Teller relation using the observed frequencies of polar modes with E(x,y) and A1(z) symmetries, respectively.

Raman scattering investigation of cesium plumbochloride, CsPbCl3, phase transitions

AbstractWe report a Raman scattering investigation of CsPbCl3 as a function of temperature in four different scattering configurations allowing us to obtain the various irreducible representations of the appropriate symmetry groups describing the substance in its successive phase transitions: cubic, tetragonal, orthorhombic and monoclinic or orthorhombic. We identify the correct ‘parentage’ of the observed modes with respect to infrared reflectivity data reported in the literature in accord with the Lyddane–Sachs–Teller relation, which was not fulfilled in previous assignments. We demonstrate the presence of strong correlation chains, which maintain the compound in a pseudo‐cubic state as far as x‐ray, infrared and Raman spectroscopy are concerned. The intensity of the related central peak was analysed on the basis of a Debye‐type relaxation as a function of temperature; the results show perfect correspondence of its variations and the temperatures of the phase transitions. In addition, an order–disorder phase transition is evidenced at low temperature, 193 K (−80 °C). Copyright © 2003 John Wiley & Sons, Ltd.

Infrared dielectric functions and phonon modes of high-quality ZnO films

Infrared dielectric function spectra and phonon modes of high-quality, single crystalline, and highly resistive wurtzite ZnO films were obtained from infrared (300–1200 cm−1) spectroscopic ellipsometry and Raman scattering studies. The ZnO films were deposited by pulsed-laser deposition on c-plane sapphire substrates and investigated by high-resolution x-ray diffraction, high-resolution transmission electron microscopy, and Rutherford backscattering experiments. The crystal structure, phonon modes, and dielectric functions are compared to those obtained from a single-crystal ZnO bulk sample. The film ZnO phonon mode frequencies are highly consistent with those of the bulk material. A small redshift of the longitudinal optical phonon mode frequencies of the ZnO films with respect to the bulk material is observed. This is tentatively assigned to the existence of vacancy point defects within the films. Accurate long-wavelength dielectric constant limits of ZnO are obtained from the infrared ellipsometry analysis and compared with previously measured near-band-gap index-of-refraction data using the Lyddane–Sachs–Teller relation. The ZnO model dielectric function spectra will become useful for future infrared ellipsometry analysis of free-carrier parameters in complex ZnO-based heterostructures.

Infrared dielectric constant of gallium arsenide

The real dielectric constant of gallium arsenide has been determined at 300 and at 5 K from fits to observed interference in transmission of thin samples with parallel surfaces. Measurement was carried out over all or part of the range 30–4000 cm−1. An accuracy of ±0.5% is estimated based on the quality of the analytic fits and the sample thickness measurement technique. We find at 300 K, ε0=12.90 and ε∞=10.86. At 5 K, ε0=12.46 and ε∞=10.58. An analytic expression for the dielectric function is given which allows accurate values of the real dielectric constant to be determined throughout most of the 0–4000 cm−1 spectral range. The observed ratio ε0/ε∞ agrees with the Lyddane–Sachs–Teller relation calculated with Raman values of transverse and longitudinal optical phonon frequencies to better than 0.1% at 300 and at 5 K.

Phase transitions sequence in a PbZr0.99Ti0.01O3single crystal studied by raman light scattering

Abstract Temperature dependent Raman scattering measurements were performed on a PbZr0.99Ti0.01O3 single crystal in the temperature range from 300 K to 750 K. The modifications of Raman spectra were examined in the vicinity of two structural phase transitions occuring in this crystal: the antiferroelectric (A)—ferroelectric (F) (500 K on heating and 480 K on cooling) and ferroelectric (F)—paraelectric (P) (511 K on heating and 510 K on cooling). In each phase, soft mode behaviour has been found close to the phase transition. On the basis of LST relation the contribution of the soft mode to e'(T) in the P phase was calculated.

Infrared dielectric constant of cubic SiC

The real dielectric constant for chemical vapor deposition 3C-SiC grown on silicon (Si) has been determined at 300 K and at 5 K from an analytic fit to interference fringes in transmission over the spectral range from the near infrared to the submillimeter region. This technique is capable of high accuracy being limited typically by the sample thickness and accuracy with which the thickness is measured. The resulting real dielectric constant is lower than the values usually attributed to this material. We find: at 300 K ε 0=9.52 and ε ∞=6.38; at 5 K ε0=9.28 and ε ∞=6.22. In all cases the estimated error is ±0.8%. The observed ratio ε0 /ε∞ agrees with the Lyddane–Sachs–Teller relation to 0.1% at 300 K and 0.2% at 5 K.

GENERALIZED KUROSAWA RELATION AND LST RELATION AND THEIR EXPERIMENTAL VERIFICATION

Under the condition of qc?ω, the generalized frequency dispersion relation of polar pho-nons is simplified- The generalized Kurosawa relation and LST relation are derived and verified by the Raman spectra of TGS singal crystal.

Generalized Lyddane-Sachs-Teller relation for electron liquids.

By defining the longitudinal and transverse frequencies in terms of the frequency moments of the response functions, the Lyddane-Sachs-Teller (LST) relation for electron liquids is derived from the Kramers-Kronig relations. The extension of the LST relation for finite wave numbers is possible if the dielectric function obeys the Kramers-Kronig relations at finite wave numbers. It is pointed out that the LST relation in principle allows one to experimentally check the validity of the Kramers-Kronig relations for the dielectric function at finite wave numbers.

Moment representation of the Lyddane-Sachs-Teller relation for the Debye equation.

For various materials, including liquids and disordered systems, the dielectric function in the microwave region is represented by the Debye equation. Recently, with the use of the second-moment representation for the solenoidal and irrotational losses, the generalized form of the Lyddane-Sachs-Teller (LST) relation was derived based on causality and the f-sum rule [T. W. Noh and A. J. Sievers, Phys. Rev. Lett. 63, 1800 (1989)]. However, the second-moment representation cannot be applied to the Debye equation, which does not obey the f-sum rule. A moment representation is applied to the Debye equation, and a relation equivalent to the generalized LST relation is found. In this relation, the pth moments (-1p1) should be used instead of the second moments.